3.1 Mean states
The climatological signatures of detected MSDs over Central America and Mexico, including frequency (Figure 2a), mean onset (Figure 2b), peak (Figure 2c) and end (Figure 2d) dates, and calculated climatological MSD intensity (Imsd) (Figure 2f), show significant spatial variabilities. The generally high frequencies of the detected MSD signals reveal robust bimodal characteristics of annual precipitation over most parts of the domain, including the Pacific coast of southern Mexico and Central America, Yucatán Peninsula, coasts around the Gulf of Mexico and Cuba. To the southeast, detected MSD signals tend to start earlier and end later, corresponding to relatively longer climatological durations (Figure 2e). Compared to other signatures, the mean peak dates of the MSD signals show higher spatial variabilities, indicated by more noisy signals and irregular spatial patterns. Several areas exhibiting climatologically intense and long MSDs can be identified, including the Pacific coast of Central America, and coastal areas around the Gulf of Mexico and Cuba.
The temporal variability of MSD signals is also examined. The proportion of areas exhibiting MSD events demonstrates a time series with high frequency at the interannual scale (Figure 3a). The time series does not have significant autocorrelation (Figure 3b), implying its predictability cannot be modelled by an autoregressive model, and which has been widely used in studies associated with predictions of climate indexes (e.g., Seo et al., 2009, Ubilava and Helmers, 2013, Oliver and Thompson., 2016). The time series is also shown to have no correlations with other large–scale climate modes, such as ENSO and the Pacific decadal oscillation (PDO) (not shown here), which is consistent with previous research (Fallas-López and Alfaro, 2012). Additionally, there is no significant linear trend in the time series. Generally, the annual number of MSD signals over the domain can thus be interpreted as a complex time series with significant interannual variability, which may not be well modelled by its own autocorrelation characteristics.
By spatially averaging the major characteristics of MSD signals (onset, peak and end dates, duration, and Imsd) in each year, the temporal variabilities of MSD signatures are explored. The cross-correlation among the five signatures and annual ONI show a well-organized pattern (Figure 4). The onset/end date has significantly negative/positive correlation with the duration, which is intuitively reasonable. The Imsd is positively correlated with the duration, indicating that a stronger intensity MSD signal is also generally part of a longer duration event. It is specifically notable that the annual ONI is positively correlated with both the duration and Imsd, 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. Significant wind shifting during the development of MSD signals is notable. When the MSD starts over Central America and Mexico, the Pacific 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 (flux) from the Caribbean region and subsequently suppressing the convection. The influence of the NASH is not significant in the climatological composites.
3.2 Connections with ENSO and the MJO
According to previous studies (Magaña et al., 1999, 2003, Chen and Taylor, 2002, Curtis, 2002, Peralta-Hernández et al., 2008, Hidalgo et al., 2017), MSDs are highly variable interannually. MSDs can be modulated by ENSO and/or the MJO, as has been shown previously for the generation and development of the MSD in Costa Rica (Martin and Schumacher, 2011, Perdigón-Morales and Romero-Centeno, 2019, Zhao et al., 2019, 2020). In this section, we further explore the connection between MSDs and both ENSO (Section 3.1) and the MJO (Section 3.2) across Central America and Mexico over the period from 1979 – 2017.
The climatological precipitation over Central America and Mexico in each ENSO phase is separately calculated for June, July, August and September. Choosing the three time-segments is undertaken to better illustrate the variabilities of precipitation during common MSD periods (e.g., Rauscher et al., 2008, Corrales‐Suastegui et al., 2020). In El Niño years, generally negative precipitation anomalies exist in most parts of the region, including the Pacific Coast of the domain and coastal areas around the Gulf of Mexico, where MSD signals with high frequency are detected from June to September (Figure 6a-c). It is notable that areas exhibiting bimodal precipitations, such as the Pacific side of Central America, tend to be dominated by suppressed precipitation during July and August in positive ENSO phases. Opposite patterns exist in La Niña years (Figure 6d-f), indicating relatively wet rainy seasons in the July-August period over most parts of the domain.
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 significant influences 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 Pacific 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 influence of the NASH in El Niño years is more significant, 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 Imsd 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 intensified 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 flux associated with the easterly flow suppresses the convection. This feature makes MSDs in El Niño years more intense (larger Imsd) and longer, resulting in a generally drier summer. In negative ENSO phases (La Niña years), the influence of the NASH tends to be insignificant and the peak of the CLLJ is suppressed. The easterlies on the peak date of the MSD is replaced by strong westerlies from the Pacific, 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 Pacific 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 influence the interannual variability of MSD signals. Similar features have been observed in Central America (e.g., Zhao et al., 2020).
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 30th 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 70th 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 definition, 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 specific 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 Pacific 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 wind–pressure 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 Pacific 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 Pacific weaken in MJO phases 2–3, shown by their general geostrophic balance and weaker meridional pressure gradient. This result indicates the strength of the westerlies from the Pacific associated with the MJO phases is positively correlated with the onset/end of the MSD events along the Pacific coast of Central America and Mexico. Specifically, the westerlies and their associated convergence zone can induce strong convection and enhanced precipitation, corresponding to the precipitation maxima at the dates of MSD onset and end. This is consistent with previous MSD-MJO related-research for Costa Rica (Zhao et al., 2019), but here extending over the larger domain that includes most parts of the Pacific coast of Central America and southern Mexico. In MJO phases 4–5 and 6–7, easterly anomalies from the Caribbean Sea contribute to a divergence system centered over the Gulf of Mexico, which suppresses the precipitation and subsequently induces the dry trough of the MSD signal.
3.3 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 definition, 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 first confirm the definition 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 definition 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 specifically define 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 filter, an empirical orthogonal function (EOF: Lorenz, 1956) analysis is applied to the resultant spatiotemporal precipitation data. The first EOF (EOF1, Figure 11), which explains 77.71% of the total annual climatological cycle precipitation variance, shows higher precipitation along the Pacific 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 defined 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 17th to October 27th). 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, b0 – b4 correspond to the fitted coefficients 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 R2 and higher order polynomials (fifth-order or above) induce overfitting problems shown by a generally insignificant coefficient on the largest order term (not shown here). In this study, we focus on analyzing the coefficient of fourth-order polynomial term, b4, which is the key factor to determine the polynomial shape of the fitted model. The resultant R2 and coefficient b4 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 R2 (~0.8) across much of the domain. It is notable that R2 is still reasonable (R2 > 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 find that the performance of b4 varies with the strength of the bimodal precipitation. In areas exhibiting MSD signals, b4 is generally negative and statistically significant (at the 95% level), whereas it tends to be insignificant or significantly positive in non–MSD characterized areas. The tendency is clearer after the climatological precipitation is spatially averaged based on the performance of b4 (Figure 13). The bimodal annual cycle of precipitation is evident in areas characterized by significantly negative b4, 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 b4 and R2 are temporally averaged (Figure 14). It is notable that, while the temporally averaged b4 generally follows the pattern shown in Figure 12, the spatial R2 drops significantly (<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 filtered during the calculation of seasonally varying climatology.
To reveal these unresolved intraseasonal variabilities, the polynomial model is modified 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 R2, b4 and regression coefficients on the MJO covariates (a1 and a2) are shown in Figure 15. Although the R2 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 b4 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 significances of the a1 and a2 coefficients 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 overfitting or overdispersion. It is notable that a1 and a2 are significantly negative in most characteristic MSD regions, while they tend to be positive or insignificant in characteristically non–MSD regions. Based on the RMM1 – RMM2 phases (phases 1 – 8), the performance of a1 and a2 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 first 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.