Towards improved seasonal rainfall prediction in the tropical Pacific Islands

The El Niño Southern Oscillation (ENSO) is a major influence on interannual variability of rainfall in stations in the tropical southwest Pacific. Predictions of seasonal rainfall, especially a season or two ahead, are of great value to these countries. This paper therefore examines the correlations over ~ 60 years between seasonal rainfall and 8 ENSO indicators at 16 island stations, allowing for lead times. The results show the influence on rainfall of the position and movement of the South Pacific Convergence Zone (SPCZ) during ENSO events, and that the Southern Oscillation Index (SOI), the sea surface temperature anomaly in the central Pacific (Niño 3.4), and the warm water volume in the eastern Pacific (WWV1) have longer lead times compared to most other ENSO indicators. These indicators can therefore be used with confidence in SCOPIC, a widely used statistical tool for prediction of seasonal rainfall. (As global climate models generally have systematic errors in their depiction of the SPCZ, they cannot yet be used directly to reliably predict seasonal rainfall in this region.) For several sites near the SPCZ, we find that a moderately good forecast of rainfall in both spring and summer can be made from indicators measured in June–July (i.e., 3–6 months in advance.)


Importance of seasonal forecasts
The small island developing states of the southwest tropical Pacific feature considerable interannual and seasonal variation in rainfall (PCCSP 2011a).This variation encompasses, but is not limited to, extreme weather and climate events such as droughts and tropical cyclones, both of which cause considerable loss and damage to settlements and to subsistence and commercial agriculture (Bettencourt et al. 2006;Mycoo et al. 2022, Sect. 15.3.4).In islands reliant on subsistence agriculture for survival, traditional adjustment mechanisms, notably changes in crops cultivated and drawing on crops that can be stored (including in the ground), can provide a measure of food security.However, such adjustments can take months to come into full effect (McGuigan et al. 2022).But overall, for small island developing states, with limited economic resources, it can take years to get development back on track after an extreme weather event, which is why these countries, already recognized as "vulnerable" in the UNFCCC (UNF-CCC 1992), are among those pushing in international negotiations for funding for loss and damage caused by climate change (Benjamin et al. 2018; Nand and Bardsley 2020)-a push that gained recognition at the COP27 conference in November 2022 (Harvey et al. 2022).
Tropical cyclones are the most common disaster-related event in the Pacific Islands, accounting for 157 (76%) of reported disasters from 1950 to 2004 (Bettencourt et al. 2006).Over the past 70 years, cyclones have continued to affect the Vanuatu and Fiji groups with 1.5-2.0 and 1.0-1.5 per cyclone season, respectively (Sharma et al. 2019).(The cyclone season is November-April.)There is wide agreement that cyclones will continue to feature with similar frequency, but probably with stronger intensity, in those Pacific islands between 10° S and 20° S and between 160°E and 170° W (Seneviratne et al. 2021, Sect. 11.7); this includes all the countries in the study region except Tuvalu (where cyclones are rare but not unknown).
Droughts, both agricultural and meteorological, are another climatic hazard that affects all countries in the study region from time to time.According to McGree et al. (2016), stations in the "South SPCZ" region experienced 7 droughts totalling 120 months in the 30 years 1981-2010. 1Availability of freshwater is a priority issue for the numerous low-lying islands with no surface water, which are subject to ENSO-related droughts, including small islands and atolls (Sinclair et al. 2012).Droughts are expected to continue as a feature of climate in the region, possibly with increased frequency (Seneviratne et al. 2021, Sect. 11.6).
Therefore, predictions of seasonal rainfall are of great value for agriculture and other purposes, especially if they can be made with reasonable accuracy a season or two ahead, as such forecasts allow some of the agricultural and social adjustments that will be necessary to be made ahead of time.

ENSO
The dominant influence on the interannual variation in rainfall in the Pacific Islands and the countries bordering the tropical Pacific Ocean is the El Niño Southern Oscillation (ENSO) (Murphy et al. 2014;PCCSP 2011a).ENSO is a Pacific-wide phenomenon, of irregular period (but typically 4-7 years) involving close coupling of ocean and atmosphere.The effects of its extreme phases are clear right across the Pacific, from Australia to Peru (Sarachik and Cane 2010).Therefore, using knowledge of the current state of ENSO should provide a good starting point for seasonal forecasts of rainfall.
In a "warm" phase of ENSO (an El Niño event), warm tropical water shifts from the western Pacific to the central Pacific Ocean, thus moving the pattern of evaporation, rainfall, and cyclones eastwards, resulting in drought in Vanuatu and neighboring islands.In many Pacific Islands, there are long-established vernacular words for El Niño which literally mean "hunger" or "nothing left in the sun." (See list of vernacular terms in Supplementary Material.)Since cyclones arise in regions of unusually warm sea surface, it is not surprising that El Niño is associated with an increased frequency of cyclones in the more eastern parts of the southwest Pacific (Terry 2007).
In the opposite phase (a La Niña event), the western pool becomes warmer than normal, giving increased rainfall and incidence of cyclones in Vanuatu, Fiji, and nearby islands.Years in between an El Niño event and a La Niña event are referred to as "neutral." The strength of the relationship between rainfall and ENSO is shown by the strong correlations between annual rainfall and various indicators of the state of ENSO, of which the Southern Oscillation Index (SOI) is the longest established (BOM n.d.)The evolution of an ENSO event (except perhaps for its inception) is now reasonably well understood in terms of the interaction between ocean and atmosphere in the tropical Pacific Ocean (Sarachik and Cane 2010).However, there remains considerable scope for improvement in the predictability of ENSO events (Santoso 2019).
Paleoclimatological evidence (coral cores) shows that there have been ENSO events at varying intensity and frequency for at least the past 400 years (Freund et al. 2019).Projections show that ENSO is expected to persist in broad form for the foreseeable future (Lee et al. 2021).

SCOPIC: a simple tool for seasonal forecasting
SCOPIC is a simple and widely used computer tool for predicting seasonal rainfall in the Pacific.It gives probabilistic predictions based on past records of the correlation of seasonal rainfall with an indicator of ENSO (Cottrill and Kuleshov 2014).A major reason for its widespread use is that having been developed with Pacific Island users in mind, it is easy for them to use, as it requires only basic computer facilities and only fairly elementary statistical and mathematical competence, and draws on only readily available datasets.This contrasts with more sophisticated seasonal forecasting based on global climate models, such as by Lee et al (2022) discussed later in this paper.Therefore, it is worth examining if the accuracy of seasonal rainfall predictions using SCOPIC can be improved by using different indicators of ENSO than those used so far.

This paper
Therefore, this paper investigates the research question: what is the best indicator of the state of ENSO on which to base predictions of seasonal rainfall in particular subregions of the tropical southwest Pacific, especially using SCOPIC?We address this question primarily via the subsidiary question: what is the indicator with strongest correlation with rainfall the most months in advance?
We do this by examining for a range of sites across the region, the correlation of rainfall against an indicator of the state of ENSO, with the indicator leading the rainfall by various intervals.The data range for indicators and rainfall is usually about 60 years (e.g., 1953-2012).We examine 16 sites from Solomon islands (3 sites), Vanuatu (3), Fiji (6), Tonga (2), and Tuvalu (2), and 8 indicators, of which the SOI, the Oceanic Niño index (Niño 3.4), and the warm water volume in various regions of the tropical Pacific turn out to be the most promising for seasonal forecasting.Further details of sites and indicators are given in Sects. 2 and 3.
We find the most promising lead correlations for forecasting are those for rainfall in spring or summer, and for sites near the South Pacific Convergence Zone (SPCZ).For such sites, we find that a fairly good indication of rainfall in both spring and summer can be made from indicators measured in June-July (i.e., 3-6 months in advance).For those sites and indicators, we extend our analysis forward in time to 2022, which includes what may be the first few years of a new phase of the Interdecadal Pacific Oscillation, for which the geographical pattern of rainfall may differ from previous decades.
Our main results are presented in Sect.4, with an extended discussion in Sect. 5.This discussion includes the effect of movement of the SPCZ, a comparison of results by season, other approaches to prediction of seasonal rainfall (including global climate models), and the possible effect of recent and future climate change.

Study area
A dominant climatic feature is the SPCZ, which is a belt of cloud running from NW to SE of the region, as shown in Fig. 1.
The SPCZ moves ~ 200 km to northeast during Vanuatu dry season (May-October), and does so also in an El Niño.As this rain belt moves away from islands near its southern edge (e.g., most of Vanuatu), they become drier, whereas islands near the northern edge of the SPCZ become wetter at this time.The mechanism for this is further discussed in Sect. 5. Thus, rainfall in both Vanuatu and Tuvalu depends strongly on the position of SPCZ, but with their drier seasons at opposite times of year and phases of ENSO.
Note that PCCSP (2011a) cautions that "the image of a continuous SPCZ with a line of high rainfall and strong convection represents the seasonal or long-term average, rather than the conditions on any single day."Also, the edge is not sharp-as discussed in Sect. 5.The SPCZ is strongest in December-February and is weaker and less well-defined in June-August.Therefore, Fig. 1 depicts an average (typical) position over a November-April season.
Table 1 lists some further details of all the sites used in this study.See also Fig. 2. The selected sites were chosen on the basis of the length and quality of their rainfall records.Records for major stations in the Pacific Islands were all carefully curated as part of the PCCSP and PAC-CSAP programs sponsored by Australia (Power et al. 2011).General climate data for many of the study sites is given in PCCSP (2011b) and/or through the Pacific Climate Change Data Portal of the Australian Bureau of Meteorology at http:// www.bom.gov.au/ clima te/ pccsp/.However, numerical time series data can be obtained only directly from the respective national meteorological services, which we did.
As can be seen in Table 1 and Fig. 2, the wettest sites in this study are Lata, Rotuma, and Funafuti, none of which has an appreciable "dry" season.Most of the other sites have a noticeable dry season in the austral winter.This seasonal variation is particularly strong at Honiara, Nadi, and Labasa, each of which is on the "dry" (leeward) side of a mountainous island.However, in contrast to some other parts of the world, in most years, there is still appreciable rain in the "dry" season.El Niño seasons can be an exception to this, with severe consequences for both subsistence and commercial agriculture.

Methods
Table 2 lists the ENSO indicators used in this study, brief definitions of each, and the data sources for them.
A season as conventionally defined is a 3-month period, although in many of the tropical locations in this study, the only marked difference in climate is between the wet and the relatively dry seasons, which are typically each about 6 months long (Kumar et al. 2014).Therefore, the first step in assessing the correlations we assess for their usefulness for seasonal prediction of rainfall, is as follows: for each site and each pair, calculate the 3-month centered average of rainfall P and indicator I for each month m.Call these averages P 3 and I 3 .For each pair, we then calculate the correlation between P 3 (m + n) and I 3 (m) across all years for which the relevant data is available (which is usually about 60 years), where n is the lead time (in months).If n is negative, it is called a lag.
For historical reasons-mainly for compatibility with an earlier study by Tigona and de Freitas (2012)-our main calculations use not the rainfall P but a rainfall index P', which is effectively the cube root of P. Spot checks indicate that the transformation of rainfall to rainfall index has the effect of slightly increasing the corresponding correlation coefficients with SOI and other "predictors" compared to those calculated directly with rainfall (with differences less than 0.02 in |r|), but without changing the lead time corresponding to maximum correlation. 2hus, to calculate the correlation in which (e.g.) SOI leads rainfall index by 4 months, the 3-month average of SOI centered on (say) Feb 1961 is paired with the 3-month average of rainfall index centered on June 1961, and so on, with the correlation coefficient calculated across all such pairs for that site.So, what this paper refers to as a "4-month lead time" has a gap of only one month between the last month of the 3 months over which an indicator is averaged to the first month of the 3-month period over which rainfall is averaged. 3o compare the strength of correlations between different times of year, we fixed the lead time n, and calculated the correlation between an indicator averaged one season and the rainfall averaged over the following season.For example, for each particular site and indicator, to examine "predictions" of spring rainfall, we considered each pair of I 2 (JJ) and P 3 (SON), where I 2 (JJ) denotes the average value of the indicator over June-July and P 3 (SON) denotes the 3-month centered average of rainfall over September-October-November.In effect, this corresponds to n = 3.5.We then calculate the correlation over such data pairs over all available years (typically N ~ 60), and similarly for "predictions" of rainfall in summer (DJF), autumn (MAM), and winter (JJA).

Results
For each site, we first calculated the correlation coefficient for each pair of indicator I 3 and rainfall index P' 3 , for lead times n ranging from − 12 to + 12 months.We denote by r the average of this correlation coefficient over all months  R), though it is a separate question whether that correlation is strong enough to be useful for predicting rainfall.Guided by our subsidiary research question, for each site and indicator we then identified the maximum magnitude of r.These values are shown in Table 3, along with the corresponding value of lead time n.Note that Table 3 shows values of r with their actual signs; some are negative, notably for indicators Niño 3.4 and WWV1, and for site Funafuti signs are the reverse of those for most other sites studied.Based on Table 3, we then selected the sites with the most promising combination of large correlation and long lead time.In practice, this meant |r|> 0.35 and n > 3.For the sites thus selected, Fig. 3 shows charts of r vs n for all indicators studied.(Note that in Fig. 3, the sign of r is reversed for some indicators to enable easier comparison with other indicators.) Several features emerge from Table 3 and Fig Physical reasons for these findings are discussed in Sect. 5.

Seasonal variation of correlations
Tables B1-B4 in the Supplementary Material show the correlations between ENSO indicators and rainfall for each of the 3-month seasons (namely austral spring, summer, autumn, and winter), each calculated with an effective lead time of n = 3.5 months and for the periods shown in Table 2 (i.e., for ~ 30 to ~ 50 years up to 2012).The most striking result is that the correlations are much stronger for rainfall in summer and spring than for rainfall in autumn or winter.For example, the correlation between summer (DJF) rainfall and Niño 3.4 in September-October exceeds 40% for 12 of the 16 sites studied, including 8 for which it exceeds 50%, and similarly for WWV1.For winter rainfall, the corresponding figures are 2 for Niño 3.4 and 1 for WWV1.Similarly at Port Vila, all 8 indicators except SST9 and WWV2 have correlations exceeding 50%, whereas for

Recent strong correlations
There is wide agreement that the Interdecadal Pacific Oscillation changed phase around 2000 (e.g., Dong and Dai 2023), and some indications that it may have changed again around 2015 (Weir et al. 2021).It is therefore desirable to use more recent data to check the extent to which the most promising indicators remain promising from about 2012 onwards.

Movement of the SPCZ
The main effect of ENSO on rainfall in the study area is the way in which it promotes movement of the SPCZ.The most promising sites (Port Vila, Aneityum, Nadi, Nabouwalu, and Funafuti) all lie close to an edge of the SPCZ, as shown in Fig. 1.They are therefore among the sites most strongly affected by movement of the SPCZ to the NE in an El Niño event or to the SW in a La Niña event, via the mechanism sketched in Fig. 4. The mean position of the southern edge of the SPCZ rain belt is very close to that of the typical "neutral" year shown in Fig. 1 which shows Port Vila lying just south of that edge, as indicated in the schematic diagram, Fig. 4a.Therefore, as the SPCZ moves to the SW in a La Niña, Port Vila which was just outside the central rain belt4 (position N in Fig. 4a), becomes well inside the rain belt (position LN in Fig. 4a), which increases the Nov-Apr rainfall, from ~ 1400 to ~ 1800 mm.Conversely, as the SPCZ moves to the NE in an El Niño, Port Vila becomes further outside the central rain belt (position EN in Fig. 4a, thus causing a decrease in Nov-Apr rainfall from wet (~ 1400 mm) to relatively dry (~ 1100 mm).In a more severe El Niño event (SOI < − 10, say), the movement of the SPCZ can be much greater, causing a more dramatic decrease in rainfall.Thus, a positive increase in rainfall tends to go with a positive SOI (i.e., a La Niña), so that the correlation of rainfall with SOI is positive.Similar considerations apply at Aneityum, Nadi, and Nabouwalu.
However, although Fig. 1 suggests that similar factors should apply at the two sites in Tonga (Vava'u and Ha'apai), Table 3 indicates that the correlations for the Tonga sites, and even more so the lead times, are less promising than for those in Fiji and Vanuatu.A possible reason for this difference is suggested by Fig. 4b, namely that the displacement of the SPCZ in an El Niño event is less in the eastern part of the study region (e.g., in Tonga) than in the western parts (e.g., in Vanuatu) and similarly for the displacement of the SPCZ in a La Niña event (Brown et al. 2020).It may also be relevant that the Tonga sites are a little further away from the central rain belt of the SPCZ, as indicated in Fig. 4b.This would imply that the rain arising directly from the SPCZ is a smaller proportion of the total rainfall in a Tonga site like Vava'u than in a Fiji site like Nadi, so that movement of the SPCZ due to ENSO has less impact on rainfall in Vava'u than in Nadi.These surmises are broadly supported by the maps of rainfall anomalies provided by Murphy et al. (2014).
Conversely, at Funafuti, which lies near the northern edge of the SPCZ, these effects are reversed, with La Table 4 Correlations of rainfall (for periods SON or DJF and SONDJF) against indicator (June-July) for the most promising stations and indicators, for periods indicated (i.e., 1960-2012, 1991-2012, 2012-2022) Niña years being drier than neutral ones, as Funafuti tends to move out of the rain belt as the SPCZ moves towards the SW.WWV1 measures the volume of warm water (> 20 °C) in the East Pacific (5° N-5° S, 155° W-80° W).It has been known for some time that an increase in WWV1, and a corresponding increase in the depth of the thermocline in the eastern Pacific and thus in the temperature of the upwelling water, is a major driving force for an El Niño ("warm phase") event, and conversely for a La Niña event (Sarachik and Cane 2010, Sect. 1.3).Hence, WWV1 can be expected to be a good predictor of the phase of ENSO and thus of rainfall in the tropical western Pacific.That it has not been widely used in the past is largely because measurements of WWV1 as such were not made before the 1980s, unlike measurements of SOI which go back > 100 years (see Table 2).

Less promising indicators for rainfall prediction
• EMI-This measure pertains most closely to El Niño events of the Central Pacific (EN-CP or El Niño "Modoki") flavor.Freund et al. (2019) report that since about 1980, El Niño events have more often had this EN-CP flavor, meaning that their strongest warm anomaly of SST is in the Central Pacific, as opposed to "classical" El Niño events, in which the warm anomaly is in the Eastern Pacific (EN-EP).Consequently, for the period examined here, EMI performs better than might have been expected as a predictor of rainfall, even though our analysis did not distinguish such events from those of the "normal" Eastern Pacific (EP) type.Even so, its maximum correlation in Table 3 of 0.33 is too low to warrant further investigation.• OLR-Data for this parameter (effectively a measure of cloud cover) is across a wide range of longitude (160°E to 160°W) and extending well northwards of our study region (15°N to 15°S).It might be thought that as cloud cover at a particular location varies from week to week, OLR would not be a good predictor of rainfall for more than a week or two in advance at any particular location, even though it offers high r at n = 0. Nevertheless, our results suggest that OLR may offer performance comparable to that of WWV1 as a predictor of seasonal (3-month) rainfall.We surmise that this may be because OLR indicates the presence of rain somewhere in the study region, and as winddriven rainfall fronts move over a region, this averages out over a 3-month period.
The following indicators give poor predictions, for the reasons indicated.
• SST9-Although its formal definition is more complicated, in effect this parameter is a measure of the sea surface temperature in the Coral Sea, i.e., roughly 150°E-175° E, 2° N-10° S. Therefore, it is unlikely to be a good predictor of rainfall outside that area.• WWV2 measures the volume of warm water (> 20 °C) in the West Pacific, 5° N-5° S, 120° E-155° W. Thus, its peak coincides with higher rainfall there, and so is not much use as a predictor.• WWV3 measures the volume of warm water (> 20 °C) across the entire equatorial Pacific, 5° N-5° S, 120° E-80° W. While of interest as a measure of the extent of the ENSO warm phase, it is averaged across so broad an area that its correlation coefficients with rainfall in any more specific area are too low to be useful as a predictor of rainfall.

Seasons with most promise for good predictions of rainfall
Our results clearly show that the correlations between ENSO indicators and rainfall several months later are much stronger for rainfall in summer and spring than for rainfall in autumn or winter, for most indicators and most sites studied (see Supplementary Material).This strongly suggests that predictions of seasonal rainfall based on these correlations will generally be much more accurate for rainfall in summer and spring than for rainfall in autumn and winter, which is consistent with Table 4 and with what Cottrill and Kureshov (2014) found for a smaller set of indicators.
Physically, this difference can largely be attributed to the way in which ENSO events evolve, with the first signs appearing in winter, and the full effects showing in summer (Sarachik and Cane 2010).The strong correlations with WWV3 in summer but not earlier are another indication of evolution, since WWV3 shows when an ENSO effect has run its full course (i.e., is felt across a wide range of longitude).
Mathematically, the correlations in Table 4 and Table 2 (between indicator values in JJ and SO and rain in SON and DJF, respectively) are much stronger than those across the whole year (Table 3) because the later are "diluted" by the weak correlations for rainfall in MAM and JJA.

A basic approach to rainfall prediction
SCOPIC is a simple and widely used computer tool for predicting seasonal rainfall in the Pacific.A major reason for its widespread use is that having been developed with Pacific Island users in mind, it is easy for them to use, as it requires only basic computer facilities and only fairly elementary statistical and mathematical competence, and draws on only readily available datasets.
With our results showing a strong correlation between WWV1 and rainfall several months later, we incorporated WWV1 into a copy of the SCOPIC program, and ran hindcasts at each site for each of the four seasons, separately using Niño 3.4 and WWV1 as "predictors.""Predictions" had broadly similar accuracy for each of these indicators, as measured by tercile hit rates. 5Each of these indicators gave hit rates over ~ 60 years of around 45-60% at most sites, with WWV1 performing noticeably better than Niño 3.4 for predicting DJF rainfall from 3 months in advance.
As noted in Sect.4, the strongest indicators for prediction of rainfall (SOI, WWV1, and Niño 3.4) measured in winter (JJ) can give reasonably good predictions of rainfall at key locations not only for spring (SON) but also for summer (DJF).Of particular interest are the results in Table 4 over the most recent 10 years or so, i.e., since 2012.This period includes what may be a shift in the phase of the Interdecadal Pacific Oscillation (IPO) (Dong and Dai 2023) with a concomitant shift to the southwest of the SPCZ (Weir et al. 2021).It includes also the incidence of some particularly severe tropical cyclones (TCs Pam (2015), Winston (2016), Gita (2018), Harold (2020)-all reaching category 5, which is the highest rating-and TCs Judy and Kevin (both cat.4) which hit Port Vila in the same week of 2023).Such an increase in severity is a predictable physical consequence of increasing sea surface temperatures in the region, as noted by IPCC (2021).Although it is rash to attribute too much statistical significance to correlations over only ~ 10 years, it is nevertheless striking that those between SOI in JJ and rainfall 6 months later (DJF) exceed 60% at both Nadi and Vila, as does that with Niño 3.4 at Vila.
In both these places, Table 4 shows the correlations between this and other indicators in the 2-month "warning" period (JJ) against rain in the 6-month period of what is normally the bulk of rainfall (Sep-Feb).This is strong predictive power by the normal standards of climatology.The results for Aneityum, slightly further south in Vanuatu than Port Vila, are however much weaker, even when [slightly] strengthened by using 3-year averages for both indicators and rainfall (as in Fig. 5).For comparison, also shown in Table 4 are recent results for Rarotonga (from www.bom.gov.au), 6 which lies considerably further east, near the eastern end of the SPCZ (Weir et al. 2021).Rainfall there, particularly when measured over the 6 months Sep-Feb, shows a strong correlation with WWV1, an indicator characterizing the eastern side of the Pacific.Funafuti normally lies inside the SPCZ but towards the northern edge of the SPCZ (Fig. 1), so its rainfall over Sep-Feb correlates fairly well with atmospheric indicators over 1991-2012.But after 2012, as the SPCZ moves southwesterly, rainfall there appears to correlate well with indicators only over SON, but poorly over DJF (see Table 4).
Within the study region, in those island groups south of ~ 10° S, very high rainfall events are commonly associated with tropical cyclones.Unfortunately, broad statistical methods such as used here can predict only a probability of above normal rainfall across a subregion, but cyclone impact is typically more localized.This limits the usefulness of such methods for predicting places most likely to be damaged.Nevertheless, the correlations since 2012 in Table 4 are consistent with the incidence of severe tropical cyclones over that period.
Because a drought typically impacts a much wider region than a cyclone, a seasonal forecast of below normal rainfall is typically of more general use, not least to farmers.An attempt by Solofa and Aung (2004) to verify this by establishing a statistical relation between agricultural productivity and ENSO for Samoa was thwarted by lack of data on subsistence production.However, Table 4 and Fig. 5 would suggest that such drought periods seem to be becoming rarer in several countries of the region.

Using other or multiple indicators
A small step up in sophistication of seasonal forecasting is to first ascertain if this year is likely to include an El Niño or La Niña event, and then to base the seasonal rainfall prediction not on a correlation across all years on record, but rather on a correlation for those years which include such an event.In some cases, such as in an El Niño year at Rarotonga in the southern Cook Islands, the correlation of rainfall with a good predictive indicator can exceed 80% (Weir et al. 2021).(This enhancement works best if "year" is taken to mean "enso year" (from May to April) rather than calendar year, as this brings together the early indication in winter with its consequence in the following summer (wet) season.) Similarly, if it can be foretold that a forthcoming El Niño is of the CP-type, then EMI, which is a measure of CP El Niño, would give better predictions of rainfall than it does when applied to all available years, as we have done here.
A further step up, going beyond SCOPIC, would be to draw simultaneously on several indicators, as Magee et al. (2020) do in their method for prediction of the probability of a tropical cyclone in a subregion of the SW Pacific.As tropical cyclones originate in, and are maintained by areas of exceptionally warm SST, it is not surprising that the incidence of cyclones in the central Pacific (Cook Islands, French Polynesia) increases in El Niño events.For each subregion, they apply a multivariate regression (fitted for each subregion), comprising an ENSO index (chosen for best fit in that subregion) with indexes for the Southern Annular Mode and the Indian Ocean Dipole.

Global climate models as predictors of local rainfall
Global climate models (GCMs) use supercomputers and digital versions of the equations of motion for air and water to model the evolution over time of the state of the atmosphere and ocean from a known state.They are a major tool for short-term (< 8 days) weather forecasts and for long-term (decades or even centuries) projections of climate, but less so for medium-term (seasonal) forecasts.
Because they require expensive supercomputer facilities, they can be run directly only by rich countries, but some outputs are kindly made available to the national meteorological services of developing countries, including the Pacific Islands.GCMs differ in the details of how they parameterize various meteorological processes, but their long-term performance is compared by the long-running Coupled Model Intercomparison Project (CMIP), of which the latest iteration (CMIP6) was assessed in 2021 by IPCC WG1 (2021).Already the proportion of tropical cyclones that are especially intense (i.e., category 4 or 5) has increased globally (IPCC 2021, Sect.A3.4) and this is reflected in the recent experience of Vanuatu and Fiji.The IPCC expect this trend to increase with further global warming, as a consequence of basic physics (IPCC 2021, Sect.B2.4).
The APEC Climate Centre in Korea is making a commendable effort to make GCM forecasts more useable by Pacific Island meteorological services by means of a hybrid seasonal prediction system (PICASO), which aims to combine the strengths of both statistical and dynamical systems (Lee et al. 2022).PICASO draws on several GCMs and aims to produce predictions that are less broad-scale than the whole of the south-west Pacific, but published results so far are available only up to 2016.A fundamental difficulty at present is that the resolution and parameterization of GCMs is still inadequate to show the SPCZ in its correct place and with its correct diagonal (NW-SE) direction (Narsey et al. 2022).As a specific example of this, Beischer et al. (2021) find that the current Australian model (ACCESS-S1) does better than its predecessor (POAMA) in modelling the SPCZ but still gets it wrong.This factor limits the usefulness of GCMs for directly predicting seasonal rainfall in those islands most influenced by the position of the SPCZ.Consequently, for such islands, the predictions for the wet season so far obtained from PICASO are, if anything, inferior to those from SCOPIC (Lee et al. 2022), or-it appears-to those from our current, relatively crude, study.Although PICASO does produce rainfall predictions for southern autumn and winter that are noticeably superior to those from SCOPIC it is the rainfall in southern spring and summer that have the most effect on agricultural production (Medina Hidalgo et al. 2020).
In an effort to compensate for this weakness, we had proposed to take daily output "snapshots" from one of the GCMs which had a fair representation of the SPCZ, but which showed it displaced from its correct position.These outputs could then be compared to daily weather maps and/ or satellite photos of cloud cover to find a systematic way to adjust (downscale) the model outputs at particular locations (e.g., southern and central Vanuatu), so that the adjusted model forecasts could be used for future seasonal predictions of rainfall.Regional climate models (like GCMs but on a smaller area) offer some improvement in projections of the SPCZ and its orientation and changing position (Evans et al. 2016), but a review by Brown et al. (2020) concluded: "persistent biases in, and deficiencies of, existing models limit confidence in future projections of the SPCZ.Improved climate models and new methods for regional modelling might better constrain future SPCZ projections, aiding climate change adaptation and planning among vulnerable South Pacific communities." Our proposed approach would appear to be more suitable for use in the Pacific Islands than direct use of such complex models, but we have not yet been able to pursue it because of data limitations.

Effect of global climate change
Of particular relevance to the Pacific, the IPCC Assessment concluded that the CMIP6 suite of global climate models strongly indicate that ENSO will remain the dominant mode of interannual variability in a warmer world (Lee et al. 2021), though they differ in the extent to which its amplitude (in SST and in rainfall) may change over time (Hu 2021).Recent analysis by Geng et al. (2022) indicates that the signal from an Eastern Pacific (EP) ENSO event will become noticeably stronger as a result of climate change as soon as the 2030s, well before noticeable change in Central Pacific events.This suggests that the WWV1 indicator, which is based on ocean layers in the eastern Pacific, will become an even better predictor of seasonal rainfall than it is now.Such predictions will become even more useful if the frequency of El Niño or La Niña events increases in future, as Cai et al. (2023) suggest may be the case.

Conclusions
For Solomon Islands, Vanuatu, Tuvalu, and most of Fiji, the warm water volume in the eastern Pacific (WWV1) turns out to be about as good a predictor of rainfall as the sea surface temperature in the central Pacific (Niño 3.4), and possibly even better for stations in the central Pacific.WWV1 can therefore be used with some confidence in SCOPIC, a widely used statistical tool for prediction of seasonal rainfall.Such statistical tools show their best performance for predictions of seasonal rainfall in austral spring and summer, and for sites near the edge of the SPCZ.As global climate models generally have systematic errors in their depiction of the South Pacific Convergence Zone (SPCZ), they cannot yet be used directly to reliably predict seasonal rainfall in this region.A more promising approach may be to apply them to specific subregions, but with local corrections to those systematic errors.

Fig. 2
Fig. 2 Maps of the region showing all 16 study sites and mean monthly rainfall at each a more western sites (Solomon Islands, Vanuatu) and b more eastern sites (Fiji, Tonga, Tuvalu).Monthly . 3. a.The most promising sites (Port Vila, Aneityum, Nadi, Nabouwalu, and Funafuti) all lie close to an edge of the SPCZ, as shown in Fig. 1. b.The most promising indicators of those studied are SOI, Niño 3.4, WWV1, and (to a lesser extent) OLR and EMI.c.The least promising indicators, for differing reasons, are SST9, WWV2, and WWV3.

Fig. 3
Fig. 3 Charts of correlation r (between rainfall index and indicator, both averaged over 3 months) against lead time n for selected sites and for all indicators studied.a Port Vila, b Aneityum, c Nadi, d Nabou-

Fig. 4 a
Fig. 4 a Schematic diagram illustrating relative positions of SPCZ (shaded area) and Port Vila (big dot), in La Niña PV(LN), neutral PV(N), and El Niño PV(EN) wet seasons.Lines represent contours of rainfall (mm) for Nov-Apr.b Map of rainfall in a moderate El Niño event.Data is average over 1979-2018.Yellow line is line of maximum rainfall; red dashed line is corresponding position in a neutral year; PV, ND, HA, and VV indicate respective positions of sites Port Vila, Nadi, Ha'apai, and Vava'u (adapted from Brown et al. (2020))

Fig. 5
Fig. 5 Charts of rainfall (mm, in SON or DJF as indicated) and indicator (JJ preceding) over period 1991-2022 for stations a Port Vila with WWV1, b Aneityum with Niño 3.4, c Funafuti with WWV1.d

Table 1
Selected sites used for primary rainfall analysis.Data periods range from 34 to 70 years, with 0 to 1.6% of missing data (main source: http:// www.bom.gov.au/clima te/ pccsp/; see alsoPCCSP (2011a, b)) a Except for Tonga sites, which are degrees West b BOM portal has this station, but named as "Santa Cruz"

Table 3
Correlation coefficients r between rainfall index and various ENSO indicators for periods up to 2012 with the starting dates shown in Table2.Tabulated values are max |r| with (in brackets) the corresponding number of months n by which the indicator leads rainfall.A range of months indicates a flat peak to curve (within 0.02 in r).All variables expressed as 3-month running averages.Italics indicates correlations with magnitude greater than 0.4 and n greater than 3 with curve flat.See caution in text (sect.4 para 1) about statistical significance of entries Max correlation of rainfall index and (corresponding lead time) . Bold entries are for strong correlations (|r|> 0.40), italicized for very strong (|r|> 0.60).Italics indicate very strong correlations (|r|>0.60).Such values are significant at 1% level for 1991-2012, but only at 5% level for 2012-2022.See text sects.4.2 and 5.4