Subseasonal precipitation forecasts of opportunity over central southwest Asia

. Subseasonal forecasts of opportunity (SFOs) for precipitation over southwest Asia during January-March at lead times of 3-6 weeks are identified using elevated expected forecast skill from a Linear Inverse Model (LIM), an empirical dynamical model that uses statistical relationships to infer the predictable dynamics of a system. The expected forecast skill 10 from this LIM, which is based on the atmospheric circulation, tropical outgoing longwave radiation and sea surface temperatures, captures the predictability associated with many relevant signals as opposed to just one. Two modes of variability, El Niño-Southern Oscillation (ENSO) and the Madden Julian Oscillation (MJO), which themselves are predictable because of their slow variations, are related to southwest Asia precipitation SFOs. Strong El Niño events, as observed in 1983, 1998, and 2016, significantly increase the likelihood by up to threefold of an SFO 3-4 and 5-6 weeks in advance. Strong La 15 Niña events, as observed in 1989, 1999, 2000, also significantly increased the likelihood of an SFO at those same lead times. High amplitude MJO events in phases 2-4 and 6-8 of greater than one standardized departure also significantly increases the likelihood of an SFO 3-4 weeks in advance. Predictable atmospheric circulation patterns preceding anomalously wet periods indicate a role for anomalous tropical convection in the South Pacific convergence zone (SPCZ) region, while suppressed convection is observed preceding predictable dry periods. Anomalous heating in this region is found to distinguish wet and 20 dry periods during both El Niño and La Niña conditions, although the atmospheric circulation response to the heating differs between each ENSO phase.

Global processes and their unique interactions with local precipitation and temperature ultimately produce SFOs and can be identified by training a LIM on specific regional/large-scale interactions, as demonstrated in Breeden et al. (2022) for North American 2-meter temperature (2mT). Based on these results, here we develop a LIM for subseasonal precipitation over southwest Asia that has been designed in a similar manner. We will show that precipitation SFOs determined using LIM 75 expected skill can successfully be identified for subseasonal precipitation over southwest Asia with a LIM that is regional in precipitation and temperature but large-scale with the inclusion of hemispheric tropical outgoing longwave radiation (OLR) and sea surface temperatures (SSTs) and 200-hPa Northern Hemisphere streamfunction (Ψ !"" ). Another beneficial quality of the LIM is the negligible computational power needed to generate a long record of hindcasts. This study will focus on LIM SFOs and does not evaluate the skill of other models, though past research suggests that forecasts generated elsewise can 80 similarly be more skilful during LIM-identified SFOs (Albers and Newman 2019; Albers and Newman 2020).
The LIM developed for regional precipitation over southwest Asia is used to test the hypothesis that SFOs can be anticipated using theoretical expected skill and are associated with strong ENSO and MJO events. Section 2 introduces the reanalysis and satellite products employed, how the LIM is constructed, and how SFOs are identified using expected skill. Section 3 shows a 85 comparison of this approach to other methods of anticipating periods of elevated forecast skill, and the correspondence between forecasts of opportunity and ENSO and the MJO. Section 4 contextualizes results and proposes next future steps.
For examining relationships between skill and the MJO, the real-time multivariate MJO (RMM) index, a combined tropical 95 OLR and circulation index that is designed to capture characteristics of the MJO (Wheeler and Hendon 2004), is employed, including RMM amplitude, which measures MJO strength, and each day's associated MJO phase, which tracks MJO location.
Finally, based on results in Section 3b, we assess the strength of tropical OLR anomalies in the south Pacific Convergence Zone (SPCZ; box in Fig. 10), defined as 10°S-2.5°N, 140-180°E. The time series of OLR anomalies in this region is considered as a third metric, in addition to Niño3.4 and RMM, that might increase the likelihood of an SFO occurring. 100 6

Forecasts of Opportunity
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, 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 185 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, ) ( , ) (Eq. (5)), is selected to identify SFOs, based on the method's past success. In particular, expected skill is calculated using the pattern correlation version of the LIM signal-to-noise ratio, S 2 (Eq. (6); Newman et al. 2003) evaluated over the southwest Asian domain is calculated at each forecast lead time , and each initialization date t. As a result, 190 S 2 and expected skill are a function of time, but not space: . 195 S 2 is determined using ( τ, t ) , the forecast signal covariance matrix determined at a given lead time, which indicates the strength of the predictable signal in the forecasts, and ( τ ) , the forecast error covariance matrix which represents leaddependent, unpredictable 'noise': 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 215 and MJO phase later -but small enough so that the subset has significantly elevated skill.

Relative Risk
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 of SFOs initialized on days with index values of varying amplitude: 220 For ENSO and SPCZ OLR, changes in SFOs during positive and negative index values of varying threshold are considered, while the RMM is always positive. Instead, we assess changes in SFOs during MJO phases 2-3 or 6-7 and increasing RMM 225 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 top 20% of expected skill dates, the chance of one occurring on any date in the forecast period is 0.2: As an example, for weeks 3-4 SFOs when Niño3.4 > 1.5, 117 SFOs are found during the 269 days 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. lead times of weeks 2-4, both the median and 95 th percentile values of the PDFs of forecasts initialized on high expected skill 245 dates show statistically significant shifts towards higher PCC, with the greatest skill increases, relative to the bottom 20% group, at the shortest lead time of two weeks (Fig. 2a-c). The distribution of week 2 PCC is also the narrowest for the high expected skill group, a reflection of the more deterministic nature of forecasts at this lead time, particularly during periods of high signal-to-noise ratio (Eq. (6)). As lead time increases, the distribution of skill widens as forecast uncertainty increases, so that by week 5, the medians are indistinguishable between the two PCC distributions. Still, some skillful forecasts remain at 250 week 5 in the high expected skill group, shown by the statistically significant shift in the 95 th percentile of PCC.
Subseasonal precipitation skill, evaluated using ACC for weeks 3-4 and 5-6, is low, as discussed in past studies, but increases substantially during high expected skill periods . The LIM 'All Dates' weeks 3-4 skill of .2-.3 ACC exceeds the week 3 skill of most of the S2S models evaluated by de Andrade et al. (2018) for November -March 1999-2009 Fig. 3a to their Fig. 1). Comparing the three approaches to anticipating SFOs -high expected skill, Niño3.4, and RMMexpected skill most successfully anticipates SFOs at both weeks 3-4 and 5-6. The location of maximum skill shifts southeastward from weeks 3-4 to 5-6, with skill also weakening at longer lead times as expected. While there are some regions experiencing a skill increase during the top 20% of Niño3.4 and RMM amplitude dates, the increases are mainly indistinguishable from the skill of the remaining forecasts (Fig. 3c,d,4c,d). Splitting the Niño3.4 index to consider only strong 260 El Niño or La Niña events indicates that some regions do experience elevated skill during both phases, though in different, localized regions that only cover a limited portion of the region compared to the forecasts identified using expected skill ( Figure S1).
Considering PCC during the high expected skill, Niño3.4 and RMM dates confirms that forecasts initialized during periods of 265 high expected skill generally have higher PCC than those identified using Niño3.4 and RMM (Fig. 5). For lead times between weeks 2-4, median PCC shifts statistically significant shifts at the 95% confidence level reflect the increase in skill, as do the increased probability density of forecasts with PCC > 0.5. By week five, the distributions of PCC during high expected skill and high Niño3.4 dates become indistinguishable, consistent with greater similarity in the regions of skill found using Niño3.4 and expected skill at weeks 5-6 ( Fig. 4). Overall, the expected skill metric is more effective at anticipating SFOs than Niño3.4 270 and RMM.
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 in 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 295 as 1999, also reflect periods of high expected skill. Still, there are many high expected skill forecasts initialized 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. 300 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 weeks 3-4 (Figs. 3-4), which could 305 be due to the limited capability of ENSO alone to impact predictability, and/or elevated noise. The asymmetric response 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 days, compared to 192 days 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 310 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 the RMM and weeks 3-4 expected skill is considered, as an MJO 315 teleconnection at 5-6 weeks 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 in these estimates ( Fig. 9). Some particularly high-amplitude MJO events, including phases 2-3 in 1985 and 1994 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. Strong RMM phases 6-7, also increase the relative 320 risk of SFOs, which is elevated at lower RMM thresholds compared to phase 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.

Characteristics of Predictable Dry and Wet Initializations
This section compares the composite patterns preceding predictable wet and dry periods 18 days earlier, revealing the role for anomalous heating near the SPCZ. Next, composite wet and dry periods are split by Niño3.4 sign, revealing how different circulation responses during each phase produce like-signed precipitation anomalies over southwest Asia. 335

All Initializations
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 days earlier, and were also characterized by a PCC > 0, are considered. A lead time of 18 days is chosen because it falls within the weeks 3-4 forecast period and provides the 340 clearest circulation structures, which are similar but weaker at longer lead times (not shown). An 18-day lag is also consistent with the circulation response to tropical diabatic heating anomalies discussed in Jin and Hoskins (1995), which peaked about 15 days 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, or 18 days before the anomalous precipitation is observed. 345 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 Ψ !"" anomaly) is located over southwest Asia, consistent with downward vertical motion and suppressed precipitation. Conversely, predictable anomalously 350 wet periods are associated with enhanced anomalous central Pacific convection and a cyclonic Ψ !"" 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. 355 lifecycle differs 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. 375 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 (c.f., Fig. 11a,c; Fig.11b,d). By construction, there are clear differences in SST and OLR associated with El Niño and La Niña conditions, as well as north Pacific Ψ !"" 380 anomalies associated with ENSO-like tropical heating (Winkler et al. 2001;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 (c.f. 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 Ψ !"" pattern, with two high amplitude cyclonic anomalies located over Eurasia (Fig. 11d). Conversely, at the time 385 of initialization during wet La Niña periods, negligible Ψ !"" 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 for both wet and dry periods of each ENSO phase, there are differences in heating strength and location (c.f. Fig. 11a,b; Fig.11c,d). Dry La Niña initializations include stronger negative SST anomalies and suppressed convection in 390 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 east Pacific across North America and the north Atlantic. Dry La Niña dates are more common than wet La Niña dates, 84 vs 67 days, while wet El Niño dates are more common than dry El Niño dates, 96 vs 57 days, consistent with past research linking seasonal mean departures of southwest Asian precipitation to ENSO (Hoell et al. 395 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 (Fig. 12). Dry periods during El Niño conditions are associated with warmer SSTs in the east Pacific than wet periods (Fig. 12b), while no such differences in SSTs or OLR are observed in 400 the east Pacific during La Niña conditions. While distinct from one another, the Ψ !"" patterns during both El Niño and La Niña conditions both place an anomalous anticyclone over southwest Asia during dry events, consistent with suppressed precipitation. The Ψ !"" 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 405 southwest Asia. The orientation of such a wave train is consistent with the evolution described by Shaman and Tziperman which ultimately modulated Tibetan snow depth. Thus, while the heating difference between dry and rainy periods is similar regardless of 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 modelling experiments could be useful in disentangling the role of the basic state and thermal 430 forcing in producing this response.

Relative Risk associated with SPCZ OLR
Given the similar OLR anomalies in the SPCZ region noted during predictable wet and dry forecast initializations ( Fig. 10;   Fig. 12), a time series of OLR over the region was selected for a final metric to consider related to week 3-4 SFOs. Similar to considering Niño3.4 and RMM, using OLR alone to anticipate periods of elevated skill, the relative risk of a high expected 435 skill date increases significantly as the standard deviation of SPCZ OLR anomalies increases (Fig. 13). The response during negative and positive OLR anomaly values is more symmetric than the risk associated with increasing Niño3.4 threshold, which indicated a greater relative risk increase during El Niño than 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-day lagged regression of the southwest Asian precipitation time series with OLR (Fig. S2), although the regression pattern OLR anomalies are weaker than the composite 440 OLR during the SFOs considered in Fig. 10 and 12. 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 are 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 of these processes (Figs. 3-4). 445

Conclusions
In this study, precipitation SFOs are considered over southwest Asia using LIM expected skill, a metric related to the forecast signal-to-noise ratio that leverages the constructive interference of all signals impacting predictability. Strong El Niño, La Niña and MJO phase 2-3 and 6-7 conditions increase the chances that an SFO occurs. A third tropical heating index, based on anomalous OLR in the SPCZ region, also increases the risk of an SFO (Fig. 13). The correspondence between expected skill 450 and several indices highlights the advantage of using expected skill, in that all of these flavors of tropical heating are registered as high signals. However, there are still SFOs that do not correspond to any one of these indices, since other processes, potentially not tropically-driven, can produce a high signal too. Future work could focus on categorizing all SFOs to examine these potential additional factors.
the SPCZ region is a common element among predictable wet and dry initializations and increases the relative risk of an SFO.
Heating in this region is also associated with different circulation patterns during El Niño and La Niña conditions (Fig. 12).
How these different circulation patterns are related to similar anomalous heating anomalies is currently not well understood, but likely involves the modified tropopause-level waveguide present during each ENSO phase, which modulates the extratropical response to tropical heating (Sardeshmukh and Hoskins 1988;Newman and Sardeshmukh 1998;Shapiro et al. 470 2001). Dry baroclinic modelling experiments with idealized heating could be used to quantify the contribution of tropical heating over the Indian Ocean and West Pacific in affecting the circulation over southwest Asia on subseasonal timescales.
We also note that, while widely used, ENSO indices such as Niño3 or Niño3.4 do not capture the full spectrum of ENSO variability (Penland and Sardeshmukh 1995;Newman et al. 2009;Gehne et al. 2014;Henderson et al. 2020). Future work could employ the dynamical decoupling approach of Henderson et al. (2020) to isolate the ENSO signal and its impact on 475 precipitation SFOs more holistically.
The association between forecasts of opportunity and the MJO is less constrained given the higher-frequency nature of the MJO and small sample size once RMM is sorted by phase, but still indicates a role for strong MJO events in phases 2-3 or 6-7 to increase the likelihood of a weeks 3-4 SFO occurring, consistent with prior studies (Cannon et al. 2017;Hoell et al. 2018b). 480 Further suggesting a role for MJO-like heating, predictable heating patterns associated with forecasts of opportunity indicate a role for anomalous convection over the Indian ocean during dry periods, consistent MJO phases 2-3 suppressing southwest Asian precipitation (Fig. 10a). Future work could employ large climate simulation output to enhance sample size and revisit the MJO/expected skill relationship, to the extent the model can reproduce the mean state and MJO itself. Another remaining question that could be addressed more aptly with a larger sample size is how ENSO and the MJO act together to impact SFOs 485 for southwest Asian precipitation events, particularly concerning their magnitude and duration, which was beyond the scope of this study but merits further investigation.
to the manuscript. Andrew Hoell secured funding for this project, provided expertise on southwest Asia, frequent guidance on figures, and edits to the manuscript.

Competing Interests 505
The authors declare no conflict of interest.      anomalies are plotted positive (solid black) and negative (solid gray) at a contour interval of 3*10 6 m 2 s -1 starting at +/-3*10 6 m 2 s -1 . Full-field anomalies are shown, while the LIM forecasts are initialized on the EOF-truncated representation of the anomalies in the state vector (Table 1). Only anomalies that are statistically significant at the 95% confidence level are shown. The significance of anomalies was determined nonparametrically using bootstrapping with replacement.
Plotting conventions are as in Figure 11, except the contour interval for SST anomalies (blue/red contours) is 0.