DIs are most commonly identified during the winter season in each hemisphere, with fewer identified during the other seasons (Raveh-Rubin 2017), so the procedures described above have been applied to the ERA-Interim data for NH DJF and SH JJA. Table 1 shows the total number of fronts and DIs that are identified over the whole period for the whole of the NH during DJF, and the whole of the SH during JJA separately, as well as the percentage of the different types of fronts matched with DIs, and the percentage of DIs matched with the different types of fronts. It is worth noting that the number of “all fronts” is not the sum of the different types of fronts, since at each time point, many fronts will be split into their central and trailing front parts. In total, 62% of winter DIs in the NH and 65% of winter DIs in the SH are matched with fronts, with the highest proportion of these being trailing fronts (33% in the NH and 31% in the SH) and isolated fronts (31% in the NH and 35% in the SH). In the NH 9% of all cold fronts are matched with DIs, with 11% in the SH. This is much higher for trailing fronts at 20% and 19% in the NH and SH respectively.
Table 1 Total number of fronts and DIs over the whole of the NH for DJF and the whole of the SH for JJA In the following sections, maps of the matching frequency and the proportion of the total will show the global distribution of the co-occurrence of cold fronts and DIs.
Global distribution of matched cold fronts and DIs
A high proportion of DIs match with cold fronts, so here we start by examining the geographical distribution of DI objects (Fig. 4), and how it is modified in the cases of matching with various front types (Fig. 5). The maximum frequency of occurrence of DI objects occurs over the North Pacific storm track of up to 20%, with other lesser maxima over the North Atlantic storm track (around 10%) and over the west coast of the USA. In the SH the highest frequency of DI object occurrence lies in a band between 20° and \(40^{\circ }\hbox {S}\), with the highest values to the west of the continents of around 11%. The patterns of DI frequency look very similar to the counts of DI trajectories 24 to 48 h after descent begins (shown in Figures 3 and 4 in Raveh-Rubin 2017). This is consistent with the requirement that the DI trajectory must be below 700 hPa (and therefore must have already descended quite far) to be part of a DI object in the present study. In the present study, the occurrence frequencies are slightly higher than those in Raveh-Rubin (2017). This stems from the process employed to generate two-dimensional DI objects, which takes into account DIs at multiple relative times from the start of descent, as long as they lie below the 700-hPa height. In Raveh-Rubin (2017), the frequency of occurrence statistics consider only single relative time steps, resulting in lower trajectory counts.
Since the three front types occur in rather distinct geographical regions, the DIs that match with each type of front are also preferentially located in different regions (Fig. 5). DIs matching with trailing fronts are located equatorward of the main storm tracks, but covering an area extending beyond the highest trailing front frequencies (compare Fig. 5a with 3a). A strong east–west dipole emerges in the main ocean basins in both hemispheres. While over 70% of DIs occurring in the central and western ocean basins match with trailing fronts, less than 30% do so in the eastern parts. A mutually exclusive pattern exists for DIs matching with isolated fronts, such that a low proportion of matching exists in the western ocean basins, and a high proportion in the east (Fig. 5c). An exception to this pattern is the area of increased DI frequencies west of the Andes, which do not match with any type of front. Matching of DIs with central fronts occurs in localized coastal regions (Fig. 5b), which indeed sums up to the lowest matching proportion of the front types (Table 1).
We consider now the proportion of each of the front types that are matched to DIs (Fig. 6). Figure 6a indicates that the highest proportion of matching for all cold fronts occurs south of the major NH storm track regions (over the North Atlantic and North Pacific Oceans), and in a latitude band between \(20^{\circ }\) and \(40^{\circ }\hbox {S}\), with maxima in the eastern ocean basins. In the NH the maximum reaches around 60% of cold fronts matching with DIs in the North Pacific region. This is consistent with the highest frequency of DIs occurring in this region (Fig. 4). Overall the highest proportion of matching for all fronts corresponds closely to the pattern of DI object frequency, suggesting that the matching of fronts is limited by the DI occurrence (see also Table 1).
Very high proportions of trailing fronts are matched with DIs (Fig. 6b) in both the NH and SH with maxima above 75%. The highest proportions occur at lower latitudes than for all fronts. In the NH there is also a distinctive southwest to northeast tilt to the pattern in both the NH storm track regions. These features indicate that many cyclones propagating along the major storm track axes that have trailing cold fronts will be associated with a DI. This is also consistent with DIs being potentially important for the equatorward propagation and reach of these trailing fronts. In the SH, the highest proportions of trailing fronts that match with DIs are seen in the Indian Ocean sector, north of \(20^{\circ }\hbox {S}\), to the west of South America, and to the west of South Africa. Interestingly, trailing front frequencies are lowest in the eastern ocean basins in the SH, but when they do occur there, it is often in association with a DI (Figs. 2b, 3a, 6b). Yet, isolated fronts are a more common type of front in the eastern ocean basins, thus making up the largest proportion there (Fig. 5c).
The pattern for the proportion of central fronts matched to DIs (Fig. 6c) indicates a lower overall matching proportion. Although the frequency of central fronts in the SH regions where DIs occur during JJA is very low (Fig. 2) and the proportion of DIs matched with central fronts is low, up to 35% of central fronts are matched with DIs in the SH where the central front frequency is above 2%.
The isolated fronts matched with DIs (Fig. 6d) follow a similar pattern to that of all fronts with maxima across the regions of highest DI frequency. Despite due to the low frequency of occurrence of DIs at low latitudes, there are low proportions of isolated fronts matched with DIs at these low latitudes (Fig. 6d). Maxima occur off the west coast of South America and South Africa, over the north Pacific ocean (between 20° and 40°N), and over the Indian Ocean. Supplementary Figure S4 shows that the frequency of isolated fronts is quite sensitive to the minimum length requirement of 5 grid boxes. However, the frequency of isolated fronts matching with DIs is not. The proportion of trailing and isolated fronts associated with DIs is slightly lower when the minimum length criterion is not applied (Supplementary figure S8), but is insensitive to the search radius parameter used in the front identification.
Statistical distributions of front intensities
In order to determine the importance of the link between cold fronts and DIs on the characteristics of fronts, we have determined the statistics of the strength of matched and non-matched fronts (defined as the gradient of \(\theta _{w}\) across the front). The strength is known at each point along a front, and for each front object the maximum strength within the object is used to determine the strength of that front. For all the following statistics, only fronts that have their maximum strength between 0° and \(60^{\circ }\hbox {N}\) and between 0° and \(60^{\circ }\hbox {S}\) are considered. This excludes the many fronts that are found around the Antarctic coast, which are associated with the strong temperature gradients at the edge of the continent, and have rather different environments. We have tested the sensitivity to choosing the average strength over the front instead of the maximum strength, and find the conclusions unchanged.
Table 2 shows the average maximum front strength for the different types of fronts in the NH and Table 3 the SH. Considering all fronts together (before the fronts are separated into central, trailing, and isolated fronts), matched fronts tend to be 26% stronger in the NH and 23% stronger in the SH than non-matched fronts. All types of fronts are stronger in the NH than in the SH, consistent with Naud et al. (2015). Matched central fronts are the strongest types of fronts in both hemispheres, which could be expected due to their location closest to the strong baroclinic zone indicated by the maxima in cyclone frequency (Fig. 2). Matched central fronts are 22% stronger in the NH and 11% stronger in the SH compared to non-matched central fronts, but the matching of this type occurs most rarely (Table 1). The matching of trailing fronts with DIs gives a smaller difference, with matched trailing fronts 13% stronger in the NH and 17% stronger in the SH on average, however, trailing fronts match most commonly with DIs, out of all front types. Finally, isolated fronts in the NH are 16% stronger when matched with DIs, and 19% stronger in the SH.
Table 2 Front strength (gradient of 850-hPa wet bulb potential temperature across the front) for matched and non-matched fronts for NH DJF Table 3 Front strength (gradient of 850-hPa wet bulb potential temperature across the front) for matched and non-matched fronts for SH JJA We have already shown above that the different front types occur at different latitudes, and that the maximum frequency of matching with DIs is not necessarily at the same latitude as the maximum front frequency. In addition, previous work has shown that front strength varies with latitude (Catto et al. 2014). In order to investigate whether the statistics indicated above are due to differences in the characteristics of the matched and non-matched fronts, or simply an artefact of the latitude at which matching occurs, Fig. 7 shows the two-dimensional density function of front strength with latitude, plotted using a kernel density function with the bins detailed in the figure caption.
For all front types and in both hemispheres, the maximum front strength for both matched and non-matched fronts increases with latitude (Fig. 7, consistent with Catto et al. (2014)). The fronts tend to be stronger in the NH than the SH, consistent with the findings of Naud et al. (2015). Another feature that is common to the different front types in the NH is the maximum density in non-matched fronts at around \(5^{\circ }\hbox {N}\). Inspection of the maps of cyclone frequency suggest this is associated with the fronts identified near the coast of West Africa. DI trajectories do not tend to reach this latitude by 48 h from descent (Raveh-Rubin 2017) so none of these fronts appears to be matched with DIs.
Matched trailing fronts in the NH (red contours in Fig. 7a) are most common between 20° and \(40^{\circ }\hbox {N}\), and at those latitudes the distribution of front strength lies shifted to stronger fronts compared to the non-matched fronts. The same is true in the SH (Fig. 7d), with the front strengths stronger at all latitudes for the matched fronts compared to the non-matched fronts. Central fronts (Fig. 7b, e) show similar characteristics to trailing fronts. In the NH there is a peak in density for the matched central front strength at \(40^{\circ }\hbox {N}\) with strength of greater than \(2\,K/100\) km. There is also a high density in the matched central fronts around \(30^{\circ }\hbox {S}\) with strength of \(2\,K/100\) km. Isolated fronts (Fig. 7c, f) tend to occur at lower latitudes, with the matched cases peaking around \(30^{\circ }\hbox {N}\) and S. Again, in both hemispheres the matched fronts have higher peak front strengths at all latitudes.
The rest of the front characteristics will be considered for only the trailing and isolated fronts since these appear to be quite different, and occupying different regions of the globe.
Statistical distributions of front size
On visual inspection of case studies of matching and non-matching fronts, a feature that seems to differ is the length (or area) of the fronts with or without matched DIs. This has also been investigated statistically with the mean front area of the expanded front object shown in Table 4, and the two-dimensional histograms of front area against latitude shown in Figs. 8a, d (trailing fronts) and 9a, d (isolated fronts). For both hemispheres and for both trailing and isolated fronts, there is a clear large mean positive difference in front area when associated with DIs, in some cases more than double for matched fronts compared to non-matched fronts (Table 4). For trailing fronts the highest density for matched fronts occurs around \(2\times 10^{6}\,\hbox {km}^2\) at \(40^{\circ }\hbox {N}\) and at \(40^{\circ }\hbox {S}\) and \(25^{\circ }\hbox {S}\). For the isolated fronts matched with DIs the peak density is at much smaller front areas (close to \(0.5\times 10^{6}\,\hbox {km}^2\)) at \(30^{\circ }\hbox {N}\) and S, but there is a much broader spread of front areas for the matched fronts, going up to \(4\times 10^{6}\,\hbox {km}^2\).
Table 4 Properties of matched and non-matched fronts for NH (0–\(60^{\circ }\hbox {N}\)) DJF and SH (0–\(60^{\circ }\hbox {S}\)) JJA for trailing fronts and isolated fronts with matched DIs and without matched DIs
Statistical distributions of frontal precipitation
Clearly at all latitudes there is an increase in front strength when fronts are matched with DIs (Sect. 3.2). In previous work extreme precipitation events were found to be associated with fronts that are up to 30% stronger than for less extreme precipitation events (Catto and Pfahl 2013). The influence of DIs on front strength may, therefore, also contribute to increasing the precipitation associated with the fronts. We have calculated the average precipitation within the front object area referred to above. This area (using the expanded front objects) is comparable to the search area used to define frontal precipitation in Catto et al. (2012); Catto and Pfahl (2013). Table 4 shows the mean precipitation and mean convective precipitation associated with matched and non-matched trailing and isolated fronts. In the NH during DJF, where the largest influence of the matching of DIs can be seen, the mean precipitation associated with trailing fronts matched with DIs is 1.5 times that without a DI (1.47 mm/6 h and 0.96 mm/6 h respectively), and the convective precipitation is 1.4 times as large (0.56 and 0.40 mm/6 h). This decreases slightly the proportion of total precipitation that comes from convection in the case of matched trailing fronts in the NH from 42% to 38% (since the total precipitation is greater). When considering the average proportion of convective precipitation in latitude bands of \(10^{\circ }\), Fig. 10a reveals that the proportion of convective precipitation is greater for non-matched trailing fronts in most latitude bands. Figure 8b, c, e, f shows the two dimensional histograms of total precipitation and convective precipitation for trailing fronts. In the NH the larger total precipitation associated with matched fronts can be clearly seen, with peaks in the density around \(35^{\circ }\hbox {N}\) and at 1 mm/6 h, while the peak density for non-matched trailing fronts occurs near \(60^{\circ }\hbox {N}\) with very low precipitation values. There are higher precipitation values for matched fronts at all latitudes in the NH, seen by the extension of the red curves to much higher precipitation intensities.
In the SH there are smaller differences in the mean precipitation values between matched and non-matched trailing fronts (1.42 mm/6 h and 1.32 mm/6 h respectively), and the convective precipitation is even slightly greater for the non-matched fronts. However, the two-dimensional histograms show a more complex picture, with the matched trailing fronts having higher total and convective precipitation between 20° and \(40^{\circ }\hbox {S}\), but lower values between 45° and \(60^{\circ }\hbox {S}\). This may explain the smaller SH average precipitation difference compared to the NH. The highest density for the non-matched trailing front mean precipitation can be seen close to \(60^{\circ }\hbox {S}\), with a value of around 0.6 mm/6 h, whereas the peak for the matched trailing fronts is at \(45^{\circ }\hbox {S}\) at over 1 mm/6 h. There is also a second peak density at \(25^{\circ }\hbox {S}\) with lower precipitation values. This double peak structure can also be seen for the convective precipitation (Fig. 8f) but with intensities around half of the total precipitation.
Isolated fronts in the NH during DJF show, on average, a much weaker influence of the matching with DIs but total and convective precipitation are both larger for the matched fronts. Figure 9b shows that the peak density for precipitation in non-matched isolated fronts is around zero over a broad latitude band, and in fact the median value is 0.23 mm/6 h over all latitudes. There is a maximum in precipitation shown equatorwards of \(10^{\circ }\hbox {N}\), which is not seen for the matched isolated fronts since the frequency of matching at this latitude is very small. Over the latitude band of 20°–\(50^{\circ }\hbox {N}\), the total and convective precipitation (Fig. 9b, c) are higher for the matched isolated fronts, but the peak density is still close to zero (a median of 0.31 mm/6 h for mean precipitation).
In the SH, a similar picture for isolated as trailing fronts can be seen, with higher mean total precipitation for matched fronts compared to non-matched fronts, but lower mean convective precipitation (Table 4). The two dimensional histograms (Fig. 9e, f) show some similarities with the trailing fronts in the SH, but are quite different to the NH. The peak density in total and convective precipitation can be seen around \(25^{\circ }\hbox {S}\) and is very similar for the matched and non-matched fronts. Since precipitation is averaged within the front area, the combined increase of front area and mean precipitation for matched fronts, indicates that total precipitation amounts are even larger, compared to non-matched cases.
The variation with latitude of the proportion of convective precipitation (Fig. 10) reveals that it generally increases towards lower latitudes for trailing and isolated fronts as we would expect from the global distribution of convection. For both types of fronts and in almost all latitude bands, the fronts not matched with DIs have higher convective precipitation proportions. So, while the association with DIs shows climatologically higher total and convective precipitation over the fronts, the increase in total precipitation is greater than the increase in convective precipitation when DIs are present.
Characteristics of fronts in different DI regions
Raveh-Rubin (2017) identified distinct characteristics of the DIs in different regions, which were ultimately reduced to “storm-track” or “non storm-track” DIs. Here we have investigated the regional differences in the front characteristics in these same regions (Figs. 11, 12), to examine whether matches of DIs and fronts in the storm track regions have different impacts to similar matches outside of the main storm tracks. Here we highlight the main results of this investigation.
For trailing fronts, the differences between fronts matched and not matched with a DI are consistent across the storm track regions (NA, NP, SP), with higher front strength, area, precipitation, and convective precipitation for matched fronts, (shown by boxplots in Fig. 11). In fact, almost all regions show stronger fronts with DIs, except the WUS region. All regions show larger front area, with much higher variability (shown by the whiskers) for fronts matched with DIs. The Mediterranean is the only region in which the mean precipitation for fronts with DIs is lower than for fronts without DIs, which is consistent with the very dry DI trajectories in this region (Raveh-Rubin 2017). WUS trailing fronts have some of the highest front strengths, but the lowest associated precipitation, possibly related to these fronts being at the end of the storm track and no longer experiencing strong frontogenesis.
The isolated fronts have the median values of front strength and area higher for fronts matched with DIs in all regions (Fig. 12). Considering the mean precipitation, the SH regions tend to show either smaller differences between matched and non-matched isolated fronts, or higher precipitation for the non-matched fronts. This is consistent with the 2D histograms shown in Fig. 9 and indicates that it is common across the hemisphere.
The boxplots indicate that the characteristics of the fronts do not necessarily all vary together, so to investigate the co-variability and how this is influenced by the association with a DI, Fig. 13 shows the correlations between front strength and the three other front characteristics (precipitation, convective precipitation, and area). Correlations between the strength of trailing front without DIs and their associated mean precipitation are positive everywhere except the NP and WUS regions. For the positive correlations, they are further enhanced in all regions by the matching with DIs. Convective precipitation is mainly negatively correlated with front strength for the non-matched fronts, and weakly positively correlated for the matched fronts. The correlations between front strength and area are also positive everywhere for the trailing fronts, but for most regions, this correlation is higher for the non-matched fronts. This indicates that without the presence of a DI, when mean frontal area is comparatively smaller, there is a stronger tendency for strong fronts to be larger.
The isolated fronts show mostly the same features as the trailing fronts, i.e., more positive correlations between front strength and precipitation for matched fronts. However, the opposite effect to that for trailing fronts is seen for the front area, with higher correlations between front strength and area for the matched fronts in all regions except SWAM, indicating that the presence of a DI contributes both to stronger and larger fronts.