1 Introduction

Rainfall seasonality is defined through numerous components including the timing, duration, and magnitude of wet- and dry-seasons (Raziei 2017; Deng et al. 2019). Although rainfall seasonality can be qualitatively described through analysing annual rainfall cycles, quantitative methods are preferred as these are valuable for investigations exploring changes and variability of rainfall regimes, for instance (Feng et al. 2013; Pascale et al. 2015). Therefore, a plethora of metrics have been proposed for quantitative analyses, including wet-season start- and end-dates (Smith et al. 2008; Dunning et al. 2016), the precipitation concentration index (PCI; Oliver 1980), the seasonality index (SI; Walsh and Lawler 1981), and the dimensionless seasonality index (DSI) with relative entropy (RE; Feng et al. 2013; Fig. 1).

Fig. 1
figure 1

Flow diagram of selected seasonality metrics, which quantify rainfall seasonality components, input data and quantitative outputs of rainfall seasonality

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Since 1938 many rainfall seasonality metrics, with varying levels of accuracy and usability, have been applied for classification and mapping across South Africa (see review by Roffe et al. 2019). From these, agreement exists for three distinct rainfall zones, with consensus that the summer rainfall zone (SRZ) spans much of the interior and eastern coast, the winter rainfall zone (WRZ) spans the southwestern Cape and west coast, and the year-round rainfall zone (YRZ) spans the southern coast (Roffe et al. 2019). Although a combination of factors (e.g. topography and surrounding oceans) contribute to the existence of these rainfall zones, it is primarily due to South Africa’s subtropical latitude, resulting in weather and climate being associated with tropical, subtropical and temperate weather systems (Tyson and Preston-Whyte 2000; Chase and Meadows 2007; Lennard and Hegerl 2015; Fitchett and Bamford 2017). The seasonal dichotomy, primarily between SRZ and WRZ conditions, is largely driven by the seasonal expansion/retreat of Antarctic sea-ice, the seasonal migration of the Inter-Tropical Convergence Zone (ITCZ), and resultant seasonal displacements of the subtropical high-pressure belt and mid-latitude westerlies (Chase and Meadows 2007; Lennard and Hegerl 2015). The eastern coast and most interior regions primarily experience convective summer rainfall, during October–March, which is predominantly produced from tropical temperate troughs (TTTs; i.e. cloud bands at the South Indian Convergence Zone, produced through tropical low and temperate westerly wave interactions; Hart et al. 2013; Macron et al. 2014) and is also associated with tropical low-pressure disturbances (Lennard and Hegerl 2015; Munday and Washington 2017); both of which primarily derive moisture from the western Indian Ocean (Rapolaki et al. 2020). During the austral winter half of the year (April–September), the southwestern Cape and western coast mainly receives rainfall from mid-latitude cyclone cold fronts which transit in the mid-latitude westerly flow and derive moisture from the southwest Atlantic Ocean (Lennard and Hegerl 2015; Burls et al. 2019). Along the southern coast, the year-round rainfall regime exists primarily due to rainfall contributions from tropical, subtropical and temperate weather systems (i.e. ridging high-pressure systems, TTTs, cut-off lows and cold fronts; Engelbrecht et al. 2015)

Despite agreement regarding existing rainfall zones across South Africa with a broad, although not complete, understanding of the spatio-temporal characteristics of weather systems largely responsible for these, there is no coherent understanding of rainfall seasonality as dispute exists for the boundary locations and rainfall seasonality classification at the transition between known rainfall zones (Roffe et al. 2019). Although this is related to the spatio-temporal characteristics of input data, it is mainly from applying metrics with dissimilar rainfall seasonality definitions, producing results which are often difficult to compare (Roffe et al. 2019). Indeed, this dispute would always exist, especially when applying the same metric for different temporal periods, as rainfall seasonality varies over a range of temporal scales (i.e. interannual to interdecadal; Tadross et al. 2009; Moeletsi et al. 2011; Dieppois et al. 2016; Dunning et al. 2016). However, without consensus regarding a standard metric or set of metrics, effective cross-study and spatio-temporal comparisons are virtually impossible. This issue of dispute and need for method standardisation is especially highlighted by transition region locations such as Sutherland (SUT in the Northern Cape province; Fig. 2), where classifications, across a range of methods, of SRZ, WRZ and YRZ have been assigned (Roffe et al. 2019). Similar results of classification variability using the same metric, however, become an important result acknowledging and measuring variability. Beyond the realm of climatological research, this dispute, specifically regarding result comparability, similarly poses an issue as the rainfall seasonality, and changes and variability thereof, of a location influences decision-making for rainfall dependent activities including agriculture (Tadross et al. 2009), conservation management (van Wilgen et al. 2016), tourism (Fitchett et al. 2017), and water resource management (Botai et al. 2018). Thus, a concentrated effort towards standardising the method(s) to quantify South African rainfall seasonality is needed.

Fig. 2
figure 2

Map of South Africa displaying elevation, the surrounding oceans and weather stations used in this study, and adapted from Roffe et al. (2020a)

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As it is evident that South African rainfall regimes are changing in response to anthropogenically induced climate change (e.g. van Wilgen et al. 2016; Botai et al. 2018; Mahlalela et al. 2020; Roffe et al. 2020b), it is clear that it is currently an important time to propose a more systematic approach for rainfall seasonality investigations, to consistently measure such changes. For this it is imperative to identify a metric or set of metrics which can be applied uniformly to all regions of South Africa, and can provide meaningful quantitative outputs on what rainfall seasonality entails. Following a literature analysis of existing rainfall seasonality metrics (Sect. 2), we critically apply a ratio of monthly rainfall: temperature, developed by Thackeray and Fitchett (2016), primarily because it offers statistical discrimination between SRZ and WRZ conditions, being an important requirement for a metric applied to South Africa (Fitchett and Bamford 2017). To assess utility of this ratio, it is applied to meteorological data spanning 1987–2016 from 46 weather stations spread across South Africa. To determine whether the ratio is applicable to the various datasets typically applied in climate studies, it is applied to gridded data, similarly spanning 1987–2016. To establish whether this ratio accurately models South African rainfall seasonality, outputs are assessed through their representation of rainfall seasonality in comparison to what is known in literature and through compatibility with the characteristics of known weather systems. We acknowledge that rainfall seasonality has been extensively studied for South Africa (e.g. Schumann and Hofmeyr 1938; McGee 1977; Schulze and Maharaj 2007), however, to our knowledge, no studies, except for Roffe et al. (2020a), have evaluated metric performance in such a manner, and through exploration of metric strengths and limitations to assess the value of further application.

2 Existing rainfall seasonality metrics: application across South Africa

A range of rainfall seasonality metrics have been applied for various regions globally, and across South Africa (e.g. McGee 1977; Sumner et al. 2001; Zhang and Qian 2003; Odekunle 2006; Fujita 2008; de Luis et al. 2010; Rajah et al. 2014; Dunning et al. 2016; Thackeray and Fitchett 2016; Raziei 2017; Deng et al. 2019; Roffe et al. 2019). As all metrics have been successfully applied in literature it can be argued that each inherently defines rainfall seasonality through quantifying various components which describe this concept (Fig. 1). Commonly applied metrics include DSI with RE (Deng et al. 2019), PCI (Zhang et al. 2019), wet-season start- and end-dates (Dunning et al. 2016), and SI (Li et al. 2016).

All metrics rely on daily- or monthly-scaled rainfall data, providing outputs over these scales (Fig. 1). Few metrics rely on temperature data, and only those developed by Thackeray and Fitchett (2016) and adopted by Herrmann and Mohr (2011) incorporate temperature and rainfall measurements. The approach applied by Herrmann and Mohr (2011) is not entirely suitable across South Africa (Roffe et al. 2019), because rainfall seasonality is not necessarily quantified and the SRZ and WRZ are not statistically discriminated. Few metrics quantify the timing component (Fig. 1), to allow for discrimination, thereby limiting application of many metrics across South Africa. As the outputs of wet-season start- and end-date metrics quantify the timing component and provide a near-complete (excluding a quantified degree of seasonality output) daily-scale description, these, depending on the start- and end-date definitions applied, are very appropriate to characterise South African rainfall seasonality (Fig. 1; Roffe et al. 2020a). As these have been applied extensively across South Africa (e.g. Tadross et al. 2009; Liebmann et al. 2012; Dunning et al. 2016; van Wilgen et al. 2016; Roffe et al. 2020a), they are not applied herein.

Instead, the ratio of monthly rainfall: temperature developed by Thackeray and Fitchett (2016) is applied for three reasons. Firstly, the output accurately discriminates between the SRZ and WRZ at their boundaries (Thackeray and Fitchett 2016), however, the ratio has not been assessed for utility across South Africa (Fitchett and Bamford 2017), and its output has not been thoroughly explored. It is particularly important to determine a metrics utility, as most, if not all, metrics are spatially limited in their application and none are applicable globally. Many metrics, for instance, lack applicability for regions not characterised by a uni-modal wet-season (Dunning et al. 2016; Deng et al. 2019). Since rainfall across the southern coast YRZ lacks a distinct uni-modal seasonal structure (Engelbrecht et al. 2015), application of many metrics is limited here, thus highlighting the necessity of assessing a metrics utility. Second, it is the only metric which quantifies the timing and degree of seasonality from one output (i.e. seasonality score, described under Sect. 3.2). This importance is emphasized by the fact that South Africa is characterised by SRZ and WRZ regimes, thus this score would characterise seasonality as it is experienced on the ground through a simple calculation procedure, whereas most other metrics (e.g. RE and DSI; Feng et al. 2013) require much additional computation for this. Therefore, it can provide a useful degree of seasonality measurement which together with a wet-season start- and end-date metric, for example, could be used to completely describe rainfall seasonality for a given location (Roffe et al. 2020b); where a complete description quantifies the timing, duration, magnitude and intensity of wet- and dry-season rainfall, and the degree of seasonality (i.e. contrast in rainfall amount and length of wet- and dry-seasons; Feng et al. 2013). Third, it considers rainfall and temperature for quantification (Fig. 1). This is important because rainfall and temperature act in conjunction driving numerous land surface processes and human activities (e.g. wildlife and vegetation phenological stages including breeding and budding, agricultural crop planting dates, and climate suitability for tourism), which are also influenced by rainfall seasonality (Herrmann and Mohr 2011; Suepa et al. 2016; Brawn et al. 2017; Fitchett et al. 2017; Byakatonda et al. 2019).

3 Methods

3.1 Study region and weather station locations

South African climate is influenced by: (1) its subtropical latitude (~ 22–35° S), (2) the southeastern-to-southern bordering Indian Ocean with the warm Agulhas Current (AC) and the western bordering Atlantic Ocean with the cool Benguela Coastal Current (BCC) and Benguela Upwelling System (BUS), and (3) the topography which comprises low-lying coastal regions (excluding southwestern-to-southern coast Cape Fold mountains) separated, by the Great Escarpment mountains, from a high-lying interior plateau (Landman et al. 2017; Fig. 2). Climate across most regions is semi-arid, due to the continuous influence of the South Indian Anticyclone (SIA), Continental Anticyclone (CA), and South Atlantic Anticyclone (SAA; of the subtropical high-pressure belt; Xulu et al. 2020); although generalised it ranges from warm, wet and humid in the east to warm, dry and arid in the west (Landman et al. 2017). Most regions experience mean annual temperatures > 16 °C (reaching ~ 24 °C in northeastern regions), however, high-lying mountainous regions have lower mean annual temperatures, ranging from 8 to 16 °C (Landman et al. 2017).

As is typical of subtropical climate, rainfall is annually and seasonally heterogeneous (Botai et al. 2018). Mean annual rainfall (MAR) ranges from > 600 mm year−1 (up to ~ 1500 mm year−1) across eastern regions to < 300 mm year−1 across western regions, however, southwestern-to-southern coast regions windward of the Cape Fold mountains receive ~ 600–1500 mm year−1 (Landman et al. 2017). Seasonally, as discussed further in Sect. 1 and 5.2, rainfall varies resulting in the SRZ, WRZ and YRZ (Lennard and Hegerl 2015).

As our aim is to assess the ratio’s utility, it is only necessary to utilise a sample of weather stations which broadly represents the above-mentioned annual and seasonal rainfall characteristics. Therefore, to produce a representative sample, 46 South African Weather Service (SAWS) stations were specifically selected with a gridded layout, with a spatial distribution across South Africa (Fig. 2; Table 1), following an approach similar to van der Walt and Fitchett (2020). Sample stations were limited to those with continuous datasets (≥ 90% data availability, for all input variables, following quality control) for 1987–2016. We acknowledge that this approach produced a relatively coarse station network, hence our application of gridded data.

Table 1 Details of the study weather stations
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3.2 Data and statistical analyses

Total daily rainfall, and maximum and minimum daily temperatures (Tmax and Tmin) were utilised from the stations (Table 1; Fig. 1). Raw data were subject to quality control measures, as detailed in Roffe et al. (2020b). To determine representativity of the station sample, MAR and mean monthly rainfall totals were quantified for 1987–2016.

The method to quantify rainfall seasonality, for individual stations, follows directly from Thackeray and Fitchett (2016). It considers the relationship (i.e. correlation) between rainfall and temperature, where a positive (i.e. high temperatures correspond to high rainfall, and vice versa), negative/inverse (i.e. low temperatures correspond to high rainfall, and vice versa) and no (i.e. no correspondence between rainfall and temperature) relationship represents SRZ, WRZ and YRZ regimes respectively (Fig. 3). This is modelled using the standard least-squares linear regression equation:

$$y = mx + c,$$
(1)

here, y refers to square-root (sqrt) transformed mean monthly rainfall (MMR) values and x refers to sqrt transformed mean monthly temperature (MMT) values, and the unitless m-coefficient (i.e. seasonality score or score) quantifies rainfall seasonality (Thackeray and Fitchett 2016). MMR and MMT are sqrt transformed to reduce skewness, improve normality assumptions, and produce values with a comparable magnitude such that the variables have equal weighting for the regression analysis (Schuurmans et al. 2007; Sideris et al. 2014; Stauffer et al. 2017; Fig. 1a, b). Daily rainfall and temperature values, for months with < five missing/deleted days, were averaged to calculate MMR and MMT respectively. Daily temperatures were quantified as the mean of Tmax and Tmin, and were regarded as missing when Tmax and/or Tmin were missing/deleted.

Fig. 3
figure 3

Graphical description of the seasonality score calculation and definition for representative winter-, summer- and year-round rainfall zone (WRZ, SRZ and YRZ) weather stations, including Cape Town Wo (CTW), Johannesburg INT Wo (JIW) and Oudtshoorn (OUD) respectively. a Mean annual cycles of rainfall (using monthly mean of daily rainfall totals, i.e. MMR) and temperature (using mean monthly temperature values, i.e. MMT) per station for 1987–2016. b Total period seasonality score calculation per station for 1987–2016. c Annual cycles rainfall (using MMR) and temperature (using MMT) per station for selected years (i.e. 1987, 2001 and 2016). d Annual seasonality score calculation per station for selected years (i.e. 1987, 2001 and 2016)

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Scores can be calculated for a range of temporal periods, from one year to n years (i.e. any user defined sample of years; Fig. 3b, d). To explore the robustness of the ratio, scores were calculated over varying temporal periods, for 1987–2016 (i.e. total period scores), per annum, and over 5-, 10-, 15-, 20-, and 25-year resampling periods using four randomly selected subsets. This procedure was applied to the station data, and resampling periods were standard for each station. Determining the consistency of the scores across these temporal periods is important to assess the ratio’s statistical stability (Broadbent 2013). While all monthly values were used to calculate the total and resampling period scores, annual scores were not calculated if > 2 months of MMR and/or MMT were missing. Pearson correlation coefficient values (i.e. r values quantifying the relationship strength between sqrt MMR and sqrt MMT) were calculated to further describe seasonality characteristics.

The score quantifies the degree and timing of seasonality (Figs. 1, 3; Thackeray and Fitchett 2016). Summer- and winter-season rainfall are represented by positive and negative scores respectively, and the range in scores represents varying degrees of seasonality (Thackeray and Fitchett 2016). Scores tending away from zero reflect a greater degree of seasonality and unevenly distributed rainfall with distinct wet- and dry-seasons, while scores tending towards zero indicate a weaker degree of seasonality and more evenly distributed rainfall with no distinct seasonality (Thackeray and Fitchett 2016). Considering this, class limits were developed to classify SRZ, WRZ and YRZ conditions (Table 2).

Table 2 Classification of summer, winter and year-round rainfall zone (SRZ, WRZ and YRZ) based on resulting seasonality score value
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To explore spatial patterns of seasonality, the total period scores were spatially interpolated through ordinary kriging analysis (Frazier et al. 2016). This was undertaken using the geostatistical analyst on ArcMap, using the exponential semivariogram.

To deem a seasonality metric useful, it must be applicable to the various datasets typically used in climate studies. Hence, the ratio was applied to gridded data, of daily rainfall (mm) and daily Tmax and Tmin (°C), from the Climatology Prediction Centre (CPC) of the National Oceanic and Atmospheric Administration (NOAA; https://psl.noaa.gov). Daily surfaces are available for 1979 to present, and are interpolated from station data to a 0.5° spatial resolution on a global grid. These temperature and rainfall datasets were selected primarily for consistency in data provider and spatial resolution. In particular, the Tmax and Tmin surfaces were utilised for consistency with raw temperature data for the stations. Daily surfaces for 1987–2016 were used to calculate annual scores per grid cell to subsequently produce an average score surface for the study period.

4 Results

4.1 Annual and monthly rainfall characteristics of the weather station sample

MAR across South Africa demonstrates high spatial variability (Landman et al. 2017), which is similarly evident across the sample stations (Fig. 4a). Primarily due to contrasting sea surface temperatures (SSTs), these display a statistically significant west–east longitudinal gradient (r = 0.79, p < 0.0001), ranging from 72.4 mm year−1 at PNO (Port Nolloth), north along the west coast, to 1099.6 mm year−1 at PAD (Paddock), southeast within KwaZulu-Natal (Fig. 4a; Reason 2017). This is most pronounced across the interior, whereas southern coast and southwestern Cape regions do not conform to this spatial gradient and experience relatively high MAR, as is reflected across the stations (Fig. 4a; Landman et al. 2017). This results primarily from the influence of moist frontal air (Reason 2017). However, the Cape Fold mountains induce much spatial variability in MAR, and the stations similarly reflect this (Fig. 4a; Landman et al. 2017).

Fig. 4
figure 4

a Map displaying mean annual rainfall, and b–g graphs of mean annual rainfall cycles for the 46 weather stations for 1987–2016

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The annual rainfall cycles across the stations demonstrate SRZ, WRZ and YRZ conditions (Fig. 4b–g). OUD (Oudtshoorn), PEW (Port Elizabeth Wo) and RIV (Riversdale), along the southern coast, demonstrate aseasonal conditions with relatively equable monthly rainfall, with slight peaks mainly during autumn and spring months (Fig. 4c). Thirty-four central and eastern locations demonstrate a summer wet-season (Fig. 4d–g). This begins along the eastern coast, for locations including CED (Cedara), PAD (Paddock) and UMW (Umtata Wo), with higher rainfall from September and October to March and April, peaking during December–January (Fig. 4d). Within central eastern and northeastern regions, for locations including BET (Bethal), BLW (Bloemfontein Wo), JIW (Johannesburg INT Wo), MWO (Mafikeng Wo), and PWO (Polokwane Wo), rainfall is higher from October and November to March and April, peaking during December-January (Fig. 4e, f). For locations including DAW (De Aar Wo), POF (Pofadder) and WIL (Willowmore), within the western interior, the summer wet-season spans November and December to March and April, peaking during February–March (Fig. 4g). Across the southwestern Cape and western coast, for locations including CWO (Calvinia Wo), CTW (Cape Town Wo), and PNO (Port Nolloth), the winter wet-season spans April-September, peaking during June (Fig. 4b).

4.2 Metric outputs: seasonality scores, r values and associated spatial characteristics

Although notable variability exists, the annual scores, resampling period scores and total period scores are very similar (Supplementary Fig. 1, 2; Supplementary Table 1; Table 3). This consistency across varying temporal periods highlights that the score is reproducible and the ratio is statistically stable and robust. Strong similarity exists between the mean annual and total period scores, demonstrating that the latter are representative of the overall rainfall seasonality conditions for 1987–2016 (Table 3; Supplementary Fig. 1, 2). Hence, this section primarily focuses on the total period scores.

Table 3 Location specific total period seasonality scores, r values and p values for 1987–2016
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First, it is necessary to consider what the score represents and how it models rainfall seasonality. As rainfall is inherently more variable, over interannual to interdecadal scales, than temperature, and such variability of temperature is relatively low, the resulting score relies primarily on MMR variation across the range of MMT (Herrmann and Mohr 2011; Fig. 3c, d). For instance, across the stations presented in Fig. 3, MMT is relatively similar, however, in comparison to CTW (Cape Town Wo) and JIW (Johannesburg Wo), with relatively strong total period scores due to large MMR contrasts for lower and higher MMT, OUD (Oudtshoorn) has a very weak score because of relatively similar MMR for varying MMT.

The range in total period scores, from − 1.04 for CTW (Cape Town Wo) within the southwestern Cape to 1.59 for NEL (Nelspruit) within Mpumalanga, reflects varying degrees of seasonality across South Africa (Table 3; Fig. 5a; Supplementary Fig. 1). Classifying these scores (Table 2), SRZ conditions are evident for 30 locations, including CED (Cedara; score = 1.13), NEL (Nelspruit; score = 1.59) and PRI (Prieska; score = 0.31), spanning central and eastern regions (Table 3; Fig. 5a, b; Supplementary Fig. 1). WRZ conditions are evident for seven locations, including CTW (Cape Town Wo; score = − 1.04), ROB (Robertson; score = − 0.33) and SWO (Springbok Wo; score = − 0.50), across the southwestern Cape and western coast (Table 3; Fig. 5a, b; Supplementary Fig. 1). Nine locations across the southern coast and western interior, including CWO (Calvinia Wo; score = − 0.21), POF (Pofadder; score = 0.13) and RIV (Riversdale; score = − 0.08), reflect YRZ conditions (Table 3; Fig. 5a, b; Supplementary Fig. 1). Spatially, this demonstrates that, according to the scores, South Africa is predominantly characterised by SRZ conditions, following west with YRZ conditions characterising to the transition to WRZ conditions further west (Fig. 5a, b). The range in scores demonstrate variation in sign and strength over west–east and south-north gradients (Table 4; Fig. 5a). Broadly, as longitude increases, negative scores tend towards zero and positive scores tend away from zero, and as latitude increases, positive scores tend towards zero and negative scores tend away from zero (Fig. 5a; Table 4).

Fig. 5
figure 5

Spatial distribution of the a interpolated total period seasonality scores adapted from Roffe et al. (2020b), b location specific rainfall seasonality classifications, and c location specific strength of relationship (i.e. r value) between square-root (sqrt) transformed mean monthly rainfall (MMR) and mean monthly temperature (MMT) for 1987–2016

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Table 4 Analyses of the total period seasonality scores correlated with strength of relationship, and of these variables correlated with latitude, longitude, and elevation for each station (as presented in Tables 1 and 3)
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SRZ scores range from 0.31 (PRI: Prieska) to 1.59 (NEL: Nelspruit; Table 3). Overall, a longitudinal pattern of stronger (weaker) scores for eastern (western) regions exists, however, the strongest scores are evident for northeastern locations (i.e. JIW: Johannesburg INT Wo; NEL: Nelspruit; PWO: Polokwane Wo; SKU: Skukuza), also highlighting a latitudinal pattern (Table 4; Fig. 5a). Moreover, some locations further south (e.g. CED: Cedara; SHA: Shaleburn) are also characterised by strong seasonality, relating to very high MMR, where seasonality is strongly influenced by the steep eastern Drakensburg mountains which promote orographic rainfall (Fig. 5a). For locations with the strongest scores, these are largely driven by very high MMR during warmer months, however, in comparison to CED (Cedara) and SHA (Shaleburn), more frequent zero MMR during cooler months also drive scores for northeastern locations (Supplementary Fig. 1). Further, a pattern is evident between interior plateau and southeastern low-lying coastal/near-coastal locations. Although characterised by relatively similar MMR during warmer months, compared to further eastern interior plateau locations, coastal/near-coastal locations (e.g. ELW: East London Wo; PAD: Paddock; UMW: Umtata Wo) receive more rainfall during cooler periods with less frequent zero MMR, thus scores for these locations are moderated by the smaller contrast between MMR for varying MMT (Supplementary Fig. 1; Fig. 5a, b). Interior plateau locations have more frequent zero MMR, thus the scores are driven by this, but more strongly by the magnitude of MMR during warmer periods (Supplementary Fig. 1; Fig. 5a, b).

WRZ scores range from − 0.33 (ROB: Robertson) to − 1.04 (CTW: Cape Town Wo; Table 3). The western Escarpment mountains act as a barrier dictating the WRZ extent (Fig. 5a, b); as do the Cape Fold mountains, although to a lesser extent as these more strongly induce spatial heterogeneity. While insignificant, gradients of a reduction in seasonality strength to the north and east are evident (Table 4; Fig. 5a). Moving north from CTW (Cape Town Wo), weaker scores are driven by more frequent zero MMR during warmer months, with lower MMR during cooler months (Supplementary Fig. 1; Fig. 5a). Moving east from CTW (Cape Town Wo), weaker scores are driven by lower MMR during cooler months and during warmer months infrequent zero MMR moderates these scores (Supplementary Fig. 1; Fig. 5a).

YRZ scores range from − 0.27 (PEW: Port Elizabeth Wo) to 0.23 (WIL: Willowmore; Table 3). These scores are driven by relatively evenly spread MMR for varying MMT (Supplementary Fig. 1). The Cape Fold mountains act as a topographic barrier, distinguishing OUD (Oudtshoorn), RIV (Riversdale) and PEW (Port Elizabeth Wo) from locations north of these mountains (Fig. 5a, b). To the south, scores are also driven by infrequent or no zero MMR, with slightly higher rainfall during cooler months driving slightly negative scores, which is particularly evident for PEW (Port Elizabeth Wo; Supplementary Fig. 1; Fig. 5a). To the north, scores are similarly driven by relatively even spread and low MMR for varying MMT, however, scores are also driven by more frequent zero MMR (Supplementary Fig. 1; Fig. 5a). Within eastern (western) regions closer to SRZ (WRZ) locations, slightly higher warmer (cooler) period rainfall drives slightly positive (negative) scores (Supplementary Fig. 1; Fig. 5a).

The sign and magnitude of the r value complements the score in describing the timing and degree of seasonality (Table 3). As positive and negative scores tend away from zero, r values generally tend away from zero, demonstrating that locations within the SRZ and WRZ extremes have stronger r values, whereas YRZ and adjacent locations, with more evenly distributed rainfall, are characterised by weaker r values which tend towards zero (Table 3, 4; Fig. 5c). Moreover, owing to appreciable cool season rainfall, southeastern coastal SRZ locations (i.e. ELW: East London Wo; MAN: Mandini; PAD: Paddock) have relatively weak r values, despite their relatively strong scores (Fig. 5a, c). These locations highlight the importance of the r value in describing location-specific seasonality characteristics. Consider MAN (Mandini) and MWO (Mafikeng Wo), for instance, which both have a score of 0.93, their r values (r = 0.38 and r = 0.65 respectively) together with their total period scatter plots (Supplementary Fig. 1) highlight notable seasonality differences exist, largely due to differences in the contribution of cool season rainfall to their annual rainfall totals.

4.3 Applying the ratio to gridded data and exploring correspondence to the weather station results

Successful application to gridded data demonstrates usefulness of the ratio as it is applicable to multiple datasets (Dunning et al. 2016). Confidence is thus established in the ratio and its score output, as strong agreement exists between mean scores calculated for the stations and corresponding grid cells, and the interpolated total period score surface corresponds to the gridded surface of the mean scores (Figs. 5, 6). Further confidence is established by strong consistency in the SRZ, WRZ and YRZ spatial distribution across the gridded and station data (Fig. 5a, b, 6). Moreover, correspondence exists between the annual station and gridded data scores, where time series correlations between all stations and corresponding grid cells were statistically significant (with p values < 0.05), with r values ranging from 0.64 to 0.99 for OTT (Ottosdal) and BLW (Bloemfontein Wo) respectively (Supplementary Fig. 2). Despite much agreement, notable inconsistencies exist for the annual score magnitude (Supplementary Fig. 2). While most mean value differences were < 0.10, the differences for CTW (Cape Town Wo), JIW (Johannesburg INT Wo), MAR (Mara), MRC (Makatini Research Centre), NEL (Nelspruit), PEW (Port Elizabeth Wo), PNO (Port Nolloth), POF (Pofadder) and SHA (Shaleburn) were ≥ 0.10, with the largest difference of 0.35 for NEL (Nelspruit; Supplementary Fig. 2). These can be attributed to dataset differences, and, in particular, the relatively coarse resolution of the gridded data used. As our aim was only to demonstrate whether the ratio is applicable to gridded data, this remains a topic for further study.

Fig. 6
figure 6

Mean seasonality scores, for 1987–2016, calculated for the gridded data (surface) and weather stations (circles)

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5 Discussion and conclusions

5.1 Representativity of the weather station sample

SAWS maintain a network of ~ 200 stations. However, these are unevenly distributed, record lengths vary and gaps exist (Kruger 2006). Accounting for this to collate an evenly spread station network, without particularly large gaps and without stations concentrated in some, but not all regions, while relying only on SAWS stations for consistency, we purposively selected stations for a representative sample (Arsenault and Brissette 2014).

Despite the coarse spatial resolution, the sample size and spread of stations is consistent with studies using station data to assess the performance of various metrics across northern Australia (Smith et al. 2008), Nigeria (Odekunle 2006) and the Tropics (Feng et al. 2013). Moreover, Roffe et al. (2020a) utilised this sample, and their interpolated spatial representation of South African wet-season characteristics corresponds to similar representations using gridded datasets (e.g. Liebmann et al. 2012; Dunning et al. 2016).

Considering Sect. 4.1, the characteristics, magnitude and spatial distribution of MAR and mean monthly rainfall are consistent with studies using different temporal periods and observational data (Fig. 4; e.g. Rouault and Richard 2003; Philippon et al. 2012; Hart et al. 2013; Engelbrecht et al. 2015; Landman et al. 2017). Compared to Favre et al. (2016), for instance, where CORDEX models were assessed on their annual and monthly rainfall representation for southern Africa, the characteristics represented by our results are consistent with features reported therein. For MAR, for instance, our sample demonstrates notable spatial heterogeneity and importantly captures the west–east rainfall gradient (Fig. 4a), a key feature for most subtropical regions (Crétat et al. 2012). Over South Africa this basically results from the SIA and SAA influence over neighbouring oceans with their contrasting SSTs (Xulu et al. 2020). Broadly, together with the influence of cool BCC SSTs, the SAA limits incoming moisture, promoting subsidence and dry western conditions, while the SIAs (and SAA ridging anticyclones) easterly winds favour western Indian Ocean moisture fluxes, promoting wetter eastern conditions (Crétat et al. 2012; Ndarana et al. 2020; Rapolaki et al. 2020; Xulu et al. 2020). Inland, regional topography modifies such moisture fluxes producing much spatial heterogeneity (Tyson and Preston-Whyte 2000). Stations representative of summer, winter and year-round rainfall regimes exist, with peak rainfall totals linking to peak activity of systems driving these regimes (Favre et al. 2016). While the next section details their existence, these are essentially a consequence of various moisture sources (e.g. Southwest Atlantic Ocean, tropical southeast Atlantic and western Indian Ocean), the origins and tracks of rain-producing systems (e.g. cold fronts and TTTs), and their timing of influence (Hart et al. 2013; Munday and Washington 2017; Sousa et al. 2018; Ndarana et al. 2020).

We therefore argue that our station sample broadly represents South African rainfall characteristics, and is appropriate to assess the ratio’s veracity. Although this sample omits spatial detail, the ratio will work for stations in between the sample stations, as it is accurate across these stations and was successfully applied to gridded data.

5.2 Classifying and characterising rainfall seasonality across South Africa using the seasonality scores

A useful statistical method for classification must be proven stable, robust, valid, and reproducible (Hattie and Cooksey 1984; Broadbent 2013). Therefore, a seasonality metric applied to South Africa must be applicable and accurate across the entire country, and its output(s) must reliably distinguish the different rainfall zones. By demonstrating that the scores discriminate SRZ and WRZ conditions at their boundaries and capture spatial heterogeneity in seasonality strength, Thackeray and Fitchett (2016) verified the ratio’s validity and that the score inherently quantifies the seasonality degree and timing. Here, score consistency across varying temporal periods demonstrates that these are reproducible and the ratio is statistically stable and robust (Table 3; Supplementary Table 1; Supplementary Fig. 1, 2), and development of classification boundaries allows further discrimination of rainfall zones. Our application to station and gridded data confirms large-scale use (Figs. 5, 6), allowing for a shift towards a more coherent understanding of South African rainfall seasonality. Usability is verified as the score rainfall zones are consistent across multiple datasets and with previous published maps (e.g. Schumann and Hofmeyr 1938; McGee 1977; Rouault and Richard 2003), and classifications for locations (e.g. CTW: Cape Town Wo, classification = WRZ; JIW: Johannesburg INT Wo, classification = SRZ; OUD: Oudtshoorn, classification = YRZ) within rainfall zone extremes remain undisputed (Figs. 5a, b, 6). While this broadly demonstrates utility, this is only confirmed if the scores conform with known characteristics of each rainfall zone.

The ratio’s SRZ representation is validated by consistency with previous seasonality maps (Figs. 5a, b, 6; e.g. Cooke 1946; Rouault and Richard 2003; Chase and Meadows 2007). Its spatial extent largely depends on that of convective systems, primarily deriving moisture from the western Indian Ocean (Hart et al. 2013; Favre et al. 2016; Rapolaki et al. 2020). It also varies over interannual to interdecadal scales, in relation to the El Niño Southern Oscillation (ENSO; Dieppois et al. 2016), southwest Indian Ocean SSTs (Reason and Mulenga 1999) and the Southern Annular Mode (SAM; Malherbe et al. 2014), for instance. Compared to locations within the SRZ extremes (e.g. JIW: Johannesburg Wo; PWO: Polokwane Wo), locations closer to the boundary (e.g. DAW: De Aar Wo; PRI: Prieska) demonstrated heightened classification variability (Supplementary Table 1; Supplementary Fig. 2). As the principal driver of SRZ variability, ENSO with its El Niño and La Niña phases would drive this, resulting in a smaller and larger SRZ extent respectively (Dieppois et al. 2016). These phases influence the South Indian Convergence Zone (where TTTs preferentially develop; Hart et al. 2013; Macron et al. 2014), and the latitude of subtropical anticyclones, such that during El Niño (La Niña) phases TTTs are located more eastward (westward) and subtropical anticyclones are located further north (south), thus linking with anticyclonic anomalies which suppress (enhance) convection and moisture flow to South Africa (Ratnam et al. 2014; Dieppois et al. 2015, 2016).

Lower and zero MMR during cooler months for SRZ locations is consistent with more intense interior anticyclonic conditions (Lennard and Hegerl 2015; Sousa et al. 2018; Supplementary Fig. 1). Low MMR for these months is attributed to cut-off lows (which also produce warmer season rainfall) and cold fronts, however, the Escarpment mountains block westerly-derived moisture, thus these systems mainly produce rainfall across southeastern coastal/near-coastal regions (Favre et al. 2013). This is consistent with noticeably higher cool season MMR, slightly weaker scores and relatively weaker r values here (Figs. 5, 6; Supplementary Fig. 1).

The most notable SRZ characteristic is the east-to-west wet-season rainfall shift (Favre et al. 2016). Despite not showing this, as wet-season metrics would (e.g. Liebmann et al. 2012), the longitudinal and latitudinal gradients represented by the scores and r values can be linked to this and the various rain-bearing systems contributing to this wet-season (Table 4; Fig. 5a). Consistent with west-to-east track of tropical convective systems (Dyson and van Heerden 2002; Macron et al. 2014) and the warm western Indian Ocean (inland moisture flow facilitated by SIA easterly winds) as the main SRZ moisture source (Rapolaki et al. 2020), this wet-season starts along the southeastern coast, where score characteristics and r values differ noticeably from those further north and inland (Supplementary Fig. 1; Figs. 5a, c, 6). Lower, although still strong, scores for these locations reflects a lower degree of seasonality, linking to a longer wet-season. Here, early summer convective rainfall is attributed to TTTs (Hart et al. 2013), and SSA ridging anticyclones (with associated easterly winds facilitating inland moisture flow from the Indian Ocean; Ndarana et al. 2020), with orographically-induced rainfall favoured for locations including SHA (Shaleburn). Thereafter, the summer wet-season spreads inland north and west (Liebmann et al. 2012; Dunning et al. 2016), when rainfall associated with TTTs spreads further north and west (Hart et al. 2013). The stronger degree of seasonality for northeastern locations is consistent with relatively high warm season MMR (and very low cool season MMR; Supplementary Fig. 1) associated with TTTs (Hart et al. 2013), and increased local convection, associated with low-pressure disturbances (related to the Angola low, for instance) deriving moisture from the western Indian Ocean, tropical Africa (associated with ITCZ summer southward migration) and the tropical southeast Atlantic (Dyson and van Heerden 2002; Dunning et al. 2016; Munday and Washington 2017; Xulu et al. 2020). The weaker degree of seasonality for locations further west primarily links to lower MMR (Supplementary Fig. 1), consistent with lower rainfall and a reduced influence of the above-mentioned rain-bearing systems (Taljaard 1996; Favre et al. 2016), and particularly that of TTTs favouring higher rainfall for eastern regions (Hart et al. 2013).

Correspondence with previous maps (e.g. Schumann and Hofmeyr 1938; Rouault and Richard 2003; Schulze and Maharaj 2007), verifies the ratio’s WRZ representation (Figs. 5a, b, 6). Together with the western-to-southeastern Escarpment mountains, a more intense and well-established interior CA, during winter, dictates its spatial extent by restricting southwest Atlantic derived moisture penetration (Fig. 5b, 6; Sousa et al. 2018; Burls et al. 2019). Its extent varies across interannual to interdecadal scales (Dieppois et al. 2016), evident from heightened classification variability for locations closer to the boundary (e.g. PNO: Port Nolloth, ROB: Robertson; Supplementary Table 1; Supplementary Fig. 2). This region represents the marginal influencing area for cold fronts, and their landward penetration varies in relation to the SAM (Mahlalela et al. 2019), South Atlantic SSTs and sea-ice (Reason and Jagadheesha 2005; Blamey and Reason 2007) and ENSO (Philippon et al. 2012). These factors influence the position of the moisture-laden westerlies, with further equatorward (poleward) westerlies driving a larger (smaller) WRZ extent, in west–east and north–south directions (Fitchett and Bamford 2017).

Heterogeneity within the WRZ is commonly acknowledged (e.g. Philippon et al. 2012; Mahlalela et al. 2019). Scores and associated r values, reflect this through latitudinal and longitudinal seasonality strength gradients (Table 4; Figs. 5a, c, 6). More stations and finer resolution gridded data, would demonstrate further spatial heterogeneity across the Cape Fold mountains, for instance (Philippon et al. 2012). Notable differences in seasonality strength, due to topography, exist between ROB (Robertson) and CAG (Cape Agulhas), for instance, which demonstrate similar seasonality characteristics with notable warm season MMR, however, ROB (Robertson), leeward of the mountains, receives lower MMR linking to a considerably lower score (Figs. 5a, b, 6; Supplementary Fig. 1).

WRZ heterogeneity is, however, mainly linked to cool season MMR, which declines northwards and is highest for southwestern regions windward of the Cape Fold mountains (Fig. 4b; Supplementary Fig. 1; Philippon et al. 2012). This is primarily associated with the trajectory of mid-latitude frontal systems, which originate in the southwest Atlantic and track eastward towards South Africa, mostly influencing southwestern WRZ regions (producing ~ 89% of winter rainfall; Burls et al. 2019), with a declining influence moving north and east (Jones and Simmonds 1993; Sousa et al. 2018). These occur year-round, although their strongest influence is during winter when the westerlies displace northwards. Despite a stronger east–west seasonality gradient, as all negative scores were considered for correlation (Table 4), it is expected that the north–south gradient is stronger because score strength is strongly driven by MMR magnitude (Fig. 3b, d). In addition to the passage of cold fronts, this northward decline in seasonality strength is linked to cut-off lows, which similarly flow from west-to-east while transiting in the westerlies, and form when troughs of cold, high-latitude air (in the middle to upper troposphere) extend equatorward and become cut-off from westerly flow (Singleton and Reason 2007; Favre et al. 2013; Omar and Abiodun 2020). Although these systems contribute relatively little winter rainfall, and mainly to transition season rainfall totals (i.e. Autumn and Spring), they similarly produce less rainfall moving north (Favre et al. 2013; Omar and Abiodun 2020). This northward decline is also linked to atmospheric stability induced by the SAA and cool coastal SSTs associated with the BCC and BUS (Favre et al. 2016). Considering the east–west gradient, particularly across the southern WRZ (Figs. 5, 6), this reflects an increased contribution of warm season MMR contributing to reduced seasonality (Supplementary Fig. 1), which links to the influence of the warm AC and SAA ridging anticyclone easterly winds transporting moisture inland during warmer months (Mahlalela et al. 2019; Ndarana et al. 2020). During warmer months, lower and zero MMR across the southwestern WRZ is consistent with the influence of SAA ridging anticyclones (Supplementary Fig. 1; Mahlalela et al. 2019; Ndarana et al. 2020), while further north this more strongly links to the decreased influence of convective rain-producing systems (Crétat et al. 2012; Hart et al. 2013)

The YRZ spatial distribution is most disputed, being very dependent on the metric-based rainfall seasonality definition (Roffe et al. 2019). Theoretically, it is defined as the region influenced by characteristically SRZ and WRZ rain-producing systems (e.g. Chase and Meadows 2007; Engelbrecht et al. 2015). With most representations limited to the southern coast, constrained by the Cape Fold mountains (e.g. Cooke 1946; Schulze and Maharaj 2007; Engelbrecht et al. 2015), it seems this definition is not entirely considered. In agreement with ours (Fig. 5a, b, 6), some representations demonstrate that it extends northwest, from the southern coast to southern Namibia (e.g. Chase and Meadows 2007; Cordova 2013), where tropical and temperate systems do produce rainfall (Favre et al. 2013; Hart et al. 2013). The classification, of scores tending to zero from ± 0.30 with very weak and weak r values, considers this YRZ definition and the all-encompassing SRZ/WRZ boundary (i.e. zero score; Thackeray and Fitchett 2016). Thus, the ratio’s YRZ representation is accurate and meaningful, and can aid in providing new insight.

The YRZ represents the SRZ-to-WRZ transition (Fig. 5a, 6). As for the SRZ and WRZ, conditions (especially the zero boundary-line position) vary over interannual to interdecadal scales, in relation to ENSO and SAM phases, for instance (Dieppois et al. 2016; Engelbrecht and Landman 2016). Scores for YRZ locations generally reflect more variability in sign and classification, compared to SRZ and WRZ locations (Supplementary Table 1, Supplementary Fig. 2), as is expected for this transition region (Herrmann and Mohr 2011). Distinct northern and southern YRZ regions are split by the Cape Fold mountains (Supplementary Fig. 1; Cordova 2013), which restrict Indian Ocean moisture penetration (Engelbrecht and Landman 2016; Omar and Abiodun 2020).

To the south, scores and r values correctly reflect aseasonal conditions with relatively even and little to no zero MMR (Supplementary Fig. 1; Engelbrecht et al. 2015). The variety and year-round occurrence (excluding TTTs; Hart et al. 2013) of rain-producing systems drive this complex aseasonal regime (Engelbrecht et al. 2015). Despite producing dry conditions across the southwestern WRZ (Mahlalela et al. 2019), along the southern coast SAA ridging anticyclones produce easterly winds promoting onshore moisture flow from the warm Indian Ocean, producing ~ 46% of MAR (Engelbrecht et al. 2015; Ndarana et al. 2020). Cut-off lows (similarly favoring onshore moisture flow), TTTs and cold fronts are also important rain-producing systems here (Engelbrecht et al. 2015). Across this region, notable heterogeneity exists in the annual rainfall structure (Engelbrecht et al. 2015), which scores for OUD (Oudtshoorn), RIV (Riversdale) and PEW (Port Elizabeth Wo) allude to (Supplementary Fig. 1). For instance, in comparison to PEW (Port Elizabeth Wo), OUD (Oudtshoorn) has a much weaker negative score, reflecting relatively higher TTT rainfall contributions, evident from relatively high MMR during warmer months (Supplementary Fig. 1; Engelbrecht et al. 2015). Although commonality exists in the rain-producing systems, their regional contributions vary (e.g. TTT influence decreases south, while ridging anticyclone influence decreases north) and are also influenced by the topographically complex Cape Fold mountains, which modify moisture fluxes by producing rain-shadows or enhancing moisture uplift producing orographic rainfall (Engelbrecht et al. 2015; Engelbrecht and Landman 2016).

Across the northern YRZ, the slightly negative (west) and positive (east) regimes characterised by the scores are consistent with the adjacent WRZ and SRZ, and the uni-modal annual rainfall structure for these locations (Figs. 4a, g, 5a, 6; Supplementary Fig. 1). For many rainfall seasonality classifications these regions represent marginal and drier SRZ (or late SRZ) and WRZ areas (e.g. Schulze and Maharaj 2007; Liebmann et al. 2012). Despite this, good correspondence exists between the scores (especially considering the sign) and rain-bearing systems influencing this region. TTTs, flowing from the east during warmer months, produce more rainfall across the east of this region, while cut-off lows, occurring year-round, but mainly during slightly cooler transition season months, contribute a relatively even amount of rainfall across this region (Favre et al. 2013; Hart et al. 2013). Given their moisture origin and tracks, cold fronts, primarily during cooler months, contribute slightly more rainfall over the western part of this region (Jones and Simmonds 1993; Taljaard 1995, 1996).

Considering the scores, our sample contains stations representative of each rainfall zone, thus reiterating that it was appropriate to assess the ratio’s accuracy. Importantly, the scores for each station across each rainfall zone are spatially consistent, comparing well to scores calculated using gridded data, and these correspond to the spatial characteristics of rainfall seasonality and associated weather systems determining South African climate. Confidence is thus established in the scores rainfall seasonality representation and classification, thereby supporting its utility and further use across South Africa.

5.3 Towards a standard metric quantifying and classifying the degree of seasonality across South Africa: advantages, limitations, and application

Successful application of the ratio to all stations and gridded data, and confirmation of known seasonality characteristics demonstrates that the score is a relevant South African rainfall seasonality measurement. Therefore, it is valid to propose the ratio as a standard degree of seasonality metric, which is important to coherently understand South African rainfall seasonality, and for consistent and comparable investigations. In promoting further use, we highlight potential application, but more importantly explore associated advantages and limitations, representing essential user considerations.

The ratio’s simplicity, stability, objectiveness, and large-scale applicability are advantageous. Statistical stability, confirmed by score consistency across varying temporal periods, offers accuracy and consistency in results regardless of the calculation period. Reliance on location-specific rainfall and temperature measurements without relying on a predefined climatological year makes the ratio objective. Many metrics rely on this for meaningful results (Feng et al. 2013; Dunning et al. 2016). In Roffe et al. (2020a), for instance, meaningful quantification of the aseasonal southern coast wet-season relies on a January-December climatological year, and for locations with a uni-modal regime this starts after the month of minimum rainfall. Although our climatological year spanned January–December, it is flexible as the ratio defines when warm and dry, warm and wet, cool and dry, or cool and wet conditions occur, regardless of when these conditions occur. The ability to define a standard climatological year applicable to any location, using the ratio, offers a consistent basis for large-scale investigations. As the ratio worked for each location and gridded data, large-scale application is confirmed. It is notable that it worked for arid climate locations (e.g. PNO: Port Nolloth) and those without a well-defined wet-season (e.g. OUD: Oudtshoorn), as some metrics are limited for such regions. Deng et al. (2019), for instance, note that the DSI and RE metric is not suitable to characterise seasonality across China’s arid northwest river basin region, which also experiences a multi-modal wet-season. Moreover, Dunning et al. (2016) note that the metric applied is limited across arid northern WRZ regions, and the southern coast YRZ as the wet-season is not well-defined.

The score has the advantage of being easy to calculate and is the only degree of seasonality output which quantifies seasonality timing. This makes it appropriate for application across South Africa, and regions with similarly distinct rainfall regimes (e.g. Australia; Gaffney 1971), because SRZ and WRZ regimes are easily distinguished and classified with one output. This is advantageous over other degree of seasonality outputs which, without additional calculations, only classify seasonal or aseasonal regimes (e.g. Walsh and Lawler 1981). Although the score classification groupings were subjectively defined without testing, the boundaries are robust as any score can be classified, and these would not only apply across South Africa. As the scores are numerically continuous, these boundaries are valuable to explore year-to-year regime shifts (e.g. SRZ to YRZ to WRZ, and vice versa), particularly for transition region locations (e.g. CWO: Calvinia Wo; Supplementary Fig. 2). While all metrics quantifying the degree of seasonality annually are useful for such investigations, wet-season start- and end-date metrics, for instance, are not as fixed classification boundaries cannot be defined (Dunning et al. 2016; Roffe et al. 2020a). Overall, the annual scores make the ratio valuable for change and variability investigations, however, all metrics with annual outputs are. Nonetheless, convergence on one metric or a set of metrics is necessary for comparable results. Tadross et al. (2009), for instance, apply two start-date definitions which produced contrasting results with some locations demonstrating earlier and later start-dates during El Niño years, thus highlighting necessity for method standardisation. For such investigations the ratio is advantageous as, to date, it represents the only metric applicable to palaeo and contemporary records (Thackeray and Fitchett 2016), offering an invaluable means to explore long-term (> 1000 years) rainfall seasonality dynamics and associated driving mechanisms. Current applications demonstrate that the scores reliably reflect change and variability, as scores for ~ 80,000 cal. yrs BP to present demonstrate an expected Last Glacial Maximum winter seasonality peak (Thackeray and Fitchett 2016), and score changes using instrumental records compare well to literature and results from a percentile-based wet-season metric (Roffe et al. 2020b). Considering such application, and although already highlighted, it must be noted that any seasonality deviations the scores reflect are primarily due to MMR, because MMT is relatively stable (Herrmann and Mohr 2011).

Several limitations exist, and reliance on a distinct seasonal temperature cycle represents the most notable limitation. As weak seasonal temperature cycles typify tropical regions (0–23° N/S; e.g. Majaliwa et al. 2015), this limits application to extratropical regions (> 23°N/S). However, further testing is required to establish whether the ratio could provide appropriate results for tropical regions. Despite considering wet-season rainfall timing in relation to warmer and cooler months, the ratio does not consider the wet-season regime with regards to the monthly rainfall temporal distribution, thus differences in regime structure and timing, could yield similar scores. Nevertheless, the score still provides a good degree of seasonality indication, however, this limitation highlights the importance of considering the metric output(s) in relation to the desired use. This influenced our SRZ description, where distinguishing between early and late summer rainfall, for instance, was difficult; though for South Africa, a wet-season metric is most appropriate to quantitatively represent this (e.g. Liebmann et al. 2012). Moreover, Herrmann and Mohr (2011) defined numerous wet-season structures (e.g. bimodal and multimodal single wet-seasons) across South Africa, which the score cannot define, but since the method applied similarly relies on the relationship between rainfall and temperature, it offers a valuable extension to overcome this limitation.

Although considered a limitation, the coarse monthly-scale resolution does no discredit the ratio as the degree of seasonality is sufficiently defined at this scale (Walsh and Lawler 1981; Feng et al. 2013), however, some applications (e.g. agricultural seasonality) will require a metric considering a daily-scale resolution. In describing seasonality, the score does not offer a complete description. The metric developed by Feng et al. (2013) represents the only metric affording a complete description (Fig. 1), however, the degree of seasonality output does not quantify seasonality timing as the score does. If it is necessary to overcome these limitations, given the specific application, a daily-scale wet-season start- and end-date metric would be appropriate to apply with the ratio, as these metrics are comparable (Roffe et al. 2020b), and flexibility in the ratio’s climatological year offers consistency for calculations. Care must be taken as numerous start- and end-date definitions exist (Tadross et al. 2009; Smith et al. 2008; Dunning et al. 2016). Subjective threshold-based definitions are only locally applicable (Dunning et al. 2016). Objective definitions allowing large-scale application are most appropriate. For South Africa these include definitions applied in Roffe et al. (2020a) and Dunning et al. (2016). The former demonstrates utility across South Africa (Roffe et al. 2020a), however, the latter has more value for agricultural and should, for consistency, be the only definition used for crop farming applications (Dunning et al. 2016).

Application of the ratio represents the most important contribution from this research. As it relies on rainfall and temperature measurements, which are commonly measured at meteorological stations, many application avenues exist. Where records are poor or stations are limited, we demonstrate that it is easily applicable to gridded data products. Hence, the ratio would be valuable for climate model verification (Li et al. 2016), and to develop future rainfall seasonality projections (Dunning et al. 2018). Considering current research and concerns surrounding South African rainfall changes, quantifying seasonality changes and exploring variability in relation to ENSO and SAM, for instance, is possibly the most important application avenue, as such information has societal value for devising coping strategies surrounding water resource management, for example. With concerns surrounding heightened WRZ drought conditions, primarily through a poleward displacement of the austral westerlies (Sousa et al. 2018; Mahlalela et al. 2019), forthcoming work explores links between the scores and cold fronts. Overall, this represents an interesting application, where there is value in exploring seasonality characteristics, and changes and variability thereof, in relation to that of weather systems.