A common approach to anticipate SFOs is to focus on a specific predictability source, e.g., strong tropical heating associated with ENSO or the MJO. However, many potentially predictable signals may be evolving at any given time (Albers et al., 2022), and the constructive or destructive interference between each signal's teleconnections may enhance or degrade the overall predictable forecast signal for variables that we are interested in, e.g., southwest Asian precipitation. Thus, it is more desirable to use a method that considers all relevant signals and their combined influence to anticipate the overall likelihood of a skillful forecast over the region of interest. Here, following Sardeshmukh et al. (2000), the theoretical expected skill of a perfect, infinite ensemble member forecast, ρ∞(τt) (Eq. 5), is selected to identify SFOs, based on the method's past success. In particular, ρ∞ is calculated using the pattern correlation version of the LIM signal-to-noise ratio, S2 (Eq. 6; Newman et al., 2003), and is evaluated over the southwest Asian domain for each forecast lead time τ and each initialization date t. As a result, S2 and ρ∞ are a function of time but not space: 5ρ∞τ,t=S2(τ,t)S2τ,t+1S2τ,t0.5,6S2τ,t=tr[Fτ,t]tr[Eτ]. S2 is determined using Fτ,t, the forecast signal covariance matrix determined at a given lead time, which indicates the strength of the predictable signal in the forecasts, and Eτ, the forecast error covariance matrix which represents lead-dependent, unpredictable “noise”: 7Fτ,t=〈x^t+τx^(t+τ)′〉,8Eτ=C0-GτC0Gτ′, where ′ denotes the matrix transpose. Note that E is not a function of time, which is consistent with the assumption of state-independent noise (Eq. 2), but does vary with forecast lead time τ.

We define SFOs as the top 20 % of expected-skill forecasts as this subset accurately identifies significantly more skillful forecasts for a range of lead times (Fig. 2). The ACC and PCC during these dates are compared to the skill when, instead of expected skill, the top 20 % of Niño3.4 amplitude and RMM amplitude values are used to identify periods of elevated skill. The skill during these three subsets of forecasts (ρ∞, Niño3.4, RMM) is compared to the skill of the remaining 80 % of expected-skill forecasts, and the 95 % confidence level in the skill differences during the three subsets is assessed nonparametrically, using bootstrapping with replacement. Similar skill differences were found for a range of 10 %–25 % of the forecasts in the SFO group, and 20 % was chosen because it provided the greatest number of samples – useful for further separating forecasts by ENSO and MJO phase later – but was small enough so that the subset has significantly elevated skill.

A relative-risk ratio is used to quantify shifts in the likelihood of an SFO occurring as a function of ENSO, MJO, and SPCZ OLR strength. This is done, for each index, by determining the fraction (FRAC) of SFOs initialized on days with index values of varying amplitude: 9FRAC=no.SFOs/no.dates. For ENSO and SPCZ OLR, changes in SFOs during positive and negative index values of varying threshold are considered, while RMM is always positive. Instead, we assess changes in SFOs during MJO phases 2–3 or 6–7 and increasing RMM thresholds. To determine the relative risk of an SFO compared to the probability of one occurring on any random day, we divide FRAC calculated for each threshold and index group by 0.2 – since for the top 20 % of expected-skill dates, the chance of one occurring on any date in the forecast period is 0.2: 10relativerisk=FRAC/0.2. As an example, for weeks 3–4 SFOs when Niño3.4 > 1.5, 117 SFOs are found during the 269 d exceeding that threshold, corresponding to FRAC = 0.44 and relative risk = 2.2. The robustness of these estimates is evaluated by determining the 95 % confidence bounds around the relative-risk estimates using bootstrapping with replacement.

The advantage of using high expected skill to anticipate SFOs is that it measures when the combined signal of all forcings (e.g., ENSO, MJO) is high relative to unpredictable noise. High expected skill occurs during periods of constructive interference between signals, while low expected skill reflects periods of deconstructive interference (e.g., Farrell, 1988; Farrell and Ioannou, 1996; Albers and Newman, 2019), and such interference is more intermittent than the individual forcing elements (Figs. 6, 8). As such, despite what is shown in Figs. 2–4, many high-expected-skill dates occur during strong ENSO and MJO events, as indicated by the overlay of SFOs (black dots) with time series of Niño3.4 (Fig. 6) and RMM (Fig. 8). The bottom 20 % of expected-skill forecasts are also shown by the vertical light gray lines to contrast the higher-frequency expected skill with the lower-frequency Niño3.4 and RMM. The correspondence to Niño3.4 is considered first. Both El Niño events of 1983 and 2016 coincided with high-expected-skill dates at weeks 3–4 and 5–6, though on different dates; conversely, the 1998 event was not associated with any high-expected-skill dates at weeks 5–6 but was for weeks 3–4. Strong La Niña events, such as in 1999, also reflect periods of high expected skill. Still, there are many high-expected-skill forecasts initialized on dates with weak Niño3.4 values, as in 2017, since other processes – including ENSO-related heating not captured by Niño3.4 – can produce a high signal-to-noise ratio. Moreover, some of the lowest-expected-skill dates occur during strong ENSO events, such as in 2016 for weeks 3–4 at the beginning of February, suggesting other processes may have been destructively interfering with the ENSO-related component.

High Niño3.4 index amplitude during both El Niño and La Niña events leads to increases in the risk of SFO occurrence, though more strongly during the former than the latter (Fig. 7). There is a greater relative risk for SFOs in weeks 5–6 than weeks 3–4, suggesting that at longer lead times within the subseasonal forecast period, ENSO conditions are increasingly important for SFOs. However, it is important to note that skill during these periods is overall lower than for weeks 3–4 (Figs. 3–4), which could be due to the limited capability of ENSO alone to impact predictability and/or to elevated noise. The asymmetric relative risk during El Niño and La Niña conditions may reflect the fact that there are more frequent high-amplitude El Niño events than La Niña events, increasing the number of samples at higher Niño3.4 thresholds. Indeed, Niño3.4 exceeds 1.5 ∘C on 269 d, compared to 192 d where Niño3.4 is less than -1.5 ∘C. The stronger response during El Niño conditions than La Niña could also be consistent with Hoell et al. (2018a), who found precipitation shifts during both CP and EP El Niño events but only CP La Niña events, although future work is needed to better explore these nuances.

Discerning a relationship between MJO phases 2–3 and 6–7, the phases that impart known teleconnections to southwest Asian precipitation (Hoell et al., 2018b), can be more difficult given the more transient nature of the MJO compounded with transient expected skill (Fig. 8). Only the relationship between RMM and weeks 3–4 expected skill is considered, as an MJO teleconnection at 5–6-week lead times is not physically plausible (e.g., Tseng et al., 2018). Still, we do find that particularly strong events for phases 2–3 and 6–7 increase the relative risk of weeks 3–4 SFOs, though sampling introduces spread into these estimates (Fig. 9). Some particularly high-amplitude MJO events, including phases 2–3 in 1985 and 1993 and phases 6–7 in 2005 and 2018, overlap with periods of weeks 3–4 high expected skill, while some weaker-amplitude events overlap with some of the lowest-expected-skill dates, such as phases 2–3 in late January 2002. The strong RMM phases 6–7 are also associated with an increase in the relative risk of SFOs, which increases at lower RMM thresholds compared to in phases 2–3 and does not display the exponential increase at the highest thresholds. These subtle differences in relative-risk sensitivity could reflect true differences in the MJO teleconnection to the region or could be due to sampling, as there is high uncertainty in the relative-risk estimates given the small number of events observed at such high thresholds.

First, we consider the patterns preceding anomalously wet and dry periods regardless of ENSO phase, where “wet” and “dry” are defined using the top and bottom terciles of southwest Asian precipitation anomalies, respectively. Wet and dry dates that were associated with weeks 3–4 high-expected-skill dates initialized 18 d earlier and were also characterized by a PCC > 0 are considered. A lead time of 18 d is chosen because it falls within the weeks 3–4 forecast period and provides the clearest circulation structures, which are similar but weaker at longer lead times (not shown). An 18 d lag is also consistent with the circulation response to tropical diabatic heating anomalies discussed in Jin and Hoskins (1995), which peaked about 15 d after the heating occurred. For these skillful, high-expected-skill forecasts associated with the development of anomalously wet or dry precipitation anomalies, we consider the composite circulation and heating patterns observed at the time of initialization, meaning 18 d before the anomalous precipitation was observed.

Figure 10 shows that during weeks 3–4 SFOs initialized before predictable wet and dry periods over southwest Asia, anomalies are roughly equal and opposite in sign. Before dry periods, positive OLR anomalies are located over the western and central tropical Pacific, signifying suppressed convection, while a 200 hPa anticyclone (positive Ψ200 anomaly) is located over southwest Asia, consistent with downward vertical motion and suppressed precipitation. Conversely, predictable anomalously wet periods are associated with enhanced anomalous central Pacific convection and a cyclonic Ψ200 anomaly over southwest Asia. One feature present during dry initializations is a small but statistically significant negative OLR anomaly in the eastern Indian Ocean, which does not have a counterpart during wet initializations. Southwest Asian precipitation is strongly linked to heating variability in this location (Hoell et al., 2012), and the results here suggest that the relationship might be particularly important for anomalously dry periods.

Section 3.1 indicated that, while anticipating SFOs based on the Niño3.4 index alone is less successful than expected skill (Figs. 3–4), periods of strong ENSO activity increase the likelihood of a forecast of opportunity occurring, particularly during the strongest events (Fig. 7). During either ENSO phase, periods of anomalously high and low precipitation can occur due to transient disturbances forming along the subtropical jet. However, the manner in which precipitation anomalies develop differs between El Niño and La Niña, due to ENSO's influence on the mean jet and baroclinic waves (Shapiro et al., 2001), whose life cycles differ under different mean states (Thorncroft et al., 1993). This section examines how predictable wet and dry initializations differ by ENSO phase given the hypothesized differences in teleconnections in each phase.

Splitting dry and wet forecast initializations into periods when Niño3.4 is positive or negative to reflect El Niño or La Niña conditions, without losing any samples, indicates that even when preceding same-signed precipitation anomalies, El Niño and La Niña conditions are associated with different large-scale circulation patterns (cf. Fig. 11a, c and b, d). By construction, there are clear differences in SST and OLR associated with El Niño and La Niña conditions, as well as North Pacific Ψ200 anomalies associated with ENSO-like tropical heating (Winkler et al., 2001; Breeden et al., 2020; Henderson et al., 2020). During La Niña conditions, dry periods include an anticyclonic anomaly over southwest Asia, while during dry El Niño initializations there are cyclonic features north and east of southwest Asia and weak anomalies directly over the region (cf. Fig. 11a, c). In contrast to the circulation pattern during dry El Niño periods (Fig. 11c), during wet periods, El Niño conditions are associated with an amplified Ψ200 pattern, with two high-amplitude cyclonic anomalies located over Eurasia (Fig. 11d). Conversely, at the time of initialization during wet La Niña periods, negligible Ψ200 anomalies are observed (Fig. 11b).

What distinguishes rainy La Niña or El Niño periods from dry La Niña or El Niño periods? While the heating and SST dipole patterns are consistent with each ENSO phase for both wet and dry periods, there are differences in heating strength and location (cf. Fig. 11a, b and c, d). Dry La Niña initializations include stronger negative SST anomalies and suppressed convection in the central Pacific compared to rainy periods, which instead involve enhanced convection over the Maritime Continent. Dry El Niño periods include stronger suppressed convection over the Maritime Continent than wet El Niño dates, coinciding with a hint of a wave train emanating from the eastern Pacific across North America and the North Atlantic. Dry La Niña dates are more common than wet La Niña dates, 84 vs. 67 d, while wet El Niño dates are more common than dry El Niño dates, 96 vs. 57 d, which is consistent with past research linking seasonal mean departures of southwest Asian precipitation to ENSO (Hoell et al., 2018a).

Differencing the dry and wet composites between each ENSO phase reveals the common element of suppressed SPCZ convection and cooler central Pacific SSTs during dry periods relative to wet periods (Fig. 12). Dry periods during El Niño conditions are associated with warmer SSTs in the eastern Pacific than are wet periods (Fig. 12b), while no such differences in SSTs or OLR are observed in the eastern Pacific during La Niña conditions (Fig. 12a). While distinct from one another, the Ψ200 patterns during both El Niño and La Niña conditions place an anomalous anticyclone over southwest Asia during dry events, consistent with suppressed precipitation. The Ψ200 patterns during dry versus wet periods differ, with La Niña conditions displaying weak anticyclonic anomalies in the subtropical North Pacific and North Atlantic and El Niño conditions associated with an upper-level wave train emanating from the eastern tropical Pacific, across the North Atlantic to Europe, potentially linked to the anomaly over southwest Asia. The orientation of such a wave train is consistent with the evolution described by Shaman and Tziperman (2005), who found a northeastward-propagating wave train emanating from the eastern central Pacific during strong ENSO events, which ultimately modulated Tibetan snow depth. Thus, while the heating difference between dry and rainy periods is similar regardless of the ENSO phase, the impact of the anomalous heating on the circulation is different but coincidentally yields a reduction in precipitation over southwest Asia. The different circulation responses are consistent with the modified mean states of each ENSO phase, though more work is required to further understand these nuanced relationships, preferably with a larger sample size. Dry baroclinic modeling experiments could be useful in disentangling the role of the basic state and thermal forcing in producing this response.

Given the OLR anomalies in the SPCZ region noted during both predictable wet and predictable dry forecast initializations (Figs. 10, 12), a time series of OLR over the region was selected for a final metric to consider related to weeks 3–4 SFOs. Similarly to considering Niño3.4 and RMM, the relative risk of an SFO occurring increases significantly as the standard deviation of SPCZ OLR anomalies increases (Fig. 13). The response during negative and positive SPCZ OLR anomaly values is more symmetric than the risk associated with an increasing Niño3.4 threshold, which indicated a greater relative-risk increase during El Niño than during La Niña conditions (Fig. 7), or comparing the impact of MJO phases 2–3 vs. 6–7 (Fig. 9). This symmetry is further supported with the 18 d lagged regression of the southwest Asian precipitation time series with OLR (Fig. S2), although the regression pattern OLR anomalies are weaker than the composite OLR during the SFOs considered in Figs. 10 and 12. The SPCZ OLR time series is correlated with the Niño3.4 index at r = -0.25, an indication that the SFOs associated with SPCZ OLR are not redundant with Niño3.4-related SFOs and therefore contain additional information about SFOs related to tropical variability. As such, the expected-skill approach to SFOs benefits from measuring shifts in the likelihood of a forecast of opportunity captured by several distinct indices tracking tropical variability, Niño3.4, RMM, and SPCZ OLR, a distinct advantage over using an index that tracks only one of these processes (Figs. 3–4).