Introduction

Long-lived mesoscale convective systems (MCSs) may cause heavy to extreme rainfall that can lead to large economic and human damages. MCS arises from convection initiation and upscale growth of the system (Du et al. 2020). For an MCS to develop, abundant moisture, lifting mechanism, instability, and vertical wind shear are essential (Wang et al. 2013; Schumacher and Rasmussen 2020).

Multiple observational (Kawashima et al. 2011; Keenan et al. 2000; Kuo and Chen 1990) and numerical (Du et al. 2020; Yulihastin et al. 2022; Zhang et al. 2003; Miao and Yang 2020) studies have already been conducted over the western North Pacific and Maritime Continent to investigate the processes related to the initiation and development of convective storms. Convections in the Maritime Continent are strongly influenced by coastal and diurnal effects (Yang and Slingo 2001; Yulihastin et al. 2022). Mori et al. (2004) found that convections over Sumatra Island, Indonesia are initiated by local convergence of sea breeze encountering the mountain range along the coastline and land breeze converging with the background wind flow. Qian (2008) also identified similar convection development mechanisms over Java Island, Indonesia, and are mainly associated with sea breeze convergence over the island, enhanced by mountain–plain winds, and further intensified by cumulus merger processes.

Meanwhile, over the Philippines, Natoli and Maloney (2019) studied the relationship between the diurnal cycle of precipitation and the Boreal Summer Intraseasonal Oscillation (BSISO). Results showed that during boreal summer (May–October), the precipitation diurnal cycle peaks over land from late afternoon to early evening and propagates westward towards the South China Sea. Bañares et al. (2021) also examined the seasonal and diurnal characteristics of localized convective rainfall events in Metro Manila, Philippines, using weather station observations from 2013 to 2014. Results show that high rainfall amounts were observed over the northern and central areas of Metro Manila as compared with the southern area during the northeast monsoon season (November–March), summer season (April–May), and southwest monsoon season (June–October). During the summer season, wherein tropical cyclones (TCs) and monsoonal influences are absent, convective rainfall events tend to occur in the afternoon.

Mindanao Island in the southern part of the Philippines frequently experiences heavy rainfall, and studies have shown its interaction with strong synoptic-scale systems (Faustino-Eslava et al. 2011; Olaguera et al. 2021; Yumul et al. 2013). However, during the summer season, where apparent large-scale systems are absent, the fraction of MCS rainfall to the total rainfall still reaches 30–65%, suggesting that localized convective systems largely contribute to the rainfall in Mindanao Island (refer to Additional file 1: Fig. S1). Understanding the initiation and development of localized heavy rainfall under weak large-scale forcings using numerical simulations have recently been examined in Oahu, Hawaii (Hsiao et al. 2020) and south of Beijing, China (Xiao et al. 2022), for example. However, to the best of the authors’ knowledge, there is no literature yet on numerical studies on MCSs related to localized convection over Mindanao Island, Philippines.

The present work investigates the local convective processes over Mindanao Island by employing numerical simulations on an event under a condition where large-scale systems have seemingly little influence on convection development. On 03 May 2017, a severe rainfall event over Davao City in Mindanao Island, Philippines, resulted in flooding in the urban area. A previous hydrological study has investigated the flood during this event (Macalalad et al. 2021). Still, a better understanding of the physical processes related to the development of the convective systems that caused the flood is needed to improve the prediction of these hazardous systems. This is the first attempt to use numerical simulations on MCSs over Mindanao Island.

Case overview

Figure 1a shows the synoptic environment over the Philippines on 03 May 2017. No frontal system was present near Mindanao Island. The vertically integrated moisture flux from the surface to 100 hPa was also calculated using the European Center for Medium-Range Weather Forecasts (ECMWF) ERA5 (Hersbach et al. 2020) reanalysis to examine the moisture coming from large-scale systems and is given by

$$\begin{aligned} \langle q{\textbf {v}} \rangle =\frac{1}{g}\int _{100 hPa}^{p_{{\textrm{surface}}}}q{\textbf {v}}\,{\textrm{d}}p, \end{aligned}$$
(1)

where q is specific humidity, \({\textbf {v}}\) is wind vector, p is pressure, and g is the gravitational acceleration. As shown in Fig. 1b, easterlies were the prevailing winds, with weak wind conditions (<5.5 m s\(^{-1}\)) during the summer season. High moisture fluxes were present over the northern Philippines due to the frontal systems, but these were far from Mindanao Island. This implies that only a little moisture from large-scale systems was directly transported to Mindanao Island. The absence of apparent synoptic forcing suggests that the rainfall event over Mindanao Island was due to localized processes.

Fig. 1
figure 1

Synoptic conditions on 03 May 2017 based on a the Asia Pacific surface analysis map from Japan Meteorological Agency and b vertically integrated moisture flux from surface to 100 hPa (shade), mean sea level pressure (grey contour), and 850 hPa wind vectors from ERA5 reanalysis at 20:00 LST. The three major islands of the Philippines (Luzon, Visayas, and Mindanao) are labeled in (b), and the surface elevation map of Mindanao Island where the basin (solid pink line), Davao City (broken blue line), Mount Apo, and location of the Matina Weather Station (red dot) are demarcated in c

Full size image
Fig. 2
figure 2

a-l Hourly evolution of convection distribution from TBB of Himawari-8 Satellite with topography (contour with intervals of 400 m) over parts of Mindanao Island. The “X” markers in i, j denote the locations of MCS-1, MCS-2, and MCS-3

Full size image

Figure 2 shows the hourly evolution of the convection distribution observed over parts of Mindanao Island on 03 May 2017 from the temperature black body (TBB) of the Himawari-8 satellite. At 11:00 LST, there were no convections yet over the basin area of Mindanao Island (see Fig. 1c). As it reached 12:00 LST, convections were observed over the basin, which developed into a meso-\(\beta\) scale convective systemFootnote 1 at 14:00 LST and weakened over time. Meanwhile, two more meso-\(\beta\) scale convective systems developed around the Mount Apo terrain (see Fig. 1c) at 19:00 LST, referred to as MCS-1 and MCS-2 in Fig. 2i. A weather station in Davao City (Matina Station of the Manila Observatory; refer to Fig. 1c) measured a 62.25 mm h\(^{-1}\) rainfall in the evening (20:00 LST) as MCS-1 and MCS-2 organized into a single larger meso-\(\beta\) scale convective system (referred to as MCS-3 in Fig. 2j) resulting in the heavy rainfall that caused the flooding in Davao City at night. Afterwards, MCS-3 weakened and dissipated. The target MCSs of this study are these MCSs.

Numerical simulations

In this study, the MCSs were simulated using the Advanced Research Weather Research and Forecasting (WRF-ARW; Skamarock et al. 2019) model version 4.2.2. The simulations were run from 19:00 UTC 02 to 0:00 UTC 04 May 2017 at 60 vertical levels. As shown in Fig. 3, five nested domains were used. Two-way nesting was applied to horizontal resolutions dx of 27, 9, 3, and 1 km, while one-way nesting to \(dx = 200\) m. The initial and boundary conditions of the parent domain were from the hourly ERA5 reanalysis data at 0.25 degree resolution. The physics parameterization schemes used in the model include the Kain–Fritsch (Kain 2004) cumulus scheme, WRF Single–Moment 6–Class (WSM6; Hong and Lim 2006) microphysics scheme, and Asymmetric Convection Model 2 (ACM2; Pleim 2007) planetary boundary layer (PBL) scheme, Dudhia (Dudhia 1989) shortwave scheme, and Rapid Radiative Transfer Model (RRTM; Mlawer et al. 1997) longwave radiation scheme. The parameterization schemes and calibrated values for the Kain–Fritsch cumulus scheme of Tolentino and Bagtasa (2021) were followed. The model configuration is summarized in Additional file 1: Table S1. Note that the cumulus scheme was turned off for dx = 3 km, 1 km, and 200 m, assuming the grid spacings were fine enough to resolve convection. Meanwhile, the innermost domain (\(dx = 200\) m) was run on a large-eddy simulation (LES) mode where the PBL was turned off, and three-dimensional turbulence diffusion was turned on.

Fig. 3
figure 3

Model domains with surface elevation (m)

Full size image

Results and discussion

Model evaluation

Figure 4 shows the hourly evolution of the derived reflectivity from \(dx = 200\) m and was compared with the Himawari-8 satellite observation (Fig. 2) to evaluate the model performance. The model reasonably reproduced the convections over the basin area from 11:00 LST and captured MCS-1 and MCS-2 at 19:00 LST, and MCS-3 at 20:00 LST.

Fig. 4
figure 4

a-l Hourly evolution of the simulated radar reflectivities (the maximum in a vertical column at each horizontal position) of \(dx = 200\) m with topography (contour with intervals of 400 m) over parts of Mindanao Island. The black and purple transects in i represent the cross-sections used in Fig. 8. The “X” markers in i, j denote the locations of MCS-1, MCS-2, and MCS-3

Full size image

The model outputs at different horizontal resolutions were compared with the observation data. Rainfall data from 53 automated weather stations of the Department of Science and Technology-Advanced Science and Technology Institute (DOST-ASTI), Philippines, were used as observation in Fig. 5.

Fig. 5
figure 5

Spatial distributions of 9 h of accumulated a observation and b–f model rainfall (14:00–23:00 LST of 03 May 2017) at different horizontal resolutions, and g area-averaged hourly mean rainfall over the area in a; h threat scores at different threshold values of the 9 h of accumulated rainfall in a–f

Full size image

Figure 5a–f shows the spatial distribution of the 9 h of accumulated rainfall (from 14:00 LST to 23:00 LST of 03 May 2017) of observation and model. The model was able to generally simulate the spatial distribution and peaks of the localized rainfall across resolutions. Increasing dx from 27 km to finer resolutions resulted in simulating higher rainfall intensities and sharper spatial patterns.

The hourly mean rainfall is also shown in Fig. 5g and is calculated by area-averaging the rainfall values based on the observation points demarcated in Fig. 5a. The hourly model rainfall across various resolutions generally shows good correspondence with the observation. However, there is 3-h delay for the largest rainfall peaks of the models. Meanwhile, downscaling the model to \(dx = 200\) m produced an overestimated peak. Nevertheless, \(dx = 200\) m resulted in better performance, as demonstrated by evaluating the threat scores of the 9 h of accumulated rainfall (similar timesteps to Fig. 5a–f) at a given threshold, as shown in Fig. 5h. The results clearly show that the threat scores of \(dx = 200\) m at thresholds above 25 mm prevail over those of coarser resolutions, which reveals the improved reproducibility of heavy rainfall.

Regardless of the differences between the model and observation, there is still a generally good agreement which made it reasonable to use the model results in the analyses of the convection development. Specifically, \(dx = 200\) m results are used in “Convection development” and “Merging and splitting of MCSs” sections.

Convection development

Simulations show that MCSs indeed caused the heavy rainfall in Mindanao Island. Two prominent meso-\(\beta\) scale convective systems are found to develop west and east of the Mount Apo terrain in Mindanao Island (MCS-1 and MCS-2, respectively). This section aims to identify the processes that influenced the formation and development of these MCSs.

Development of MCS-1 (west of Mount Apo)

Figure 6a–d shows the evolution of the vertically integrated moisture fluxes (from the surface to 900 hPa) of \(dx = 200\) m. The results show that the concave basin played an important role in accumulating the moisture brought from the ocean towards the inland. In fact, from 11:00 LST to 17:00 LST, moisture has been gradually transported to the basin. At 17:00 LST, the presence of abundant moisture within the basin made it conducive for convection development as the concave geometry of the terrain promoted inland low-level moistening (Du et al. 2020). The instability in the basin is also demonstrated by the large increase of maximum convective available potential energy (MCAPE) from 1661.6 J kg\(^{-1}\) at 11:00 LST to 2284.0 J kg\(^{-1}\) at 14:00 LST (area-averaged over the black-boxed area in Fig. 6c). Figure 6e shows the Hovmöller diagram of 10 m zonal winds (shade) and 950 hPa specific humidity (contour), area-averaged over the black-boxed region in Fig. 6c. It demonstrates that the moisture movement from the ocean to inland was due to sea breeze circulation. The sea breeze circulation gradually started at 10:00 LST and was strongest at around 13:00 LST to 17:00 LST, followed by an increase in the low-level specific humidity over the basin. The convection due to sea breeze circulation is further supported by the cross-section of winds (black transect in Fig. 6b) shown in Additional file 1: Fig. S2. As the strong winds from the northwest coastline reached the center of the basin, the convergence with the opposing southeasterly winds triggered convection.

Fig. 6
figure 6

a–d Vertically integrated moisture flux with vectors (from surface to 900 hPa) and topography for a 11:00 LST, b 14:00 LST, c 17:00 LST, and d 20:00 LST. e Hovmöller diagram of 10 m zonal winds (shade) with specific humidity at 950 hPa (contour) area-averaged over the black-boxed area in c. \(dx = 200\) m results are used. The black transect in b represents the cross-section used in Additional file 1: Figs. S2 and S3. The values on the lower right of a–d represent their corresponding MCAPE value. MCAPE values are area-averaged over the black-boxed area in c

Full size image

As shown in Fig. 4e–g, convections formed over the foot of the mountains and the center of the basin triggered by sea breeze circulations. The convections that developed over the center of the basin generated cold pools due to evaporative cooling of the precipitating downdrafts (Fig. 7): to investigate the formation of cold pools, we use the isentropic analysis method of Iwasaki et al. (2014), where a cold air mass is defined as an air mass below a threshold potential temperature. Cold air mass amount (DP), which is the pressure difference between the ground and \(\theta _T\) surface, and DP flux \((\overrightarrow{MF})\) are calculated as follows:

$$\begin{aligned}{} & {} DP\equiv p_s-p\left( \theta _T\right) , \end{aligned}$$
(2)
$$\begin{aligned}{} & {} \overrightarrow{MF}\equiv {\int _{p\left( \theta _T\right) }^{p_s}{\textbf{v}\,dp},} \end{aligned}$$
(3)

where \(\theta\) is potential temperature, \(p_s\) is surface pressure, \(p(\theta _T)\) is pressure on isentrope \(\theta\) = \(\theta _T\), and \(\textbf{v}\) is horizontal wind vector. After trial-and-error, a threshold of \(\theta _T\) \(=\) 300.5 K is used based on the \(\theta\) boundary of the cold air mass (see Additional file 1: Fig. S3).

Fig. 7
figure 7

Simulated DP (shade) and \(\vec {MF}\) (vectors) for \(dx = 200\) m with topography (contour with intervals of 400 m), vertical velocity at 200 m height (\(\ge\) 0.5 m s\(^{-1}\); green contour, with an interval of 0.5 m s\(^{-1}\)), and rainfall (red contour, with an interval of 15 mm) at a 17:00 LST, b 20:00 LST, and c 23:00 LST. The black transect in b represents the cross-section used in Additional file 1: Fig. S5

Full size image

The cold pools developed at 17:00 LST have a DP thickness of \(\sim\) 60 hPa (Fig. 7a). At 20:00 LST, the initial cold pools spread over the basin, and new cold pools were generated due to new convective cells forming (Fig. 4j). Lifting of air along the leading edge of a cold pool has been known to trigger new convective cells (Fovell and Tan 1998; Rotunno et al. 1988; Tompkins 2001). The cold pool-driven convections in the basin are demonstrated by the low-level convergences in Fig. 7. Deep convection growth driven by cold pool interactions is found to be more effective when cold pool boundaries collide (Feng et al. 2015). In this case, the interaction of multiple cold pool outflow boundaries contributed to the upscale growth of convections to MCS-1 in the basin area. In addition, the cold air masses remained for hours in the basin (Fig. 7c), which suggests that the geometry of the concave basin also assisted in blocking the cold air masses within the basin area. The Froude numbers (Fr) are calculated to further support the topographic blocking around the basin (see Additional file 1: Fig. S4). Results show that Fr is always below 1 during the duration of the case event, indicating that the airflow is blocked within the basin area.

Development of MCS-2 (east of Mount Apo)

MCS-2 developed separately over the Davao area, east of the Mount Apo terrain (refer to Fig. 4i). Southeasterly winds brought in low-level moisture from the ocean and interacted with the Mount Apo terrain resulting in convergence in the coastline (see Figs. 6d, 7b). The southeasterly winds at this time are due to the ambient trade winds. Rainfall developed over the southeast foot of Mount Apo at 20:00 LST (Fig. 7b) and a cold pool formed over the northeastern base of Mount Apo (Fig. 7b, c). A vertical cross-section of the cold pool is demonstrated by thermal buoyancy in Additional file 1: Fig. S5, where the initially developed cold air mass over the foot of the mountain expanded southeastward. As the cold air mass propagated southeastward, the cold air outflow strongly converged with the warm moist southeasterly flow. The continuous convergence between the cold air outflow and southeasterly flow resulted in the growth and maintenance of MCS-2 as new convective cells were initiated.

Merging and splitting of MCSs

As shown in the horizontal model reflectivity in Fig. 4i, j, MCS-1 and MCS-2 merged into a seemingly larger meso-\(\beta\) scale system (MCS-3) along the basin towards the Davao area at 20:00 LST. In reality, a river monitoring station (Matina Station of the DOST-ASTI) observed a peak water level of 4.73 m at 21:50 LST that resulted in the flooding of some areas in Davao City. The merging of MCSs is further demonstrated in Fig. 8b, where the vertical cross-section of the black transect in Fig. 4i is shown. Considering that the merging process occurred during the evening, it is possible that the area growth and strength of the cold pools developing over time could have contributed to the merging of MCSs. Meanwhile, the splitting of MCS-3 to smaller meso-\(\beta\) scale MCSs occurred at 23:00 LST as the MCS over the Davao area propagated southeastward (Fig. 8f), and both MCSs subsequently weakened.

Fig. 8
figure 8

Vertical structures of the simulated reflectivities of a–c black and d–f purple transects in Fig. 4i at 19:00 LST, 20:00 LST, and 23:00 LST for \(dx = 200\) m. The black shades represent topography

Full size image

Summary and conclusion

During the summer season (April–May), MCS rainfall contributes a large fraction of the total rainfall over Mindanao Island, Philippines. This study examined the mechanisms involved in localized convection under weak large-scale forcing over Mindanao Island using high-resolution numerical simulations. A severe rainfall event on 03 May 2017 was chosen as the case study as it occurred during the summer season, where influences of large-scale systems (e.g., monsoonal flows, TCs) were minimized. Results showed that the numerical simulations reasonably reproduced the heavy rainfall.

It is found that during the case event, two meso-\(\beta\) scale convective systems formed separately, west and east of Mount Apo terrain over Mindanao Island (referred to as MCS-1 and MCS2, respectively). MCS-1, located in the Mindanao basin area, formed mainly due to moisture advection from sea breeze circulation that resulted in the accumulation of moisture in the basin and made the area conducive for convection initiation. Cold pools were then generated from the precipitating downdrafts and the convergence of the outflow boundaries led to the upscale growth of MCS-1. Meanwhile, MCS-2, situated in the Davao area, formed as a result of interaction between southeasterly winds (ambient trade winds) and the high mountain terrain of Mount Apo. A cold pool was also generated from the precipitating downdrafts of MCS-2, where its outflow continuously converged with the southeasterly winds and maintained its development. At 20:00 LST, the two meso-\(\beta\) scale MCSs merged into a larger meso-\(\beta\) system (referred to as MCS-3). The long duration of rainfall accompanied by MCSs could have caused the flood over the Davao area. At 23:00 LST, MCS-3 began splitting with one of the MCSs moving southeastward. The processes involved in the development of the MCSs are visually summarized in the schematic diagram shown in Fig. 9.

Fig. 9
figure 9

Schematic diagram demonstrating the development of MCSs. Sea breeze on the western coast supplied the abundant moisture that developed MCS-1 in the basin. The precipitating downdrafts of MCS-1 formed cold pools that contributed to its upscale growth. The interaction of the southeasterly winds and Mount Apo terrain developed MCS-2, and its precipitating downdrafts formed a cold pool that assisted its maintenance and growth

Full size image

This study gives insights into the importance of local processes (i.e., sea breeze circulation, cold air masses and terrain geometry) in the initiation and development of MCSs. In addition, the results demonstrated that the rainfall is more successfully captured in a sub-km scale resolution. These findings could be valuable in further understanding dynamics and improving weather forecasts of heavy rainfall associated with MCSs over the tropics.