Signatures of Midsummer Droughts Over Central America and Mexico

The annual cycle of precipitation over Central America and Mexico is climatologically characterized by a robust bimodal distribution, normally termed as the midsummer drought (MSD), in�uencing a large range of agricultural economic and public insurances. Compared to the studies focusing on the mechanisms underpinning the MSD, less research has been undertaken related to its climatological signatures. This is due to a lack of generally accepted methods through which to detect and quantify bimodal precipitation accurately. The present study focuses on characterizing the MSD climatological signatures over Mexico and Central Mexico between 1979 and 2017. This was completed using a new method of detection. The signatures were analyzed from three aspects, namely 1) climatological mean states and variability; 2) connections with large scale modes of climate variability (El Niño–Southern Oscillation (ENSO) and the North Atlantic Subtropical High (NASH)); and 3) the potential afforded by statistical modelling. The development of MSDs across the region is attributed to changes of surface wind – pressure composites, characterized by anomalously negative (positive) surface pressure and onshore (offshore) winds during the peak (trough) of precipitation. ENSO’s modulation of MSDs is also shown by modifying the surface wind – pressure patterns through MSD periods, inducing the intensi�ed NASH and associated easterlies from the Caribbean region, which induce relatively weak precipitation at corresponding time points and subsequently intensify the MSD magnitude and extend the MSD period. Building on previous research which showed MSDs tend to start/end in Madden-Julian Oscillation (MJO) phases 1 and 8, a fourth– order polynomial was used here to statistically model the precipitation time series during the rainy season. We show that the strength of the bimodal precipitation can be well modelled by the coe�cient of the polynomial terms, and the intra-seasonal variability is largely covered by the MJO indices. Using two complete MJO cycles and the polynomial, the bimodal precipitation during the rainy season over Central America and Mexico is synoptically explained, largely contributing to our understanding of the MJO’s modulation on the MSD.


Introduction
The atmospheric circulation of Central America and Mexico plays an important role in the global climate. On the Paci c side of the domain, the annual precipitation cycle is largely dominated by a bimodal distribution (Magaña et al., 1999, Taylor and Alfaro, 2005, Amador et al., 2006, characterized by the rst precipitation peak between May and June, a reduction in precipitation typically between July and August, and a second precipitation peak between late August and early October. During the rst precipitation peak, the warming of the eastern Paci c enhances convection and is accompanied by a weakening of the easterlies. Then, the decrease in precipitation, known as the "mid-summer drought" (Magaña et al., 1999), follows with the cooling of the ocean around the Paci c coast from July to August. The second precipitation peak is characterized by relatively weak trade winds and a warmer eastern Paci c. The midsummer drought (MSD) can represent a precipitation reduction by up to 40% (Small et al., 2007), a change that amounts to a dominant proportion of the annual precipitation variability (Curtis, 2002).
The annual rainfall over the Caribbean side is more complex in terms of the spatial variability. While some studies report that MSDs are generally absent along the Caribbean coast of Central America (Magaña et al., 1999, Taylor and Alfaro, 2005, Small et al., 2007, Amador, 2008, it has been observed that similar bimodal precipitation cycles exist over the Greater Antilles , Spence et al., 2004, Ashby et al., 2005 and parts of the Caribbean side of Central America (Maldonado et al., 2016). Similar to MSDs on the Paci c side of Central America and Mexico, the rainfall reduction over the Caribbean side demonstrates a tight connection with the Caribbean Low-Level Jet (CLLJ), a moisture transport mechanism carrying reduced moisture ux from the Caribbean Sea that subsequently suppresses the convection system (Magaña et al., 1999, Wang, 2007, Muñoz et al., 2008, Amador, 2008, Whyte et al., 2008. Since the MSD was rst identi ed in the 1960s (Portig, 1961), various theories have been proposed to explain its origins and the development of its bimodal signature. Magaña et al. (1999) suggested that the MSD-sea surface temperature (SST)-radiation relationship, which uses the enhancement/suppression Although numerous studies have focused on the physical mechanisms that cause MSDs and the signatures and annual characteristics of the bimodal precipitation, including its detection and quanti cation of its climatology and variability, these studies have lacked ne-scale detail of the temporal and spatial variability. Mosiño and García (1966) determined MSDs by nding consecutive months characterized by decreased precipitation relative to those exhibiting precipitation maxima that bounded them during the rainy season (May to October). After slight modi cation, this method was later applied to examine MSDs over Mexico using Climate Hazards Group InfraRed Precipitation with Station data and subsequently quanti ed their duration and intensity using a self-de ned monthly index (Perdigón-Morales et al., 2018). Using second-order harmonic regression, Curtis (2002) demonstrated that the bimodal signature of the MSD accounted for most annual precipitation variability over Central America, and this tendency can be strengthened during positive ENSO phases. Karnauskas et al. (2013) provided the rst global distribution of bimodal precipitation using several observations, demonstrating that the MSD is a climate signal that is detectable at the global scale, albeit that it is signi cant in speci c regions, including Central America and Mexico. Maldonado et al. (2016) argued that MSDs can exist over both the Caribbean and Paci c sides of Central America, and the intensity and magnitude of those MSDs on the Paci c side are more signi cantly connected with the CLLJ and ENSO. Most previous studies that have examined the signature of MSDs were conducted using monthly precipitation data from an average annual cycle, limiting the potential of the results to reveal the interannual variability of MSDs at ne resolution.
Here, we investigate the MSD across Central America and Mexico using daily precipitation observations, with a focus on identifying the: 1) mean states and variability, 2) connection with large-scale modes of climate variability (speci cally, ENSO and the MJO), and 3) potential to skilfully statistically model the MSD.

Data
This study uses the Climate Prediction Center (CPC) global uni ed gauge-based analysis of daily precipitation , Chen et al., 2008 from 1979 -2017 to quantify the bimodal signature of precipitation annually and interannually across Central America and Mexico, the domain is shown in Figure 1. The CPC data were constructed on a 0.5 o 0.5 o spatial grid using observed data from various sources. In this dataset, the daily climatology was calculated by summing the rst six harmonics of the annual climatological (average) cycle, with the adjustment from the Parameter-Elevation Regressions on Independent Slopes Model (PRISM) monthly climatology (Daly et al., 1994(Daly et al., , 2002, which is a climate analysis system providing criteria for the evaluation of climate properties. The daily precipitation ratio with respect to the climatology was obtained by optimal interpolation methods. The CPC data have been widely used in previous studies associated with precipitation (e.g., Preethi et al., 2011, Hou et al., 2014 and their quality have been evaluated against both observations and model simulations using various statistical methods (e.g., Katiraie-Boroujerdy et al., 2013, Rana, et al., 2015. In this study, properties used to characterize climate states across the region, including 2m (above the surface) temperature, 10m horizontal winds, and surface pressure, were extracted from the ERA-Interim The ENSO index used in this study is the Oceanic Niño Index (ONI) based on ERSSTv5 data (Huang et al., 2017), which is calculated as 3-month running mean SST anomalies in the Niño3.4 region (5 o N-5 o S, 120 o -170 o W). Warm and cold periods over the record are identi ed when the +/-0.5 o C threshold is met for ve consecutive overlapping three-month periods, or longer. Subsequently, El Niño/La Niña years are determined by nding the years when ONI values, in at least ve months during September to next year's February, meet the threshold. The original ONI from September to February is averaged in each year to get the annual ONI, which is used to quantify the interannually-varying phase and magnitude of ENSO.
The MJO index used in this study was developed using a seasonally independent index based on paired empirical orthogonal functions of the combined elds of near-equatorially averaged 200 hPa and 850 hPa zonal winds, and satellite-observations of outgoing longwave radiation (OLR) data, the resultant principal component (PC) time series are termed the Real-time Multivariate MJO series 1 and 2 (RMM1 and RMM2: Wheeler and Hendon, 2004). This index has been shown to effectively capture the interannual modulation of the global variance induced by the MJO, as well as having the potential to reconstruct a variety of weather patterns induced by the variance in MJO activity. Based on the RMM index, daily MJO responses are classi ed into eight phases, which demonstrate an approximately anticyclonic propagation from phase 1 to phase 8.

MSD detecting algorithms
The detection of annual MSD events is achieved using the method recently proposed by Zhao et al. (2020). In this method, the MSD signal in a precipitation time series is detected from the rst peak maximum (onset of MSD) of the bimodal precipitation to the second peak maximum (end of MSD), covering the whole period of the precipitation reduction. This detection was achieved by two consecutive steps. First, the seasonally varying climatology of precipitation was smoothed using a 31-day Gaussian lter at each grid point, and the climatological MSD signal at each grid point was determined following three criteria: 1) two local precipitation peaks, P1 and P2, should exist separately within the periods from During the detection, some metrics are determined to describe or quantify the corresponding MSD signal, including onset, end and peak (corresponding to the minimum precipitation during MSD signals) dates, duration (period from onset to end date) and intensity of MSD (I msd , García-Martínez, 2015) calculated following where P max is the larger one in precipitation on onset and end dates and P min is the average precipitation through the MSD signal. In this study, the detection of annual MSD signals was executed for CPC precipitation data over the period from 1979 to 2017 in the domain (120 o W-60 o W,

Anomalies and composites
The anomaly for a particular time series was calculated by removing the climatological annual cycle in Julian days, where data on February 29 th in each non-leap year was lled by the mean of that on February 28 th and March 1 st . This step may also be achieved by removing the rst several harmonics (e.g., Oliver and Holbrook, 2018), but we calculated this here based on the elimination of means in each corresponding Julian day to get a more robust signature of the long-term climatology. Here, anomalies were calculated for CPC precipitation, 2m temperature, 10m horizontal winds, surface pressure and SST.
The climate composite (normally termed as the 'composite' in this study), used to characterize the mean states of a climate property through a particular time-period, is calculated by temporally averaging the climate property across the corresponding time points. The advantage of this approach is to ensure the continuity of the calculated composite at both the spatial and temporal scales, which could generate By spatially averaging the major characteristics of MSD signals (onset, peak and end dates, duration, and I msd ) in each year, the temporal variabilities of MSD signatures are explored. The cross-correlation among the ve signatures and annual ONI show a well-organized pattern ( Figure 4). The onset/end date has signi cantly negative/positive correlation with the duration, which is intuitively reasonable. The I msd is positively correlated with the duration, indicating that a stronger intensity MSD signal is also generally part of a longer duration event. It is speci cally notable that the annual ONI is positively correlated with both the duration and I msd , indicating that stronger and longer MSD signals tend to exist in El Niño years instead of La Niña years.
Large-scale climate composites of key characteristics of MSD signals are also examined. The climate composites of six properties (anomalies of precipitation, 2m temperature, 10m horizontal winds, surface pressure and sea surface temperature) over the domain were calculated for three time points (onset, peak and end dates of the MSD signals) to illustrate the changes of climate patterns during the generation of the MSD ( Figure 5). The anomalously positive precipitation over the domain exists during the onset and end dates of MSD signals, while opposite patterns are determined for peak dates, corresponding to the bimodal characteristics of MSD signals. Signi cant wind shifting during the development of MSD signals is notable. When the MSD starts over Central America and Mexico, the Paci c coast of Central America and coastal areas around the Gulf of Mexico -where robust MSD signals are found -are dominated by onshore wind anomalies. These enhanced onshore winds together contribute to a low-pressure (cyclonic) system, correspondingly inducing anomalously negative near surface temperature anomalies over both land and ocean. Then, these onshore wind anomalies transition into enhanced offshore wind anomalies on the peak dates of the MSD signals, accompanied by a corresponding high pressure (anticyclonic) system and anomalously positive near surface temperature. The climate composites on the end dates of the MSD signals are remarkably similar to those on the onset dates, indicating the retrieval process from peak to end of MSDs. The precipitation reduction on the peak date of the MSD is accompanied by strong trade wind easterlies, which may be largely due to the enhancement of the CLLJ during July to August, transporting moisture ( ux) from the Caribbean region and subsequently suppressing the convection. The in uence of the NASH is not signi cant in the climatological composites.

Connections with ENSO and the MJO
According to previous studies (Magaña et al., 1999(Magaña et al., , 2003  The climate composites of surface pressure and 10m winds in each ENSO phase at onset, peak and end dates are shown in Figure 7. Compared to climatological composites shown in Figure 5, some biases exist in these patterns. For ENSO-neutral years, the composites of near-surface winds and pressures are broadly similar to the climatological states (cf. Figure 5g, h, i), except with relatively weak cyclonic/anticyclonic patterns and more signi cant in uences of the NASH. For El Niño years, the anomalous cyclonic system during the onset of the MSD in the Caribbean Sea region, on the peak MSD dates, the climatological onshore wind anomalies at the Paci c coast of Central America (Figure 5i) are replaced by anomalous easterly winds from the Caribbean Sea, which is due to the westward extension of the NASH. The in uence of the NASH in El Niño years is more signi cant, shown by the westward extension of the high-pressure centre through the entire MSD period. For La Niña years, the wind-pressure patterns at the MSD onset and end dates are similar to the climatological patterns, while anomalous westerly winds pass through Central America on the peak dates, making the climatological anticyclonic system (Figure 5h) absent. For precipitation anomalies in El Niño years, the generally drier June and September reveal that the precipitation during the two months is lower than climatology. The two months may still be in potential MSD periods, and the onset/end dates of corresponding MSD events may thus be extended to some days in May/October. These features indicate relatively long MSD periods (shown by longer durations of MSD signals) during El Niño years, which is consistent with the positive correlation between MSD durations and ONI shown in Figure 4. The anomalously high precipitation on the peak dates of the MSD in La Niña years indicates a relatively "shallow" trough of precipitation reduction, corresponding to relatively weak MSD signals (shown by smaller I msd of MSD signals).
Generally, ENSO's modulation of the MSD over Central America is achieved by modifying the low-level wind-pressure system. In positive ENSO phases (El Niño years), the NASH strengthens during the MSD, especially from the peak to end dates. On the peak date of the MSD, the westward extension of the NASH brings stronger easterlies, inducing a more intense CLLJ. The intensi ed CLLJ can last to late boreal summer and remain through to the end date of the MSD, inducing a drier MSD throughout, since the moisture ux associated with the easterly ow suppresses the convection. This feature makes MSDs in El Niño years more intense (larger I msd ) and longer, resulting in a generally drier summer. In negative ENSO phases (La Niña years), the in uence of the NASH tends to be insigni cant and the peak of the CLLJ is suppressed. The easterlies on the peak date of the MSD is replaced by strong westerlies from the Paci c, inducing a wetter MSD period and a "shallower" MSD trough.
Another factor to induce the synchronicity between the change of wind-pressure patterns modulated by ENSO and precipitation during the MSD may be the interaction between the winds and topography -that is, the onshore/offshore winds and orographic forcing associated with steep mountainous terrains. Due to the orographic uplifting, the interaction between the onshore winds and orography act to enhance the precipitation, while offshore winds tend to have the opposite effect. The shifting of wind patterns over the major MSD areas (the Paci c Coast of Central America and coasts around the Gulf of Mexico) can contribute to the bimodal shape of MSD signals. Therefore, it can be deduced that changes of wind patterns in ENSO years may in uence the interannual variability of MSD signals. Similar features have been observed in Central America (e.g., Zhao et al., 2020).

MJO
To analyze the connection between the MSD signals across the domain and the MJO (RMM1 and RMM2), each detected MSD signal is categorized into four periods. To represent the typical signatures of the MSD signals in the different MJO phases, each period is separated based on a particular percentile.
For each MSD signal, P1 is from the onset date to the 30 th percentile between the onset date and the peak date, while P2 follows P1 and ends in the peak date. Similarly, P3 follows P2 and ends in the 70 th percentile between peak dates and end dates, while P4 covers the remained period. This is illustrated in Figure 8. Each period of the MSD has a physical meaning. P1 and P4 represent relatively short periods during the onset and end of MSD signals, so they could be intuitively named as the "onset period" and "end period". We refer to P2 as the "development period", which spans between the onset and peak date, that is the period when precipitation tends to reduce. We refer to P3 as the "recovery (or decay) period", when the summer precipitation recovers towards its second peak.
Based on this de nition, the temporal connection between MSD periods and MJO phases were analyzed by directly calculating the percentage fraction of each MSD period that occurs during each MJO phase ( Figure 9) -i.e., totals at each individual grid point across all MJO phases should sum to unity (1). While P2 and P3 do not exhibit clear signatures of speci c correspondences to MJO phase, P1 and P4 however show strong correspondences with MJO phase 8-1 in areas exhibiting robust bimodal precipitation signatures, such as the Paci c coast of southern Mexico and Central America and Cuba. This is also notable in phases 2-3 but not quite as strong. This signature indicates that detected MSD signals tend to onset/end in MJO phase 8-1 over the domain.
The MJO phases also modulate the near surface wind-pressure patterns. Figure 10 shows the windpressure composites corresponding to MJO phases during the period when MSD signals are detected. In MJO phases 8-1, westerly anomalies with approximate geostrophic balance approach the Paci c Coast of Central America, which subsequently reach the Caribbean region and become southwesterly to form a low-pressure system centered in the Gulf of Mexico. The westerlies from the Paci c weaken in MJO

Statistical modelling of the MSD.
In this section, we examine the statistical modelling potential of the bimodal precipitation signature over Central America and Mexico and infer possible physical mechanisms underpinning this. In MSD areas, the rainy season is characterized by two peaks and a trough in the summertime precipitation time series. Although only the trough of precipitation is referred to as the MSD signal in our de nition, the increase/decrease of precipitation before/after the MSD (trough) also plays an important role in characterizing the variability of annual precipitation time series since it is very different from other dry seasons. Further, we statistically model not only the MSD signals (from onset to end), but also the whole precipitation time series in the rainy season, which accounts for most of the annual variabilities.
We rst con rm the de nition of what is meant by the rainy season. Over Central America and Mexico, the rainy season is typically termed the period from May to October in associated research about the MSD (Hastenrath, 1967, Magaña et al., 1999. However, this de nition is based on the climatological unimodal precipitation maximum in most areas of the northern hemisphere, which may not be adaptable to bimodal precipitation climatologies that characterize MSD regions. Therefore, we speci cally de ne here the rainy season for MSD areas in this study. After calculating the seasonally varying climatology of precipitation at each grid point across the region characterized by MSD occurrences, and smoothing it using a Gaussian lter, an empirical orthogonal function (EOF: Lorenz, 1956) analysis is applied to the resultant spatiotemporal precipitation data. The rst EOF (EOF1, Figure 11), which explains 77.71% of the total annual climatological cycle precipitation variance, shows higher precipitation along the Paci c coast and Yucatán Peninsula, and relatively low precipitation in southern Mexico and Cuba. The pattern of EOF1 is similar to the climatological precipitation in traditionally de ned rainy seasons (May to October) over Central America and Mexico (e.g., Zhao et al., 2020), implying that EOF1 is a useful measure of the characteristic climatological precipitation variability across the region. Characterized by an obvious bimodal shape, PC1 demonstrates the annual bimodal precipitation over Central America and Mexico, which is scaled regionally across the spatial domain by the EOF1 loadings. the rainy season in this study is hence determined as the period when PC1 > 0 (May 17 th to October 27 th ). This determined rainy season is used throughout this section.
Smoothed using a 31-day moving-average window, the seasonal varying climatology of precipitation during the rainy season at each grid point across the domain is modelled using a fourth-order polynomial: where P indicates the precipitation time series at each grid point during the rainy season, b 0 -b 4 correspond to the tted coe cients for each polynomial term, and t indicates the corresponding time (day). The application of the fourth-order polynomial here is due to the fact that it gives the best modelling outputs, while polynomials of smaller order (e.g., third-order) generate lower R 2 and higher order polynomials ( fth-order or above) induce over tting problems shown by a generally insigni cant coe cient on the largest order term (not shown here). In this study, we focus on analyzing the coe cient of fourth-order polynomial term, b 4 , which is the key factor to determine the polynomial shape of the tted model. The resultant R 2 and coe cient b 4 are shown in Figure 12, with determined MSD areas indicated by the stippling. In most areas of the domain, the polynomial generates satisfying modelling outputs for the rainy season precipitation, shown by generally high R 2 (~0.8) across much of the domain. It is notable that R 2 is still reasonable (R 2 > 0.5) even in those regions where the performance is the weakest, such as the coasts around the Gulf of Mexico and Panama. Overall, we nd that the performance of b 4 varies with the strength of the bimodal precipitation. In areas exhibiting MSD signals, b 4 is generally negative and statistically signi cant (at the 95% level), whereas it tends to be insigni cant or signi cantly positive in non-MSD characterized areas. The tendency is clearer after the climatological precipitation is spatially averaged based on the performance of b 4 ( Figure 13). The bimodal annual cycle of precipitation is evident in areas characterized by signi cantly negative b 4 , while precipitation in other regions tends to be dominated by a unimodal precipitation annual cycle.
The performance of the aforementioned method proves to be unsatisfactory when applied to the daily precipitation time series in the rainy season over the 1979 -2017 period. The polynomial is applied to rainy season precipitation for every single year in each grid and the resultant b 4 and R 2 are temporally averaged ( Figure 14). It is notable that, while the temporally averaged b 4 generally follows the pattern shown in Figure 12, the spatial R 2 drops signi cantly (<0.5 in a large part of the domain). It indicates that the fourth-order polynomial model fails to reveal some interannual variations of the intraseasonal variability, which may be ltered during the calculation of seasonally varying climatology.
To reveal these unresolved intraseasonal variabilities, the polynomial model is modi ed by adding the MJO indexes: The updated model, with MJO covariates, is applied to the precipitation time series during the rainy season for every year and grid point over the domain. After temporally averaging, the resultant R 2 , b 4 and regression coe cients on the MJO covariates (a 1 and a 2 ) are shown in Figure 15. Although the R 2 magnitudes (Figure 15a) are not as large as the climatological values (cf. Figure 12), it clearly increases after adding the MJO indexes, implying that the inclusion of the MJO makes an important contribution to addressing the previously unresolved variability across the region. The temporally averaged b 4 is similar to the previous one for the climatological ( Figure 12) and daily ( Figure 14) analyses, indicating that the added covariates (MJO indexes) do not disturb the performance of the other polynomial terms. This implies that the added covariates are generally orthogonal to the polynomial terms. The widespread statistical signi cances of the a 1 and a 2 coe cients over the domain imply that the inclusion of the MJO indexes add considerable value to the model's explanation of the overall variability, with relatively little effects of over tting or overdispersion. It is notable that a 1 and a 2 are signi cantly negative in most characteristic MSD regions, while they tend to be positive or insigni cant in characteristically non-MSD regions. Based on the RMM1 -RMM2 phases (phases 1 -8), the performance of a 1 and a 2 can be interpreted as the phase-shifting of the MJO. The increase of RMM1 and RMM2 together contributes to the phase shifting from MJO phase 2 to 5, corresponding to a period of precipitation reduction in the rainy season. Similarly, the decrease of RMM1 and RMM2 corresponds to the phase shifting from phase 6 to phase 1 and associated rainfall enhancement in the rainy season.
Based on the results shown above, the bimodal precipitation during the rainy seasons in the MSD characterized regions can be synoptically explained by a fourth-order bimodal signature and the modulation through two complete MJO cycles (Figure 16). Over characteristic MSD regions, the rainy season starts with a rapid increase in precipitation during MJO phase 5/6 to 8/1. After reaching the rst precipitation peak, the subsequent precipitation reduction (into the MSD trough) typically exists from late June/early July through to late August/early September, characterized by a full MJO cycle. Following the end of the MSD period, precipitation tends to rapidly decrease again through the next month, transitioning into the dry season. This coincides with a shift of the MJO from phases 8-1 to 5-6.

Spatial and temporal variabilities
In this study, we detected MSD signals over Central America and Mexico using daily time-scale data over the period from 1979 to 2017. We found that large parts of southern Mexico and Central America display constant and frequent MSD signatures, characterized by signi cant spatial and temporal variability. The detected MSD signals tend to have longer durations and wide temporal ranges, characterized by earlier onset and later end date, towards the southeast. Several regions exhibit strong MSD signatures, including the Paci c Coast of Central America, Cuba and the Gulf of Mexico. The spatial patterns of detected MSD signals are generally similar to those shown by Zhao et al. (2020), using the same dataset from 1993 to 2017, except for some minor biases in the central region of the Yucatán Peninsula. The pattern similarity highlights the temporal length of the data we used is su cient to simulate the climatological signature of MSD mean states, it also supports the robustness of the method. The temporal variability of the MSD signals is characterized by complex, noisy and no-autocorrelated signatures. This implies that the frequency of the MSD signals over the domain does not have a signi cant trend over the period 1979 -2017.
The large scale composites of climate properties are used to dynamically illustrate the development of MSD signals, including onset, peak and end dates. The most important and interesting signature found is the change of the wind-pressure system relationship for different MSD periods. Speci cally, we found that there are characteristically cyclonic anomalies for periods with higher precipitation (onset, end dates) and anticyclonic anomalies for periods with lower precipitation (peak date). During the onset/end of MSD signals, the near-surface temperature (2m temperature and SST) anomalies over the domain is generally negative, while positive temperature anomalies exist during the peak date. According to their theory, the warming eastern Paci c could induce active upward convection and corresponding intense precipitation (during the onset/end of the MSD), while oceanic cooling corresponds to the reduction of precipitation (during the peak of the MSD). However, this signature is not evident in near-surface temperature composites in the present study, which is characterized by anomalously low temperatures during the onset/end of MSD signals and anomalously warm temperatures during the peak of MSD. This bias could be due to the examination of anomalies instead of raw SST to calculate the composites in the present study. Magaña et al. (1999) used absolute SST to characterize the change of heat content during the development of the MSD, which highlights the contribution of SST warming and cooling, while the examination of anomalies in this study focuses on the in uence from near-surface wind circulations. Mechanisms proposed in previous studies (e.g., Magaña et al., 1999, Karnauskas et al., 2013, Perdigón-Morales et al., 2021 indicate that the generation of the MSD is not induced by a single factor, but rather a combination of multiple physical factors including sea-air-coast interactions and large-scale climate modes. The application of realistic and idealized climate models, which enable the removal of some physical properties, may more clearly reveal the mechanisms behind the MSD.

Connections with climate modes and associated predictability
The relationship found between MSD metrics and the ONI suggests that longer MSDs tend to be stronger and may be enhanced by El Niño and suppressed by La Niña. The positive ENSO phase (El Niño) can suppress precipitation during boreal summer and strengthen the North Atlantic Subtropical High (NASH) and its associated easterlies from the Caribbean region, which can intensify the MSD and potentially extend the MSD duration. The easterlies, which are signi cantly contributed to by the peak of the Caribbean Low -Level Jet (CLLJ) can potentially modulate the MSD through two different processes: the strengthened easterlies suppress the convection, especially during the peak to the end dates of the MSD, inducing a drier and subsequently more intense MSD period, on the other hand, the interaction between the coastal wind and steep topography can also contribute to the change of precipitation, since positive ENSO phases can bring easterly anomalies, which are offshore winds on the Paci c side of Central America and Mexico. These offshore winds can suppress the orographic uplifting, and subsequently reduce the rainfall in these regions.
ENSO's in uence on MSDs is controversial. Many studies argue that positive ENSO phases strengthen the MSD , Curtis, 2002, Hidalgo et al., 2017, Díaz-Esteban and Raga, 2018 while others suggest that the MSD signal may be weaker during El Niño years (Magaña et al., 1999, 2003, Peralta-Hernández et al., 2008. Our results indicate that ENSO's in uence on the MSD is through modulation of the NASH and associated near-surface wind elds. Furthermore, this corresponds to observations of an intensi ed NASH (Giannini et al., 2000) and CLLJ (Wang, 2007, Krishnamurthy et al., 2015, as well as their teleconnection during boreal summer, and highlights the role of the low-level circulation system in the generation of the MSD. Based on our categorization of the MSD into four periods and their relationship with MJO-phase, we have shown that a relatively high proportion of MSD periods tend to start/end in MJO phase 8-1 due to the anomalous onshore winds arising at the coasts of Central America. This result is consistent with a previous study of MSDs over Costa Rica (Poleo et al., 2014, Zhao et al., 2019 and Mexico (Perdigón-Morales et al., 2019). Additionally, the teleconnection between wind-pressure patterns in MSD P1 and P4 and MJO phases 8-1 have also been identi ed. The varying wind patterns associated with MJO phases imply that MJO affects precipitation throughout the entirety of MSD signatures, rather than being limited in starting/ending periods.
An important MSD signature investigated in this study is through the fourth-order polynomial regression modelling of the intraseasonal variability, including the phase shifting by the MJO. Overall, we found that the mean states of the rainy season precipitation over the domain were captured well by the model. Speci cally, we found that that the polynomial coe cient b 4 can be a practical index to quantify the strength of climatological MSDs over the domain. We found that a signi cantly negative b 4 dominates MSD areas, while non-MSD areas generally exhibit signi cantly positive or insigni cant b 4 . The model was found to perform much worse using annual precipitation data, while the rainy season could be optimized by adding the MJO indexes as covariates in the model, implying that the unresolved intraseasonal variability in each year could be largely covered by changes in MJO phases.
The areas exhibiting climatological MSD signals exhibit generally negative coe cients of MJOassociated covariates. We interpret this as an MJO phase-shifting effect here that signi cantly in uences the characteristic intraseasonal variabilities of precipitation during the rainy season across the MSD area. Changes in MJO phases from phase 5/6 to 8/1 lead to increased precipitation, contributing to the rst precipitation peak, corresponding to the onset of the MSD. A complete MJO cycle induces a precipitation reduction, corresponding to the trough of the MSD. Finally, the MJO transitions from phase 8/1 through to 5/6, contributing to a rapid decrease in precipitation, implying the end of the rainy season.
The intraseasonal variability of precipitation through the rainy season in the MSD areas is clearly and signi cantly modulated by the MJO.
In the conceptual model proposed in this study, we used two complete MJO cycles to explain the interannual variability of MSD signals during the rainy seasons. The duration of two complete MJO cycles (~100 days, Zhang, 2005) used in the hypothesis, however, does not critically match the period of rainy season used in this study, which is from May 17 th to October 27 th (164 days). This bias can be caused by several factors. Firstly, the MJO phases in Julian days of year vary annually, implying the MJO's modulation on intraseasonal precipitation varies interannually. Secondly, while the addition of MJO indexes in the regression model provides considerable improvement, ~20% of the total variance remains unresolved, which may be due to other large-scale climate modes such as ENSO and/or the Interdecadal Paci c Oscillation, and regional forcing such as diabatic heating (Vincent and Lane, 2018).
The implication of the MJO on regional circulation, shown by the changing wind-pressure system associated with changes in MJO phase, could largely contribute to the generation and maintenance of the bimodal precipitation signature (including the so-called 'mid-summer drought') through the rainy season. We have found that a fourth-order polynomial regression model captures a large proportion of the precipitation variability, indicating the potential predictability of the bimodal precipitation signature. Several MJO modelling approaches, including a damped harmonic oscillator model (Oliver and Thompson, 2016), linear inverse model (Cavanaugh et al., 2015), ensemble general circulation models (Seo et al., 2009, Vitart, 2014 and atmosphere-ocean coupled models, have been shown to capture MJO predictability and offer the potential to predict MJO dynamically, mathematically or statistically with lead times <4 weeks (Waliser et al., 2006). Considering the wide use and constant development of MJO indexes (e.g. Wheeler     Cross correlation among metrics of MSD signals, including onset, end, and peak dates, durations and I msd , and ONI index. The strength of red (blue) indicates negative (positive) correlation, in 95% statistical signi cance level.

Figure 5
Climate composites in typical time points of MSD. Each column indicates composites in a particular MSD period (onset, peak and end dates), while each row represents a particular atmospheric property (anomalous of precipitation, 2m temperature, 10m horizontal winds, surface pressure and sea surface temperature).

Figure 6
Climatological precipitation across June to September in different ENSO phases. Each row indicates a particular period for climatological precipitation (June, July -August and September), while each column indicates a particular ENSO phase (El Niño, La Niña and neutral years). Dots here indicate statistical signi cance in 95% con dence intervals.

Figure 7
Composites of 10m horizontal winds and surface pressure across all detected MSD events in different ENSO phases. Each row indicates a particular time point in MSD signals (onset, peak and end dates of MSD signals), while each column indicates a particular ENSO phase (El Niño, La Niña and neutral years).
Colours here indicate the proportion of MSD periods in corresponding MJO phases.

Figure 10
Composites of 10m horizontal winds and surface pressure in varying MJO phases. Dots here indicate statistical signi cance in 95% con dence intervals Page 30/35

Figure 11
Resultant EOF1 spatial patterns (upper panel) and associated PC1 time series (lower panel).

Figure 12
Performance of 4 th order polynomial models on the climatological precipitation during rainy seasons. a) The adjusted R 2 resulted from tted model in each grid. b) Coe cient in front of the 4 th order term in each grid. Regions exhibiting MSD signals are shaded by black dots.

Figure 13
Spatially averaged annual climatology of precipitation with respect to different regions, including a) domain dominated by negatively signi cant b 4 according to Figure 11  Performance of 4 th order polynomial models on the annual precipitation during rainy seasons. a) Yearly averaged adjusted R 2 resulted from tted models in each grid. b) Yearly averaged coe cients in front of the 4 th order term in each grid. Regions exhibiting MSD signals are shaded by black dots.