a. Data

As this study is carried out for the wet season, only the months from November to April will be considered in all datasets.

2) New Caledonia rainfall data

A comprehensive study of the diurnal cycle of precipitation requires the use of high-frequency rainfall data, ideally with an hourly or shorter time step. This work relies on the Météo-France hourly rain gauge data for 28 stations scattered all over the main island of New Caledonia. These stations were chosen among the available stations according to three criteria: they provided hourly rain rates, they had a sufficiently long record over the year and they were deemed reliable by the Météo-France climatological services in New Caledonia. These stations are listed in Table A1 and shown on the map in Fig. 2. We deliberately choose to focus this study on the main island owing to the smaller sizes and the very different topographic profiles of the other islands, which make them likely to exhibit a diurnal cycle that would be governed by different mechanisms. The period of available data is station-dependent and some stations present periods of missing values. To include as much data as possible, the period considered is 1 January 1991–31 December 2017 (27 years), 1991 being the year when the first hourly records started.

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Average precipitation at the 28 stations in wet season (NDJFMA). Gray lines indicate elevation levels every 200 m from 200 to 1000 m, retrieved from Shuttle Radar Topography Mission (SRTM) data.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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b. Wind regime classification

Wind regime classification aims at sorting out the regional wind maps around New Caledonia (i.e., in the selected 25°–17°S, 161°–170°E domain) into a few specific and distinct circulation patterns. For this purpose, we use the same method as Lefèvre et al. (2010), Moron et al. (2015) and Hopuare et al. (2019), which is based on a k-means clustering algorithm. Zonal and meridional components of the daily mean 10-m wind data at the 90 grid points in the domain were used for each day of the wet season. Standardized anomalies were computed at each grid point by subtracting the long-term mean and dividing by the corresponding standard deviation. Principal component analysis was performed to filter out the smallest scales of spatial variability and the first two principal components, accounting for 69% of the total variance, were retained. The 7069 days of the 39 wet seasons were partitioned in this two-dimensional space using the k-means clustering algorithm with Euclidean distance. The optimal number of clusters was chosen using a classifiability index as described by Michelangeli et al. (1995). The k-means clustering algorithm takes the user-provided k number of clusters to choose k initial centroids (the seeds) at random among the points to classify. The clusters are created by gathering each point to its closest cluster, and a new centroid is computed for each cluster. This step is repeated until the algorithm converges (i.e., no more changes in the clusters with the next iteration). The classifiability index is computed for each number of clusters k. For a given k, N different partitions are computed. The similarity between two partitions is taken as the largest of the k correlations (in the initial wind field space) between the pairs of corresponding centroids. The classifiability index is the average of the similarities in N(N − 1)/2 possible pairs of partitions. In this study, the classifiability index was calculated for a number of clusters k from 2 to 10 and N = 50. The closer the classifiability index is to 1, the less the partition depends on the random initial seeds and the more robust it is.

c. Quantifying the difference between two diurnal cycles

The first term on the right-hand side of Eq. (3) represents the contribution of the difference in daily means, and the second term is the contribution of the difference in diurnal variability.

d. Spatial classification of rain gauge stations

A classification of the 28 rain gauge stations was performed in order to distinguish several geographical zones which exhibit significantly different diurnal cycles of rainfall. Similar to any clustering problem, such a classification requires the definition of an accurate metric of the difference between the items being classified (i.e., rain gauge stations). Our main purpose in this study is to illustrate, for each geographical zone, the influence of the wind regime on the diurnal cycle. For each station, we computed the smoothed composite diurnal cycle for each wind regime by averaging hourly rainfall over the days belonging to that regime and filtering out all harmonics with periods below 8 h. Given that four wind regimes (see section 3) were finally retained, each station is characterized by 96 parameters corresponding to the 24 hourly rain rate values of its smoothed composite diurnal cycle in each of the four regimes. The metric used to quantify the difference between two stations was the square-rooted sum of the squared differences in this 96-parameter space. This metric is relevant for this case as it takes into account both the average rainfall at the station and the diurnal variation: if two stations receive similar rainfall on average, they will be close to each other but they will be even closer if, for instance, they also have similar diurnal peak. The clustering algorithm used for this classification is hierarchical clustering. At each step, the two closest clusters according to Ward’s minimum variance method were merged together. The optimal number of clusters could be determined thanks to the dendrogram to ensure that the clusters were well separated from each other.

e. Statistical testing of the influence of MJO on the frequency of wind regimes

Because they are generally assumed to follow a normal distribution with mean 0 and standard deviation 1, the Pearson’s residuals with values less than −2 or greater than +2 are considered to indicate the phases for which the deviation from the expected distribution of the wind regimes under the null hypothesis is significant. These phases are the largest contributors to the rejection of the chi-square null hypothesis. Given their regime-phase symmetry, Pearson’s residuals similarly indicate if a regime is significantly more or less frequent within a phase. The over or underrepresentation at the 95% level of a given regime within a MJO phase was also tested with bootstrapping. This method leads to conclusions that are identical to the Pearson’s residuals approach.

f. Impact of the interaction between the MJO and wind regimes on the diurnal cycle of precipitation

To understand how the interaction between the MJO and wind regimes impacts the diurnal cycle, a method is proposed based on two simple but opposite models.

This corresponds to considering that the characteristics of the regimes change between phases of the MJO, but the frequency of these regimes do not change. Equation (13) also shows that the deviations of the diurnal cycle r_iϕ can be taken from the long-term mean $\overline{\mathbf{r}}$ or from the characteristic diurnal cycle of each regime r_i.

We can expect the observed diurnal cycles to follow a pattern somewhat in between the two extreme simple models 1 and 2, and we can actually determine which model is closest to the observations.

This decomposition into 2 × N_w + 1 terms, which are scalar products of anomalous diurnal cycles against the anomalous diurnal cycle of the MJO phase, represents the contributions of all phenomena responsible for the change in the diurnal cycle within the MJO phase. The first term on the right-hand side of Eq. (16) represents the difference to the long-term mean diurnal cycle accounted for by the change in frequency of each of the N_w regimes, following Model 1. The second term on the right-hand side of Eq. (16) terms represents the difference to the long-term mean diurnal cycle accounted for by the change in the diurnal cycle of the regime within the MJO phase relative to the average diurnal cycle of the regime, according to Model 2. Here s is the second-order residual term.

a. Climatology of rainfall in New Caledonia

The average daily rainfall received in the wet season by the 28 selected rain gauge stations is represented in Fig. 2. The rainiest stations are all along the east coast and at specific locations inland that correspond to mountain peaks or passes. Stations along the west coast are comparatively drier. This east–west contrast is usually explained by two factors. First, with the presence of the central mountain range and the east-southeasterly climatological direction of the trade winds (illustrated in Fig. 1), orographic lifting on the windward side combined with foehn effect on the lee side drive a wetter climate along the east coast and a drier climate along the west coast (Météo-France 2008). Second, rainfall in New Caledonia can also be triggered by the advection of warm and moist tropical air masses by northerly and easterly winds that therefore preferentially hit the east coast (Moron et al. 2016).

The diurnal cycle of observed rainfall is represented in Fig. 3 for both the warm, wet (November–April) and the cool, dry (May–October) seasons, averaged over all stations shown in Fig. 2. While there is a strong diurnal cycle in the warm season, with a marked afternoon peak at 1600 local time and a secondary peak at night, rainfall in the dry season shows very little diurnal variation. As detailed in section 1, sea breeze and orographic effects are likely to explain the afternoon maximum in warm convection, and therefore in precipitation, over land (Cronin et al. 2015). Nighttime convection over the open ocean and advection of precipitating clouds by large-scale winds can presumably account for the secondary, nocturnal maximum. During the dry season, the sea surface temperature is lower and the troposphere is much drier than in the warm season: these inhibit deep convection, resulting in lower precipitation rates. The diurnal solar forcing is also smaller in that season, so it creates weaker land/sea surface temperature gradient and sea breeze, which is rarely strong enough to break through the convective inhibition. The diurnal cycle is therefore considered to be one major player to explain differences in rainfall rates between wet and dry season.

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Mean diurnal cycle of rainfall (mm h⁻¹) averaged over the 28 stations in the wet season (blue) and the dry season (orange).

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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b. Impact of the MJO on the diurnal cycle of rainfall in New Caledonia

The influence of the MJO on the mean precipitation in New Caledonia (averaged over the 28 stations) is displayed in Fig. 4a, along with the 95% confidence interval determined from a bootstrap procedure (for each phase, 10 000 draws of the days in the phase are performed with replacement). Daily mean rainfall variation oscillates with the MJO, following the propagation of the MJO convective envelope. Phases 4, 5, and 6 are the rainiest phases, and in particular, they are significantly rainier at the 95% confidence level than phases 1 and 2 which are the driest phases. This is in agreement with the MJO-induced OLR anomalies over New Caledonia as shown in Fig. 5: the largest negative OLR anomalies over New Caledonia, associated with intensified convection, are found in phases 4, 5, and 6, while the largest positive OLR anomalies, associated with suppressed convection, correspond to phases 1 and 2. Figure 5 also shows that New Caledonia is located at the southern edge of the strong, equatorial MJO signal and it experiences convection anomalies in advance compared to the equatorial band. Positive or negative MJO-induced convection anomalies extend southeastward from the heart of the equatorial convective patch. For instance, New Caledonia experiences intensified convection when the equatorial convective envelope is located over the Maritime Continent (phase 5), while it experiences reduced convection when the equatorial convective envelope is roughly north of New Caledonia (phase 7).

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(a) Daily mean rainfall (mm day⁻¹) averaged on the 28 stations for each MJO phase. (b) Amplitude (mm h⁻¹) of the spatially averaged composite diurnal cycle for each MJO phase. Error bars indicate the 95% confidence interval determined from a bootstrap procedure.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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NOAA OLR anomalies [OLRa as defined in Wheeler and Hendon (2004)] (shadings, in W m⁻²) and 10-m wind anomalies (vectors, m s⁻¹) in ERA-Interim for each MJO phase. The black rectangle indicates New Caledonia’s region shown in Fig. 1.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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The influence of the MJO on the diurnal cycle is summarized in Fig. 4b which shows the evolution of the diurnal amplitude with the MJO phase, along with its 95% bootstrap confidence interval. The diurnal amplitude is defined as the difference between the maximum and the minimum of the composite diurnal cycle of each MJO phase. The impact of the MJO on the diurnal amplitude is less clear than that on average precipitation considering the error bars are larger, but it also exhibits noteworthy features. The diurnal amplitude is largest for phase 4–6, which means that the diurnal cycle tends to peak approximately one phase in advance compared to the mean rainfall (phase 4 versus phase 5). This is reminiscent of Peatman et al. (2014)’s results, which documented a peak in diurnal amplitude with a one-phase lead before the arrival of the MJO envelope over the Maritime Continent. As for the time of the daily rainfall maximum, no significant modulation by the phase of the MJO has been observed (not shown). Therefore, the change in the timing of the afternoon peak in relation with the MJO will not be further investigated in this study.

The squared distance between the long-term mean diurnal cycle $\overline{\mathbf{r}}$ (as represented in Fig. 3) and the composite diurnal cycle r_ϕ for a given MJO phase ϕ is defined in section 2c. Figure 6 shows these squared distances for each MJO phase as a fraction of the squared norm ${\Vert \overline{\mathbf{r}}\Vert }^2$ of the long-term mean diurnal cycle. The distances that are significant at the 95% confidence level (see section 2c) are indicated with asterisks above. The MJO phases for which the average diurnal cycle over all stations in New Caledonia is the most modified are phases 1, 2, 5, 6, and, to a lesser extent, 4. This is consistent with the results on Fig. 4: phases 1 and 2 are the driest phases with little diurnal variability, while phases 4, 5, and 6 are the wettest phases with an enhanced diurnal peak. The same analysis for separate geographical zones (not shown) highlights similar impacts with only minor changes.

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Squared distance between the composite diurnal cycle for each MJO phase r_ϕ (weak MJO days not included) and the mean diurnal cycle $\overline{\mathbf{r}}$ expressed as a percentage of ${\Vert \overline{\mathbf{r}}\Vert }^2$ [$100\times \left({\Vert \overline{{\mathbf{r}}_{\varphi }}-\overline{\mathbf{r}}\Vert }^2/{\Vert \overline{\mathbf{r}}\Vert }^2\right)$]. The asterisks indicate distances that are significant at the 95% confidence level (see section 2c). Dark shadings: contribution from the change in daily mean. Light shadings: contribution from the change in the hourly anomalies relative to the daily mean.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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Following Eq. (3), the modifications of the diurnal cycle in Fig. 6 are also split into a contribution from the change in daily mean (in dark gray) and a contribution from the change in the hourly anomalies relative to the daily mean (in light gray). The modification of the diurnal cycle by the MJO appears to be primarily driven by the modification of the daily mean, while the modification of the diurnal variability only plays a secondary role. This is consistent with the results in Fig. 4 in which the impact of the MJO is clearer on the daily mean than on the diurnal amplitude. However, this decomposition neglects the influence of the diurnal cycle on the mean and the contribution from the diurnal anomalies should be considered a lower bound of the contribution from the diurnal cycle. The contribution of the diurnal variability is noteworthy for the five MJO phases when the deviation from the long-term mean diurnal cycle is particularly significant (e.g., in phase 4).

c. Identification of wind regimes

The surface wind anomalies associated with the MJO propagation (Fig. 5) suggest an influence of the MJO on the circulation around New Caledonia. This is an incentive to investigate how the effect of the MJO on the diurnal cycle of rainfall over New Caledonia is mediated through the synoptic wind regimes, as in Leroy (2006), Lefèvre et al. (2010) and Moron et al. (2015). The wind regimes were determined using ERA-Interim 10-m winds as explained in section 2b. The computation of the classifiability index for 2 to 10 clusters is illustrated in Fig. 7. Given the excellent classifiability for four clusters which is also a reasonable number of wind regimes, four wind regimes were retained. This number is consistent with the previous findings of Leroy (2006) and Lefèvre et al. (2010), although the classifications were carried out on different datasets.

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Classifiability index for each number of clusters, determined from the two first PCs of ERA-Interim 10-m winds in the New Caledonia domain (25°–17°S, 161°–170°E).

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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The composite wind maps for each regime are represented in Fig. 8. These regimes can be described as follows, in order of increasing average wind speed:

• Northerly regime: the flow crossing the island is slowed down on the windward side, while the wind flowing to the west remains slightly stronger. It is the least frequent regime (14.3% of wet-season days) and has the weakest wind speed.

• Southerly regime: the flow comes south-southeasterly and is stronger south of the island than north of it. It has a frequency of 19.3% of wet-season days.

• Easterly regime: the flow is straight from the east and slows down slightly in the island’s wake. It is one of the two most common regime, with a frequency of 33.2%.

• Trade wind regime: the flow is very regular, almost along the main axis of the island. This flow is very similar to, although faster than, the seasonal mean. It is the other most common regime (33.2% of wet-season days) and it has the strongest wind speed.

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Composite maps of ERA-Interim 10-m winds (arrows) and wind speed (shadings) for the four wet season regimes.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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Since wind regimes are supposed to represent recurrent patterns that may last for a few days, the probabilities of transition between regimes are also important additional information about their behavior. Table 1 displays these probabilities. The only transition that is significantly more probable than a random draw at the 95% confidence level is the transition from the northerly to the southerly regime. This corresponds to the eastward propagation of a cyclonic perturbation over the island. All other probabilities that are significantly more probable than a random draw are the probabilities of persistence of each regime. All other transitions are less likely than a random draw.

Table 1.

(top) Probabilities of transition between wind regimes. Row: regime in day d. Column: regime in day d + 1. The probabilities are expressed relative to the regime in day d (rows add up to 1). Bold: transition more probable at the 95% level than in 10 000 random sequences. Italics: transition less probable at the 95% level than in 10 000 random sequences. (bottom) Number and average duration for each regime spell. All statistics are computed for the 1979–2017 NDJFMA period.

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d. Influence of the wind regimes on rainfall and its diurnal cycle

1) Spatially averaged influence

Figure 9a displays the diurnal cycle for each regime, averaged over all 28 stations. In terms of average rainfall, the northerly regime is by far the wettest, the easterly and southerly regimes exhibit a similar, intermediate behavior, and the trade wind regime is the driest. The northerly regime can be interpreted as a southward shift of the SPCZ identified in previous studies (Lefort 2005; Leroy 2006). It corresponds to the arrival of warm, moist air from the equatorial band resulting in precipitation over the island. The difference in rainfall averages between wind regimes generally coincides with a difference in amplitude of the diurnal cycle. The afternoon peak in the northerly regime is larger in amplitude than that of the easterly and southerly regime, while the trade wind regime exhibits an even flatter cycle. Another interesting feature for the northerly regime is the secondary maximum during the night. This secondary peak is presumably due to the advection of precipitating cloud from the equatorial oceanic regions. Similar to the MJO phases (Fig. 6), the distance between the average diurnal cycle for each regime and the long-term mean diurnal cycle is illustrated in Fig. 9b. The two regimes for which there is a significant difference are the northerly and the trade regimes, that is to say the more extreme (wettest and driest) ones, in agreement with Fig. 9a.

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(a) Spatially averaged diurnal cycle of rainfall for each wind regime (mm h⁻¹). (b) Squared distance between the composite diurnal cycle for each wind regime r_i and the mean diurnal cycle $\overline{\mathbf{r}}$ expressed as a percentage of ${\Vert \overline{\mathbf{r}}\Vert }^2$ [$100\times \left({\Vert \overline{{\mathbf{r}}_{\mathbf{i}}}-\overline{\mathbf{r}}\Vert }^2/{\Vert \overline{\mathbf{r}}\Vert }^2\right)$]. The asterisks indicate distances that are significant at the 95% confidence level (see section 2c).

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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2) Spatial classification of rain gauge stations

The presence of a mountain range and the asymmetry in the island’s mean rainfall pattern (see Fig. 2) suggests that the influence of the wind regimes on the diurnal cycle might not be the same for all stations. This matter is investigated by dividing the island into distinct geographical zones following the procedure of spatial clustering detailed in section 2d. The resulting dendrogram is represented in Fig. 10a. It shows that a classification into 3 geographical clusters is relevant in order to obtain distinct, well-separated clusters. The location of the stations in the 3 clusters is represented in Fig. 10b. The clustering algorithm separates the stations into geographically consistent zones: the mountain range (“Range”), the east coast (“East”) and the west coast (“West”). The mountain stations of the Range can be identified by their altitude since they are higher than any other station in East or West. The smoothed, average diurnal cycles for each cluster are represented in Fig. 11. The mountain range and the east coast are both wetter than the west coast, as could be expected from Fig. 1. In terms of diurnal variability, the west coast and the mountain range exhibit a similar behavior with an afternoon peak as in the all-station average diurnal cycle (Fig. 3). On the other hand, the east coast features a flatter diurnal cycle with a minimum in the morning around 1000–1100 and slightly more rain from the midafternoon until the end of the night.

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(a) Dendrogram of the hierarchical clustering of the 28 rain gauge stations. (b) Location of the 3 clusters retained with elevation levels indicated by gray lines.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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Diurnal cycles of rainfall (mm h⁻¹) for each geographical zone.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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Two hypotheses can be put forward to explain the flatter diurnal cycle in the East. First, the east coast is on the windward side most of the time so it presumably undergoes precipitation that is mostly related to the large-scale wind dynamics (cloud formation due to orographic lifting, cloud advection from the open sea). This kind of precipitation is therefore independent from the local diurnal variability. Second, the local diurnal variability of winds and solar radiation is itself very weak on the east coast. This aspect has already been thoroughly investigated with numerical modeling by Lefèvre et al. (2010). Because of the higher mean cloud cover on the east coast, less solar radiation reaches the surface. The sea breeze then tends to be far weaker than that on the west coast due to this difference in insolation, but also to a difference in sea surface temperatures. Indeed, the sea surface temperature is also warmer off the east coast than off the west coast because New Caledonia is located at the edge of the western Pacific warm pool. This creates a smaller land/sea surface temperature contrast and a weaker sea breeze on the east coast. As a result, rainfall on the east coast shows less diurnal variations, while the west coast experiences a pronounced diurnal cycle of rainfall owing to its strong sea breeze, even if its average precipitation is lower than in the other two parts of the island. As for the mountain range, the diurnal cycle of thermal convection and the interaction with the sea breeze are likely to explain most of its strong afternoon peak.

3) Geographical influence of the wind regimes on the diurnal cycle

Figure 12 shows the influence of the wind regimes for each geographical cluster of stations. The influence on rainfall in clusters Range and West (Figs. 12a,c) is very similar to the influence that is observed in Fig. 9 for the diurnal cycle averaged over all 28 stations. In other words, the rainiest regime is the northerly regime, followed by the southerly and easterly regimes, and finally by the driest trade-wind regime. The diurnal amplitude is also similarly related to the average rainfall: the rainier the regime, the larger the diurnal amplitude. However, the influence of the wind regimes on the east coast (Fig. 12b) shows an altogether different behavior. While the easterly and trade wind regimes are associated with a relatively flat diurnal cycle with a minimum in late morning, the northerly and southerly regimes differ significantly from the average east coast diurnal cycle (Fig. 11). The southerly regime, that is quite dry on the east coast, exhibits a diurnal variability with a marked afternoon peak. The northerly regime is also characterized by a similar afternoon peak and by another secondary peak at the end of the night that has already been identified in Fig. 9.

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Spatially averaged diurnal cycle of rainfall for each wind regime (mm h⁻¹): (a) mountain range, (b) east coast, and (c) west coast.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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We can propose a few tentative explanations for the specific behavior of the diurnal cycle on the east coast in the southerly and northerly regimes, although the mechanisms that explain this sensitivity would deserve a thorough investigation that is beyond the scope of this article. In section 3d(2), two hypotheses have been put forward to explain the flatter average diurnal cycle on the east coast: the continuous rainfall due to large-scale dynamics, and the weaker insolation and sea-breeze diurnal variability. These hypotheses are strongly linked to the fact the east coast is the average windward coast. In the southerly regime, however, the east coast becomes the leeward coast. Sheltered by the mountain range, a sea-breeze circulation can develop and the absence of clouds favors a diurnal cycle of surface heating and afternoon convection. As a result, the diurnal cycle of rainfall on the east coast in the southerly regime exhibits an afternoon peak similar to the diurnal cycle on the west coast in the easterly regime. During the northerly regime, very weak winds and high humidity generally enhance the diurnal cycle of convection all over the island and the east coast is also affected, hence the afternoon peak it also exhibits in this case. The secondary nocturnal peak, on the other hand, can be attributed to the advection of precipitating clouds from oceanic regions further north.

a. Frequency variability of wind regimes with the MJO

We first investigate whether the MJO influences the frequency of occurrence of the wind regimes, in line with Model 1 introduced in section 2f. Following the methodology described in section 2e, we perform a statistical analysis of these frequencies of occurrence in the eight MJO phases. Table 2 shows the p values of the chi-square test applied separately for each regime. The p value is always less than 5%, which enables to reject the null hypothesis that the regime frequencies do not depend on the MJO phase. Table 3 indicates the percentage of the regimes per MJO phase. Percentages corresponding to a significantly more frequent regime within the MJO phase (according to the values of Pearson’s residuals) are in bold, those corresponding to a significantly less frequent regime are in italics.

Table 2.

The p value of the χ² test assessing the distribution of each wind regime among the MJO phases (weak MJO included).

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Table 3.

Percentage of wind regimes by MJO phase. Bold: the regime is significantly more frequent in the phase (Pearson’s residual greater than +2). Italics: the regime is significantly less frequent in the MJO phase (Pearson’s residual less than −2).

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A striking fact from Table 3 is that the easterly, northerly and southerly regimes seem to succeed each other in the MJO cycle in terms of overrepresentation. Indeed, the easterly regime occur significantly more frequently in phases 2, 3, and 4, when the MJO convective envelope is still in the Indian Ocean or over the Maritime Continent. On the contrary, it is significantly less frequent in phases 6, 7, and 8 when the convective envelope is over the Central Pacific or weak and further east. The northerly regime occurs significantly less frequently in the phases 1, 2, and 3 when convection is suppressed over New Caledonia, and it occurs significantly more frequently in the wettest phases 5 and 6. As for the southerly regime, it is also significantly less frequent in the dry phases 2 and 3 and significantly more frequent in phase 6. Trade winds are frequent in all phases, except in the phases 5 and 6 of intensified convection over New Caledonia, when they are significantly less frequent. These findings are in agreement with the wind anomalies associated to the MJO phases as represented in Fig. 5. In phases 2 and 3, New Caledonia experiences easterly MJO low-level wind anomalies. These MJO anomalies rotate counterclockwise around New Caledonia with the succession of phases: they have a northeasterly orientation in phase 4, a northerly orientation in phase 5, a westerly orientation in phase 6 and a southerly orientation in phase 7. In phases 8 and 1, which are phases for which the MJO is less active over New Caledonia, the anomalies are southeasterly, with the same orientation as the climatological trade winds. Considering these observations and the transition probabilities in Table 1, it can be deduced that there is a sequence of wind regimes (easterly → northerly → southerly) that is due to the propagation of the MJO wind anomalies. This sequence will not necessarily be observed exactly for every MJO event, because fast intraseasonal and synoptic variability allow all regimes to occur in all phases, but it corresponds to a canonical evolution that the atmosphere tends to follow during such events. It is typical of the MJO dynamical signature (Rui and Wang 1990; Zhang 2005), with easterly winds east of the convective signal and two off-equatorial cyclonic gyres propagating along with the equatorial convective center. The southern gyre is responsible for the wind anomalies around New Caledonia, with a northerly component when New Caledonia is in the poleward branch of the gyre and a southerly component when it is in the equatorward branch.

b. How does the interaction between MJO and wind regimes impact the diurnal cycle?

As seen in Figs. 4 and 6, the MJO modifies the diurnal cycle of precipitation over New Caledonia during its most active and suppressed phases. As for wind regimes, Figs. 8 and 11 also demonstrate their impact on the diurnal cycle. How do these two large-scale influences interact? And how does this interaction help understand the impact of the MJO on the diurnal cycle? The decomposition of the anomalous diurnal cycles proposed in section 2f with two simple models, for the particular case where the number of wind regimes is N_w = 4, is used to answer these questions.

The contributions of the 9 terms in the squared distance to the long-term mean diurnal cycle, detailed in Eq. (16), are represented in Fig. 13. According to Fig. 6, the deviations from the long-term mean diurnal cycle are weak for phases 3, 7, and 8. Consequently, Fig. 13 only represents the decomposition for the five other MJO phases (1, 2, 4, 5, and 6). The contributions are shown as fractions of ${\Vert \overline{\mathbf{r}}\Vert }^2$ in the same way as in Fig. 6. The first four bars correspond to the $f_{i\varphi }\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\mathbf{i}}^{\prime }\rangle$ terms for each regime, associated with Model 1 and which we will call frequency change terms, and their sum is indicated by the first background gray bar. The next four bars correspond to the $f_i\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\mathbf{i}\varphi }-{\mathbf{r}}_{\mathbf{i}}\rangle$ terms associated with Model 2 and which we will call regime change terms, and their sum is also represented in the background. The gray bar on the right indicates the value of the residual term s. Note that all these terms correspond to the decomposition of the overall distances represented in Fig. 6, without separating between the daily mean and the diurnal anomalies relative to the daily mean. The same decomposition has been carried out for these two components separately (not shown). According to Fig. 6, the change in daily mean accounts for most of the changes in the diurnal cycle. As a result, when the decomposition in Eq. (16) is carried out on the daily mean only, the results are similar as those in Fig. 13, while the contributions related to the diurnal anomalies are less prominent. The results in Fig. 13 are therefore mostly interpreted in terms of modification of the daily mean.

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Decomposition of the squared distances between the MJO composite cycles r_ϕ and the long-term mean diurnal cycle $\overline{\mathbf{r}}$ as a percentage of ${\Vert \overline{\mathbf{r}}\Vert }^2$, according to Eq. (16). The first four terms represent the contribution of regime frequency changes, the next four terms the contribution of regime change at constant frequency. N: northerly regime. S: southerly regime. E: easterly regime. T: trade winds regime.

Citation: Monthly Weather Review 148, 1; 10.1175/MWR-D-19-0177.1

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The contributions of frequency changes $f_{i\varphi }\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\mathbf{i}}^{\prime }\rangle$, associated with Model 1, need to be considered with caution. They tend to attribute prominent contributions to the northerly and trade wind regimes because the average diurnal cycles of these regimes are the most different to the long-term mean diurnal cycle, as shown in Fig. 9b. When one of these two regimes is less represented than usual, its contribution $f_{i\varphi }\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\mathbf{i}}^{\prime }\rangle$ will be negative: the decrease in frequency contributes to decreasing the deviation ${\Vert {\mathbf{r}}_{\varphi }^{\prime 2}\Vert }^2$ from the long-term mean diurnal cycle in phase ϕ. On the contrary, when one of these two regimes is more frequent than usual, the same contribution will be positive and increase the deviation to the long-term mean diurnal cycle. Moreover, owing to the propagation of the MJO, the frequency of these two regimes tend to vary in opposite ways. For instance, in phases 1 and 2, the northerly regime is less frequent and the trade wind regime is more frequent, while the contrary can be observed in phases 4, 5, and 6. As a result, the contributions of the frequencies of the trade and northerly regimes tend to compensate each other partially (phases 1 and 2) or completely (phase 4 and phases 3, 7, and 8 not shown). In the case of a partial compensation, an additional compensation by the residual term can also be noted. Therefore, except for phases 5 and 6, during which the change in frequency of the northerly regime appears to play an important role due its significant overrepresentation (see Table 3), the frequency change terms include systematic strong compensating effects and are not as physically meaningful as the regime change terms.

Phases 1 and 2 (Fig. 13, first and second panels) exhibit a similar behavior: the dominant term in the modification of the diurnal cycle is the change in diurnal cycle for the northerly regime $f_{\mathrm{north}}\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\text{north},\varphi }-{\mathbf{r}}_{\text{north}}\rangle$, associated with Model 2. According to Fig. 5, these phases correspond to large-scale conditions that are not favorable for convection. Then, the northerly regime, which is supposed to be the wettest regime cannot be as wet as usual, hence the influence of the modification of its diurnal cycle in the overall changes. This contribution is positive: the change in the diurnal cycle of the northerly regime increases the difference between the diurnal cycles of phases 1 and 2 and the long-term mean diurnal cycle. Similar contributions can be observed, to a lesser extent, for the southerly and easterly regimes. Therefore, the diurnal cycle modification for MJO phases 1 and 2 is mostly a matter of unfavorable large-scale conditions for convection that impact almost all regimes but have the most important effect on the regime with the strongest diurnal cycle. MJO phase 4 (Fig. 13, third panel) is also characterized by a positive contribution from the change in the northerly regime diurnal cycle associated with Model 2. However, unlike MJO phases 1 and 2, in MJO phase 4 convection intensifies over New Caledonia and as a result the diurnal cycle in the northerly regime is enhanced. A secondary contribution from the diurnal cycle of the trade-wind regime $f_{\mathrm{trades}}\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\text{trades},\varphi }-{\mathbf{r}}_{\text{trades}}\rangle$ is also significant, while the effects of the easterly and southerly regimes compensate. The diurnal cycle is enhanced in the northerly regime in MJO phase 4 compared to the all-phase northerly regime composite, and this can be explained by three factors: the favorable large-scale conditions for convection mentioned above, the moister air that is brought by the northerly regime, but also the weaker wind speed in this regime. Indeed, results from previous work tend to demonstrate that all other conditions being identical, the diurnal cycle will be stronger when low-level wind is weak (Wang and Sobel 2017). Finally, phases 5 and 6, as mentioned previously, are dominated by a significant effect of the change in the northerly regime frequency $f_{\mathrm{north},\varphi }\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\text{north}}^{\prime }\rangle$ that is not entirely compensated by the change in the trade regime frequency or by the residual term. This is in agreement with the findings by Moron et al. (2016, Fig. 12), for which the wettest rainfall regime, associated with a southwestward shifted SPCZ and prevalent northerly winds, also has its frequency strongly modulated by subseasonal variability. Here, the increase in northerly regime frequency in phases 5 and 6 can be held partially responsible for the intensification of the diurnal cycle, along with changes in the diurnal cycle for the easterly regime $f_{\mathrm{east}}\langle {\mathbf{r}}_{\varphi }^{\prime }|{\mathbf{r}}_{\text{east},\varphi }-{\mathbf{r}}_{\text{east}}\rangle$. The easterly regime exhibits an enhanced diurnal cycle in phases 5 and 6 owing to its orientation that is shifted northeasterly, its weaker speed and, again, the favorable large-scale conditions for convection. These different interactions between the MJO and the wind regimes have been considered for the diurnal cycle averaged on all stations. Qualitatively similar results can be found separately for the three geographical groups of stations (Range, East, and West) identified in section 3d (not shown).