Southwest US winter precipitation variability: reviewing the role of oceanic teleconnections

The current drought plaguing the Southwest US (SWUS) underscores the need for long-term precipitation predictability to inform sustainable planning of future ecological and economic systems. Precipitation predictability requires understanding the teleconnections and intercorrelations of a suite of climate indices that are known to impact the SWUS. However, decision criteria about the selection of El Niño and southern oscillation (ENSO) and non-ENSO indices, definition of winter months, geographical extent, temporal scale, computation of what constitutes a long-term mean, and determination of the study period, have not been systematically examined, yet have important consequences on the appropriate characterization of SWUS winter precipitation predictability. Here, we used Pearson’s correlations, Mann–Kendall tests, descriptive statistics, and principal component analyses to explore the statistical relationships between natural modes of climate variability and observed SWUS precipitation. We found no statistically significant persistent changes in the patterns of precipitation for a suite of SWUS geographical designations. Our results show that the choice of the temporal scale has an important impact on the determination of the strength of the climate signal. We show that ENSO indices were the primary determinants of SWUS precipitation, although inconsistencies persisted depending on the choice of ENSO index, the selection of SWUS geographical designation, and the chosen winter month combination. Non-ENSO indices in isolation were found inadequate to explain SWUS precipitation outcomes. Our analysis also indicates the predictability of SWUS precipitation must consider neutral ENSO events when non-ENSO modes are found to play an important role. We recommend the undertaking of a coordinated multi-decadal suite of numerical modeling experiments that systematically account for the individual and total impacts of this critical set of climate indices to improve understanding of past precipitation outcomes and by extension, improve predictability for a future for which tens of millions of people will require advanced planning.


Background
The semi-arid Southwest US (SWUS) has been experiencing persistent drought conditions since the turn of the century, highlighting the need for longterm climate prediction to aid water management and planning. The region is approaching the limits of water resource use with adverse implications for social, economic, and ecosystem sustainability, compounded by population growth and attendant increase in demand (Scanlon et al 2005, Zhang et al 2012. However, reliable SWUS precipitation prediction requires an understanding of a suite of climate modes, their interactions at annual to multidecadal timescales, the selection of appropriate geographical and temporal scales, the determination of what constitutes a long-term mean, the quantification of the study period extent, and the determination of winter month combinations. The literature on SWUS hydroclimate and its variability is characterized by disparate methodological applications and varying results that complicate the understanding of processes with important consequences for precipitation prediction. Users of climate information desire advanced projections of winter precipitation to improve understanding of long-term precipitation variability that can augment stakeholder decision-making. Therefore, this study provides a systematic review of SWUS (constituting the states of Arizona (AZ), Utah (UT), New Mexico (NM), Nevada (NV), California (CA), and Colorado (CO)) winter precipitation, which are considered responsive to El Niño and southern oscillation (ENSO) and non-ENSO modes. Climate modes refer to remote responses, either concurrent with or time-lagged, from a forcing region (Yeh et al 2018). In this study, we classified the natural climate modes into two: those operating within the tropical Pacific were designated as ENSO indices, which are a variety of indices measuring the same mode (Niño 3.4, Niño 4, southern oscillation index (SOI), Bivariate ENSO Index (BEST), New Zealand index (NZI), and Oceanic Nino Index (ONI) and the rest were designated as non-ENSO (Pacific North Atlantic (PNA), Atlantic multidecadal oscillation (AMO), Pacific decadal oscillation (PDO), and North Atlantic oscillation (NAO)). Appendix 1 provides definitions for all these climate modes.
ENSO has an established teleconnection across the SWUS, with El Niño conditions commonly resulting in wet winters while La Niña conditions commonly result in dry winters. Current knowledge of ENSO, however, is insufficient for understanding the full spectrum of precipitation anomalies and requires the examination of ENSO intercorrelations with a suite of additional modes of climate variability (Sheppard et al 2002, Zhang et al 2012, Yeh et al 2018, Ryu et al 2010. ENSO is limited to the explanation of interannual variance and its influence on decadal to multidecadal timescales is less understood Comrie 2004, McPhaden 2015). Determination of ENSO dynamics is challenging and attributable to changes in the ocean mean state and nonlinear teleconnections, which affect precipitation predictability Teng 2007, Yeh et al 2018). Additionally, inconsistencies in climate modeling projections undermine understanding of ENSO-precipitation relationships. Other challenges related to ENSO include inconsistent threshold values for the determination of the ENSO phase; variations of ENSO metrics; and shifts in ENSO types (Eastern Pacific (EP) ENSO and Central Pacific (CP) ENSO). Critically, the physical mechanisms driving the changes in climate modes are only partially understood. This study presents disparate arguments, based on a systematic review of the existing literature and additional statistical analyses, regarding climate modes and precipitation outcomes and attempts to establish statistical relationships associated with each (mode's) phase and varying characteristics of precipitation across different SWUS geographies.
The direct relationship between SWUS winter precipitation and ENSO has undergone a reduction since 1999, resulting in the consideration of other, non-ENSO modes, such as the PDO (see, Mantua et al 1997, Higgins et al 2000, Gutzler et al 2002, Sheppard et al 2002, Tootle et al 2005, Goodrich 2007, Shakun and Shaman 2009; AMO (e.g. Mo et al 2009, Ting et al 2011, Yang et al 2019, Mann et al 2021; NAO (Gershunov andBarnett 1998, Rajagopalan et al 2000); PNA pattern Koch 1991, Lim et al 2018) (see appendix 1). Recently, a new interhemispheric teleconnection, the NZI, has been proposed as an additional predictor for SWUS precipitation variability (Mamalakis et al 2018). The relative influences of each climate mode require a comprehensive and systematic examination to understand the interactions among the various phases of teleconnections and their associated impacts. This study tracks the phase shifts of the multiple ENSO metrics alongside the non-ENSO metrics and relates the phase shifts to mean and extreme precipitation events (defined here as above the 85th percentile and below the 15th percentile).
The SWUS is staring at potentially prolonged drought conditions and persistent scientific dissensus about precipitation projections will impede strategic and sustainable long-term planning. Therefore, this systematic review is particularly timely and seeks to illuminate the existing scientific consensus, areas of divergence, and emerging arguments on precipitation predictability and recommends possible pathways for harmonizing the disparate methodological approaches. Key questions explored include: (1) How do the Pacific and Atlantic Ocean teleconnections work independently or in concert to influence winter precipitation variability in the SWUS? (2) How do the means of analysis influence interannual, decadal, and multi-decadal precipitation predictability? (3) How does the geographical and temporal scale of studies influence outcomes of interannual to multi-decadal precipitation projections? (4) How do the various ENSO indices vary with the definition of El Nino, La Nina, and neutral events? (5) How are the SWUS winter and geographical extent defined and how does this affect the relationship between climate signals and precipitation?
We hypothesized the following: (1) We anticipate the predictive utility power of ENSO metrics to be indeterminate during the neutral ENSO phase, and the non-ENSO modes will account for anomalies during these years. (2) We hypothesize that the new interhemispheric ENSO index, the NZI, is progressively an important ENSO metric for understanding SWUS precipitation patterns. (3) Lastly, we hypothesized that the PDO phase shifts are crucial for the determination of the relationships between SWUS precipitation and ENSO metrics. These hypotheses have been informed by the systematic review we conducted. While there is near consensus about precipitation patterns and warm and cold phases of ENSO (exceptions such as the winter of 2022-2023 highlight continued research gaps that require exploration), SWUS precipitation outcomes during neutral ENSOs are only partially understood. The PDO phase changes are associated with multi-decadal precipitation changes and it is imperative to understand how it interacts with the interannual ENSO indices to influence SWUS precipitation. More so, examination of the recently determined interhemispheric ENSO index (the NZI) and its association with the various SWUS spatial units are burgeoning areas of research.

Selection of articles
We identified articles from the Scopus database using the following five keywords: 'Southwest USA precipitation' , 'EP ENSO' , 'CP ENSO' , 'Precipitation anomalies in Southwest USA' , and 'Climate teleconnections AND Southwest USA' . The search was limited to published peer-reviewed articles written in English with the last date of access being 30th April 2022; we imposed no start date. The keywords 'EP ENSO' , and 'CP ENSO' returned 1201 and 715 records, respectively. The other keywords had 168, 19, and 9 records for 'Southwest USA precipitation' , 'precipitation anomalies in the SWUS' , and 'climate teleconnections and SWUS' , respectively. We listed the articles on Scopus by relevance and evaluated the title of the records for suitability to our research. These initial processes and filters retained 519 entries. We removed 67 duplicate articles using Mendeley citation manager by arranging the articles by titles. Further, we sorted the articles based on topical relevance after reading the keywords and/or abstracts which resulted in the elimination of 121 articles. The screening of abstracts ensured we only retained articles that specifically studied SWUS precipitation and the associated influences of the Pacific and Atlantic Ocean teleconnections. Subsequent filters used included: sorting only articles discussing SWUS winter precipitation and articles that only focused on natural precipitation variability. The subsequent filters resulted in the elimination of a further 241 articles and the retention of 90 articles. As a result of snowballing (using the reference list of the selected articles to identify other relevant articles; Wohlin 2014), 18 articles were subsequently included, resulting in the final 108 articles.

Data acquisition
We acquired data for the ENSO indices and other climate modes (refer to appendix 1(b)) for the period 1950-2018. These data were retrieved from a variety of academic and governmental repositories. The selected period ensured consistent data availability across all climate modes and allowed comparison with existing literature. Only the SOI had missing values for 1950, where the long-term mean value  was used for the missing data period. The NZI data was provided by Mamalakis et al (2018). Precipitation data for all the SWUS states were acquired from the State of AZ Climate Office.

Data analysis
Different spatial configurations of SWUS were considered, consisting of the 6 states already mentioned and their combinations: Combination 1-C1: AZ, NM; Combination 2-C2: NM, AZ, CO, UT; Combination 3-C3: NM, AZ, CO, UT, NV; Combination 4-C4: NM, AZ, CO, UT, NV, CA (appendix 1(c)). We proceeded in this fashion as there is no precise and broadly accepted geographical definition of SWUS in the literature. The analysis was structured around understanding precipitation patterns, climate mode trends, and interactions between climate modes and their implications on winter precipitation.
Statistical analyses were conducted for the various spatial configurations for different winter month combinations (DJF, NDJF, JFM, and NDJFM), where the month designations are as follows (N-November; D-December; J-January; F-February, and M-March). The data for all seasons and various winter month combinations were also aligned with periods of PDO phase shifts, which are associated with changes in the climate system (e.g. Hanson et al 2004, Goodrich 2007, Arriaga-Ramirez and Cavazoz 2010. Pearson's correlations (Cohen et al 2009, Sedgwick 2012, Bayissa et al 2017 between precipitation and climate modes for all seasons were calculated for 1950-2018 and three subperiods (1950-1975, 1976-1995, and 1996-2018), coinciding with PDO phase shifts (Heord et al 2006, Goodrich 2007, Kurtzman and Scanlon 2007, Stahle et al 2009, Arriaga and Cavazoz 2010, Seager and Vecchi 2010. Correlational analyses for precipitation and climate modes were conducted to ascertain how the associations of precipitation and climate teleconnections vary across the range of SWUS spatial configurations, PDO phases, and the variety of winter month combinations.
All climate indices and precipitation totals for each SWUS spatial unit were standardized and plotted to determine their phase changes over time. The standardization formula is as shown: where x i is the i th value in the dataset, x mean is the sample mean, s is the sample standard deviation, and x std denotes the standardized value of x i . Descriptive statistics for precipitation were calculated for all spatial units, including the mean, median, variance, standard deviation, maximum value, minimum value, range, interquartile range (IQR), skewness, and Kurtosis.
The original and seasonal Mann Kendall (MK) tests (Hirsch andSlack 1984, Yadar et al 2014) were used to determine the persistent change in precipitation for the various spatial units across the SWUS, enabling the determination of whether seasonal trends were apparent in the data. The original MK test is used when seasonality is not expected and trends vary in different directions, whereas seasonal MK is used when seasonality is apparent. We used Sen's slope estimate (β) to determine the direction of change; for example, β > 0 indicates an upward trend for a precipitation time series, while β < 0 indicates a downward trend. The MK tests identified whether there was any trend, whereas Sen's slope was used to determine its magnitude (Gocic and Trajikovic 2013). The null hypothesis assumes the existence of no trend while the alternative expresses a significant change. If the MK p-value is ⩽0.05, the null hypothesis is rejected. The seasonal and original MK test was calculated for: (1) the all seasons precipitation dataset spanning the entire period 1950-2018; (2) the all seasons precipitation dataset with PDO shifts (1950-1975, 1976-1995, and 1996-2018); (3) precipitation dataset for the winter month combinations (DJFM, DJF, JFM, and NDJFM), and considering PDO shifts. Furthermore, the MK test was applied to all the climate modes to ascertain their direction and magnitude of change for the entire study period while considering PDO phase shifts. Additional methodological details (e.g. principal component analysis, determination of relationships between precipitation and climate indices) are provided in appendix 1(d).

Literature analysis
3.1. ENSO 3.1.1. ENSO metrics and phase type classification ENSO patterns have been primarily used to predict the frequency and intensity of SWUS precipitation as informed by its phase (see, Redmond and Koch 1991, Rajagopalan et al 2000, Scanlon et al 2005, Wang and Kumar 2015, Yeh et al 2018. However, confidence in its predictive skill is diminishing Kumar 2015, Mamalakis et al 2018). For example, 1948For example, -1977For example, and 1978For example, -1999 (Wang and Kumar 2015). Therefore, the statistical relationship between ENSO and SWUS precipitation appears to be reducing, yet the physical mechanisms driving this change are only partially understood. More so, being the designated primary climate signal at seasonal to interannual temporal scales (Brown and Comrie 2004, Scanlon et al 2005, Ryu et al 2010, McPhaden 2015, the inconsistent threshold value for the determination of ENSO phases (appendix 2(e)) and the choice of ENSO metric (table 1) complicates the comparability, reliability, and understanding of spatial variability in SWUS precipitation (Bamstone et al 1997, Mamalakis et al 2018.
Subsequent studies should determine how ENSO metrics and phase threshold values impact precipitation frequency and intensity in the SWUS, and the classification of ENSO phases. The reliability of purely ENSO-precipitation correlational values should be interrogated to gauge whether it is a sufficient analytical framework to conclude that the ENSO predictive skill is diminishing. Alternatively, understanding the physical changes in the climate system that are responsible for the reduction in ENSOprecipitation statistical associations is important in enhancing SWUS precipitation predictability. Additionally, an opportunity lies in determining how the different threshold values of ENSO phase determination and the selection of ENSO indices, affect the understanding of SWUS precipitation patterns spatially and temporally. A comprehensive understanding of the interannual, decadal, and multidecadal parameters of the climate system impacting ENSOprecipitation associations through statistical analysis or numerical modeling could provide a framework for comparing the outputs among studies and determining their reliability.

ENSO phases and precipitation patterns
The long-term determination of groundwater recharge (Scanlon et al 2005), impacts on ecological and economic systems (Zhang et al 2012), and impact assessment of natural and human systems (see, Yeh et al 2018) may be impaired if ENSO dynamics are not well understood. Warm ENSO (El Niño) typically translates to higher-than-normal precipitation across the SWUS, while cold ENSO (La Niña) often results in drier than normal conditions (Redmond and Koch 1991, Sheppard et al 2002, Scanlon et al 2005, Wang and Kumar 2015, Yang et al 2018. For instance, extreme El Niño potentially increases SWUS precipitation by 2.3-2.5 times the average (Scanlon et al 2005). The reverse of these ENSO trends is observable in the Pacific Northwest, creating a dipole between the SWUS and Pacific Northwest regions (Redmond and Koch 1991, Cayan et al 1999, Brown and Comrie 2004, Tootle et al 2005, Zhang et al 2012, DeFlorio et al 2013, Jiang et al 2013. Despite consensus on the impacts of warm and cold phases of ENSO, understanding how the non-ENSO indices affect SWUS precipitation during neutral ENSO conditions could  (Redmond and Koch 1991, Cayan et al 1999, Galambosi et al 1999, McCabe and Dettinger 1999, Sheppard et al 2002, Brown and Comrie 2004, Kurtzman and Scanlon 2007, Jiang et al 2013 Multivariate ENSO index (MEI) (Ryu et al 2010, Wise et al 2015 Niño 3.4 (Bamston et al 1997, Dominguez et al 2010, Gershunov 1998, Gershunov and Barnett 1998, Hamlet and Lettenmaier 1999, Harshburger et al 2002, Rogers and Coleman 2003, Goodrich 2004, Tootle et al 2005, McCabe and Clark 2006, Goodrich 2007, Goodrich and Ellis 2008, Quiring and Goodrich 2008 (Mamalakis et al 2018) offer new knowledge about the influences of the teleconnections on SWUS winter precipitation. Given that neutral ENSO conditions occur almost half of the time (Goodrich 2004(Goodrich , 2007, overreliance on warm/cold ENSO only, without considering other modes of natural climate variability may mask their cumulative effects. For instance, Wang and Kumar (2015) identified eight La Niña events and three El Niño events out of a possible 29 seasons , while neutral events numbered 19. Simultaneously, they identified five El Niño phases and one La Niña out of a possible 21 seasons, whereas neutral phases numbered 15 . Also, Goodrich (2007) identified 34 neutral ENSO events out of a possible 74 between . These examples highlight the need to explore how other climatic modes might serve as alternative leading precipitation predictors during times when the ENSO phase has a reduced impact.
The use of varied combinations of winter months (e.g. JFM, NDJFM, DJFM, and DJF for the SWUS winter period) could result in differing correlations with ENSO metrics. However, variations in the constituent winter months across spatial scales and their influences on ENSO predictive skill remain largely understudied. Additionally, the geographical definition of the SWUS remains inconsistent Comrie 2002, Yeh et al 2018), oscillating between the following individual states or their combinations (CA, NV, UT, CO, NM, and AZ) (appendix 2(a)). Here, we examine variations in ENSO phases with different combinations of winter months and different geographical definitions for SWUS and provide a matrix of how SWUS precipitation varies with climate modes other than ENSO.
Agreement exists on the climatic impacts of warm/cold phases of ENSO, although certain seasons do not conform to the established scientific consensus (e.g. the winter of 2022-2023 is a prominent exception). However, during neutral ENSO phases, precipitation predictability is primarily dependent on other decadal and multidecadal oscillations inter alia the PDO, EP oscillation, AMO, Atlantic oscillation (AO), NAO and the PNA teleconnection pattern (see, Gershunov and Barnett 1998, Higgins et al 2000, Rajagopalan et al 2000, Gedalof et al 2002, Tootle et al 2005, Goodrich 2007, Goodrich and Ellis 2008, Lee and McPhaden 2010. Unfortunately, few studies have explored more than three oscillations simultaneously (Wise et al 2015). Neutral ENSO and warm PDO conditions are largely associated with wet SWUS winters, while neutral ENSO and cold PDO conditions are almost as dry as La Niña winters (Greshunov and Cayan 2003, Goodrich 2004, Hanson et al 2004, Quiring and Goodrich 2008, Arriaga-Ramrez and Cavazos 2010, Erb et al 2020. Despite this consensus, the magnitude and spatial scale of the impacts of PDO on SWUS winter precipitation remain inconclusive (Goodrich 2004(Goodrich , 2007. One explanation is concerned with data quality between 1895 and 1930 (Goodrich 2007), highlighting the limited temporal window that is available to study neutral ENSO-PDO dynamics conclusively. For example, there have only been two recognizable PDO cycles since the 1890s and the latest PDO phase is highly uncertain (Wang and Kumar 2015). Accordingly, the relative significance of each climate mode during different phases of ENSO requires examination as their influence could vary with the phase of (non-) ENSO index spatially and/or temporally.
It is crucial to examine the intercorrelations and interactions among the teleconnections (Ryu et al 2010, Wise et al 2015 to comprehensively understand the climate dynamics across regions, as none occur in isolation. For instance, synoptic weather conditions are arguably influenced by both ENSO and PDO for SWUS (DeFlorio et al 2013). However, incorporating certain climate modes may weaken or strengthen the precipitation signal (Wise et al 2015). The period 2000-2014 saw the weakening of ENSO predictive skill (Wang and Kumar 2015) and offers a chance for studies to break up time series analyses of ENSOprecipitation associations.

CP El Niño and EP El Nino
ENSO-associated teleconnection patterns change, impacting the determination of anomalies and their predictability (Lim et al 2018, Yeh et al 2018. A canonical El Niño occurs in the EP (Niño 3.4 region) , Yang et al 2018, and is typically associated with increased SWUS precipitation. However, variations in land and ocean conditions may result in CP El Niño (El Niño Modoki), such as the 2015/2016 El Niño, occurring in Niño 4 region (Lee and McPhaden 2010, Lim et al 2018, Yang et al 2018. The latter reversed the dipole culminating in wetter conditions in Northwest US (NWUS) and drier conditions in SWUS. It has been established that oceanic conditions alone robustly accounted for canonical precipitation anomalies during EP El Niño, while it cannot fully explain anomalies during CP El Niño (Yang et al 2018). Therefore, for enhanced prediction of SWUS annual-interannual precipitation, studies should consider the physical mechanics of the climate system that better relate the type of El Niño with associated precipitation anomalies for the SWUS Meehl et al 2007, Zhang et al 2012, Liu et al 2017b, Yeh et al 2018 Additionally, mean conditions have evolved through the 20th century, driven by the combination of anthropogenic forcings and natural decadal and multidecadal variations (Lee andMcPhaden 2010, Yeh et al 2018), and these implications on SWUS precipitation prediction, are generally unknown. For example, strategically designed global climate modeling (GCM) simulations could be used to ascertain the relative contribution of anthropogenic emissions to natural climatic variability to characterize the observed evolution of oceanic and atmospheric mean (and extreme) conditions. A westward shift of El Niño events has been prominent during 1998compared to 1979(Paek et al 2017, Lim et al 2018, Yeh et al 2018 (Piechota et al 1997, Cayan et al 1999, Liu et al 2017a, Kim et al 2019. Recent advances assessing El Niño impacts have revealed that both CP and EP El Niño events can occur concomitantly; this parallel occurrence has been termed 'commingled' , further complicating the understanding of El Niño conditions (Paek et al 2017, Lim et al 2018.
The findings indicating the change of frequency of El Niño types imply that CP El Niño may become dominant, reversing the conventional precipitation patterns, the nature of teleconnections, the NWUS-SWUS dipole, and the predictive skill associated with El Niño in the SWUS. Observationally based studies are required to track multi-decadal El Niño shifts and should be combined with modeling simulations that characterize the physical processes initiating such transitions, their influence on precipitation magnitudes and patterns, and the variances in the interactions and influences of the climate modes. The frequency of occurrence of both El Niño types should be systematically studied independently and in tandem and compared with Niño 4 and Niño 3.4 indices. Furthermore, it is important to explore the physical mechanisms that produce commingled El Niño events and their implications on precipitation predictability and influences on ENSO and non-ENSO indices interactions. The literature has not adequately addressed how the different climate modes interact during the different El Niño types, which could open new possibilities in understanding natural precipitation variability.

PDO
The PDO (also referred to as North Pacific oscillation (NPO)) (e.g. Gershunov andBarnett 1998, Mantua andHare 2002) has also been deemed a robust indicator of SWUS precipitation (Tootle et al 2005, Hereford et al 2006. Several studies (e.g. Mantua et al 1997, Higgins et al 2000, Gutzler et al 2002, Sheppard et al 2002, Tootle et al 2005, Goodrich 2007, Shakun and Shaman 2009 argue that the influence of the physical mechanisms attributable to the PDO on climate is similar to ENSO and is an independent deterministic mode of the North Pacific (Mantua et al 1997, Higgins et al 2000, Gutzler et al 2002, Goodrich 2007, Shakun and Shaman 2009). On the other hand, there are many (e.g. Gershunov and Barnett 1998, Sheppard et al 2002, Newman et al 2003, Fleming and Anchukaitis 2016, Erb et al 2020 that view the PDO as a modulator of ENSO's frequency, stability, and magnitude spatially and temporally, or as a consequence of atmospheric noise. Hu and Huang (2009) concluded that PDO is an independent mode and does not significantly affect the North American climate. On the other hand, McCabe et al (2008) argued that the PDO does not invariably correlate with ENSO, hence disputing that it is a low-frequency ENSO signal.
Studies should explore whether PDO modulates or forces similar conditions as ENSO and the cumulative variance it explains for precipitation events. Additionally, whether the PDO is an independent deterministic mode, a low-frequency ENSO signal, a modulator of ENSO, or a consequence of atmospheric noise and such influence on SWUS precipitation across geographies at different temporal periods remains unclear.
PDO dynamics remain only partially examined in terms of time scale, stability, and stationarity (Mantua and Hare 2002, Brown and Comrie 2004, Goodrich 2007, Quiring and Goodrich 2008, Fleming and Anchukaitis 2016. Known PDO shifts occurred in 1925-1946(cold), 1977-1995(warm), and 1947-1976 (Mantua et al 1997, Gershunov and Barnett 1998, Mantua and Hare 2002, Brown and Comrie 2004, Goodrich 2004, Hanson et al 2004, Kurtzman and Scanlon 2007, Arriaga-Ramrez and Cavazos 2010, Seager and Vecchi 2010, Fleming and Anchukaitis 2016. Modifications of ENSObased precipitation anomalies varied when all years  were considered as a single dataset compared to when they were split into subperiods as informed by PDO phase shifts (Gutzler et al 2002). PDO shifts have been shown to influence Niño 3 predictability of winter conditions in SWUS (Gutzler et al 2002). Prior to the 1977 PDO shift, cold Niño 3 conditions adequately predicted drier winters, while warm Niño 3 had less predictive skill. After the (1977) PDO shift, the reverse trend became evident. However, Chao et al (2000) examined the 1957 PDO shift and found no apparent change in ENSO predictive skill. The implications associated with PDO shifts vary spatially and temporally (Hidalgo and Dracup 2003), and future research must determine the spatial and temporal scales of PDO influence.
The arguments above present challenges in understanding precipitation variability in the SWUS.
For example, what periodicities of PDO sufficiently characterize precipitation? What PDO phase shifts conform with established ENSO trends and which ones do not? What changes in the climate system trigger varied influences of PDO phases on precipitation? How do the influences of the PDO vary across geographical units of the SWUS? What criteria guide (non) consideration of PDO phase shifts for a given analytical framework?
Observational limitations impair the study of phase shifts before 1925 (longer-term reanalysis products notwithstanding), and recent instrumental records cover a short period which is insufficient for a conclusive analysis (Fleming and  warm ENSO signal of greater magnitude occurs with warm PDO phasing both spatially and temporally (McCabe and Dettinger 1999, Sheppard et al 2002, Brown and Comrie 2004, Hereford et al 2006. The PDO phases, just like ENSO, propagate the NWUS-SWUS dipole with a warm PDO inducing wetter conditions in the SWUS and drier conditions in the NWUS (Gershunov andBarnett 1998, Goodrich 2007). A different study (Jiang et al 2013), acknowledged that the dipole is an integrated influence of ENSO, NAO, and PDO. Understanding interannual patterns of PDO could enhance studies on SWUS precipitation (Gershunov andBarnett 1998, Arriaga-Ramrez andCavazos 2010). For instance, since 2000, PDO has undergone indefinite phase fluctuations, undermining its application for interannual precipitation variability (Hereford et al 2006, Goodrich 2007, Kurtzman and Scanlon 2007, Stahle et al 2009, Arriaga-Ramrez and Cavazos 2010, Seager and Vecchi 2010. The PDO has recently shown more interannual than multidecadal variability (Hu and Huang 2009), diminishing its usefulness as a long-term precipitation prediction mode. Its amplitude has been increasing over time and failing to decipher PDO phase shifts may render SWUS climate predictability unreliable (Mantua and Hare 2002, Hereford et al 2006, Goodrich 2007. Studies should explore the source of PDO indefinite phase fluctuations and their implications on ENSO's reliability. One explanation for the PDO source is that it could be both a tropical pacific or extra-tropical pacific mode (Shaun and Shaman 2009, Fleming and Anchukaitis 2016). Prior research has identified a southern hemisphere equivalent of the PDO, making a case for a tropically induced variability. However, PDO application in climate prediction will remain doubtful as long as the diagnosis of its phase shifts remains uncertain. This statement does not mean its incorporation in climate prediction is far from useful. Instead, its multi-season persistence (Mantua and Hare 2002) offers a different dimension for examining SWUS climate prediction.

AMO
AMO is a multidecadal (65-70 years) climate mode, although the precise time scale is indefinite (Quiring and , Ting et al 2011, Mann et al 2021. The short instrumental data period impairs the understanding of AMO and its implications on precipitation (Ting et al 2011), while no preinstrumental time series has been effectively validated (Mann et al 2021). More so, it is unknown whether its oscillatory behavior is a factor of internal or anthropogenic forcing (Ting et al 2011). Further, Mann et al (2021) did not find any internal mechanisms that explained the AMO multidecadal oscillation behavior and exclusively attributed this climate mode to volcanicity, raising doubt as to its fundamental nature. Despite the emerging debate about the origins and existence of AMO, it has been argued that in-phase PDO-AMO intensifies modulation of precipitation while out-of-phase weakens it and results in a dipole climate pattern between North China and SWUS (Yang et al 2019). Therefore, cold AMO enhances precipitation in SWUS (Mo et al 2009), not as the primary mode but as a modulator of PDO (Yang et al 2019). Yang et al (2019) concluded that the accurate prediction of AMO and PDO could help explain 52% of the spatial and temporal variance in multidecadal droughts in the USA. AMO modulates the magnitude of ENSO teleconnection on winter precipitation (McCabe et al 2004, Mo et al 2009 and is considered the most consistent indicator of decadal to multidecadal drought variability in the US during the 20th century (McCabe et al 2004). Studies should determine whether the AMO modulates ENSO and PDO phases equivalently, resulting in uniform influences on precipitation.

Combination of teleconnections
There exists temporal incongruence between ENSO and the other decadal and multidecadal climate modes (Brown and Comrie 2004), and debates persist on the efficiency of such modes of natural variability in predicting SWUS hydroclimate conditions (Hu and Huang 2009, Seager and Vecchi 2010, Jiang et al 2013. Future research combining traditional statistical analyses and numerical modeling approaches could determine the individual and cumulative reliability and influences of the climate modes. ENSO has a periodicity ranging from 2-10 years (Sheppard et al 2002, Brown and Comrie 2004, Tootle et al 2005, Cañón et al 2007, while PDO has a multi-decadal time scale of 50-80 years (Sheppard et al 2002, Cañón et al 2007Fleming and Anchukaitis) and a bidecadal scale of 10-30 years (Goodrich 2007, Fleming andAnchukaitis 2016), complicating a deep understanding of their relationships. The implications of ENSO on a decadal timescale are least understood (Brown and Comrie 2004), thus the necessity to explore the other existing modes in tandem.
The predictive skill of ENSO varies with PDO phasing (Gershunov and Barnett 1998, Brown and Comrie 2004, Goodrich 2004, Hereford et al 2006, Cañón et al 2007, DeFlorio et al 2013. El Niño events are stronger, more stable, and consistent during warm PDOs, while La Niña events are consistent during cold PDO phases (Goodrich 2004, Hu and Huang 2009). On the contrary, out-of-phase matching of PDO and ENSO minimizes the canonical relationship associated with in-phase interactions (Gershunov and Barnett 1998, Sheppard et al 2002, Brown and Comrie 2004. Therefore, confidence in ENSO-based predictability can be bolstered by incorporating PDO (Gershunov andBarnett 1998, Brown andComrie 2004). According to Brown and Comrie (2004), only a few locations in AZ had significant precipitation-PDO correlations. On the other hand, Guan et al (2005) established that PDO was a more dominant mode than ENSO in NM and locational elevation dictated the modulation between ENSO and PDO. These results imply spatial and temporal variability of the climate modes, emphasizing the need to improve understanding of each mode's spatial variations and implications before combining them.
Apart from the temporal incongruence, the interannual trends of the PDO are inconsistent and unpredictable, whereas the decadal patterns are partially predictable and persistent (Gershunov andBarnett 1998, Mantua andHare 2002). Combining the two (PDO and ENSO) does not guarantee a full understanding of precipitation patterns, thus the need to include other climate modes such as the AMO, PNA, and the NAO. Including multiple climate modes, however, introduces complexity (Wise et al 2015). Nevertheless, it is desirable to capture intra-seasonal to decadal patterns (Higgins et al 2000, Jiang et al 2013. ENSO teleconnections can only be reliable when the decadal state of the climate system is determined Dettinger 1999, McCabe et al 2004). For example, warm NAO conditions are associated with La Niña conditions, mainly when simultaneously occurring with cold PDO (Gershunov and Barnett 1998). It has been observed that the NAO is prominent during the destructive phases of ENSO-PDO (Gershunov and Barnett 1998). Lim et al (2018) established that warm NAO and AO induce drier conditions in the western USA. Future studies could examine whether NAO is an independent climate mode or a consequence of out-of-phase ENSO-PDO interactions. For PNA, its influence varies with the ENSO phase. It has positive correlations with precipitation during El Niño and negative correlations during neutral ENSO Koch 1991, Goodrich andEllis 2008). The influence of PNA also varies with the type of El Niño, whereby its warm phase is associated with CP El Niño (Lim et al 2018). PNA has been established as an exclusive winter pattern (Redmond and Koch 1991), emphasizing the need to incorporate it for winter precipitation prediction. The relative influences of each climate mode require a comprehensive examination to understand the interactions among the various phases of teleconnections and their associated impacts.
NZI (region 170-200 • E, 25-40 • S) has undergone amplification in recent decades and has been proposed as a superior metric compared to existing ENSO indices, PDO, and AMO (Mamalakis et al 2018). The NZI also captures the NWUS-SWUS dipole, although its physical mechanisms, longterm periodic fluctuations, drivers, and response to anthropogenic forcings require investigation (Mamalakis et al 2018). The varying responses attributable to ENSO require closer attention (Piechota et al 1997), and exploration of the other climate modes offers an opportunity for a comprehensive understanding. Additional critical questions worth exploring include: how crucial are the other climate modes other than ENSO for SWUS precipitation, or more broadly, hydroclimate, prediction? Is the lack of consensus on the physical mechanisms of the non-ENSO modes a justifiable argument for their exclusion from SWUS hydroclimate prediction? The temporal scale of studies should be harmonized as it may affect the number of phases of particular climate modes incorporated in the study periods. It may be impractical to capture all possible phase combinations of the different teleconnections, yet such information and their influences may hold the key to understanding climate dynamics. Other key questions to be considered are listed in table 2, which help highlight gaps in the existing literature.

Results and discussions
Motivated by the above review, we next describe the results of our analysis that directly address some of the identified research gaps and explore the statistical relationships between the natural modes of climate variability and observed SWUS precipitation.

SWUS precipitation 4.1.1. All seasons
All the geographical units (e.g. different state combinations that define the SWUS) had low annual mean precipitation of less than 350 mm, which is a characteristic of drier climates. CA and CO had the highest annual mean values, while NV and AZ had the lowest. However, across all winter month combinations, CA and C4 received the most precipitation, while NM and C1 received the least (appendix 3(a)). CA had the highest range, which translated to the highest IQR. All the spatial units had a nearly normal distribution of precipitation, as shown by the skewness and kurtosis values. Our analysis did not reveal any apparent increase or decrease in precipitation over time across the SWUS spatial units (figure 1). CA is the only state which had high precipitation variability attributable to different climatological zones existent in this geographically expansive state. Aggregation of SWUS geographical units leads to varying patterns of precipitation as shown in the four plots of combined states (figure 2). Without a specific definition of SWUS geographical extent, comparisons across studies' outputs are challenging and the understanding of precipitation-climate modes relationships may remain unclear.

Winter month combinations
Winter month combinations with the highest and lowest mean precipitation varied across the SWUS spatial units. For example, the DJF winter month combinations had the highest mean precipitation for five SWUS geographical units (AZ, CA, NV, C1, and C4), while the JFM (CO and UT) and DJFM (C2 and C3) winter month combinations each had highest mean for two SWUS geographical units (See appendix 3(a) for a breakdown of descriptive statistics for each winter month combination). Our results indicate that peak anomalies vary across the SWUS spatial units and the winter month combinations. Consequently, the relationships between precipitation of the various spatial units and climate indices vary. Our results further show inconsistent interannual variations across the spatial units; thus, their varied combinations result in different precipitation patterns (figure 2). It is unclear what combinations of spatial units adequately capture SWUS precipitation patterns. Given these results, the choice of winter month combination and geographical scale affects the output of precipitation analysis and determines the classification of a winter season as an extreme event or not.

MK test for all-season precipitation
The MK test was conducted to affirm the outputs of the descriptive statistics, which showed no significant changes in the magnitude of precipitation. The original and seasonal MK test for the entire dataset (1950-2018) returned p-values greater than 0.05 (appendix 3(c)). Therefore, the null hypothesis was accepted, which assumes no statistically significant persistent changes in SWUS precipitation. The Sen's slope values were nearly zero across all SWUS spatial units both for seasonal and original MK tests, confirming the lack of statistically significant changes for SWUS precipitation between 1958-2018 when considering annual changes. Furthermore, MK tests that considered PDO shifts resulted in p-values greater than 0.05, indicating no persistent changes in precipitation for all SWUS spatial units across the PDO phase shifts. Although there were minor variations of Sen's slope directions for certain SWUS spatial units, the increases or decreases in precipitation attributable to PDO shifts were insignificant. More so, the direction of precipitation changes did not align with established patterns of PDO and precipitation for SWUS except for the 1996-2018 PDO phase.

MK test for winter month combinations
Original and seasonal MK tests produced different results for the winter month combinations. For example, for DJFM, seasonal MK had negative slope values for CO and CA. In contrast, the original MK tests produced negative slope values for AZ, CA, and CO (appendix 3(c) (ii) and (iii)). These findings led to the following conclusions: (1) the change of winter month combinations led to varied Sen's slope direction across SWUS spatial units; (2) the choice of MK test (seasonal or original) led to a varied Sen's slope value and direction across SWUS spatial units. Both the original and seasonal MK tests produced p-values greater than 0.05, meaning no significant persistent change in precipitation patterns for all SWUS spatial units for the various winter month combinations. Niño compare and contrast in terms of their role in precipitation predictability?

PCA analysis for climate modes
The KMO and Bartlett's test of sphericity confirmed the suitability of all climate indices for the PCA analysis. For each winter month combination, one ENSO metric was selected at a time and analyzed against other non-ENSO indices. The PCA analysis was intended to determine which ENSO index had a higher variance for SWUS precipitation when combined with other non-ENSO indices. The PCA analysis largely retained two components after varimax rotation with a few exceptions (table 4). For occasions, where two components were retained, the total variance explained ranged between 59.09%-69.88%. Component 1 was explained by PNA, PDO, and ENSO indices which accounted for a total variance ranging from 35.98% to 46.09%. The PCA results indicate that the cumulative variance explained by the PDO, PNA, and ENSO indices is approximately 43%, with PDO and PNA having a higher load on component one than ENSO metrics. Future studies should explore whether these three indices are redundant to each other or are independent modes with unique influences on precipitation.

Analysis of relationships between SWUS precipitation and climate signals 4.3.1. Correlational analysis for the entire period for all winter combinations
Precipitation had statistically significant correlations with most of the ENSO indices although the patterns varied with geographical units (figure 4 and appendix 4(a)). The SOI index returned the highest correlational coefficient for most of the SWUS while BEST had the second-highest correlational coefficient. However, CA had a better response to Niño 3.4. All the indices had consistent direction of correlations across the winter months, where all indices had positive correlations with precipitation except for the NZI and SOI. CO, UT, and NV were the least responsive to the climatic modes. Generally, the non-ENSO indices had no statistically significant correlations with most of the SWUS except for a few instances where the PDO and the PNA were significant. For instance, the AMO and NAO did not register any statistically significant correlations with any of the SWUS geographical units. Among the ENSO indices, the NZI had the least correlation with precipitation. The Non-ENSO indices had very low correlational values, and future studies should examine their contribution to SWUS precipitation. Therefore, the choice of the spatial unit and ENSO index affect the strength of correlational values.

Correlations analysis for all seasons considering PDO shifts
Considering the DJF winter combination and the PDO periodicities, we observed low correlational coefficients across all the SWUS spatial units compared to correlational coefficients for the entire period. For instance, AZ, CA, C3, and C4 did not register any significant correlations with any of the   1950-1975, and 1976-1995. However, this spatial unit did not have significant correlations with any index when considering the entire period of analysis. NM had the strongest correlation with climatic indices in the warm phase of the PDO (1976PDO ( -1995. Interestingly, the NZI had the highest correlation with NM for the period 1996-2018. Given these findings, we conclude that breaking down analysis to PDO periodicities may mask some of the associations between precipitation and climate indices. Further, cold or warm PDO periodicities in isolation did not improve the understanding of SWUS precipitation. One of the key observations for the DJFM winter months combination with PDO periodicities indicated that the NZI had the highest correlation between 1996-2018 for C1 and NM despite being insignificant in the previous PDO phases. This trend is replicated in the JFM and NDJFM winter months combination. NM had a better response to the teleconnections among all the spatial units (appendix 4(b)). More so, CA had statistically significant correlations with the AMO for the period 1996-2018 for the DJFM combinations, an observation not consistent with the analysis for the entire period. In addition, the warm phase of the PDO did not translate to enhanced associations between precipitation and the (non-) ENSO indices. On the contrary, the warm PDO phase had the least number of significant correlational coefficients for NM across all the winter months combinations. Given these results, it appears that the NZI signal may be strengthening for certain spatial units of the SWUS and the physical mechanisms driving this change should be investigated in subsequent studies. The inconsistencies observed for precipitation and climate indices for the various winter month combinations emphasize the need to carefully consider the aggregation of winter months when modeling SWUS precipitation. Furthermore, the disaggregation of the analysis period into PDO periodicities may create spurious relationships, hence a systematic analysis of the implications of the decadal and multidecadal phase changes of teleconnections on the SWUS spatial units should be undertaken. Our results did not show any winter month combination that was robust for all SWUS spatial units as it varied with PDO periodicity and ENSO metric. Therefore, the choice of winter month combination, PDO periodicity, and SWUS geographical extent should be made contextually where each of these choices can be closely examined and determined.

Phases of climate modes and precipitation deviations from the mean 4.4.1. ENSO indices
ENSO indices were the primary determinants of precipitation accumulation for SWUS spatial units, although inconsistencies persisted depending on the choice of ENSO index, selection of spatial unit, and the winter month combinations. For all the analyzed ENSO indices, their phase shifts frequency varied with the choice of winter month combination.
(appendix 4(c)). For instance, Niño 4 in AZ had 33.9%, 33.8%, and 32.3% neutral, cold and warm seasons for DJF winter months, respectively, while DJFM had 44.1%, 26.5%, and 29.5% (table 5). Given these inconsistencies, we did not identify a systematic  pattern of optimal ENSO index or winter month combination for any SWUS spatial unit. Since each spatial unit had different frequencies in the ENSO phases, future research should evaluate how selections and combinations of spatial units affect the ENSO-precipitation relationship. Consequently, the criteria for selecting ENSO indices and winter months should be communicated. More so, the determination of the length of the study period and computation of the long-term mean has implications on the classification of the above mean (AM) and below mean (BM) seasons. Although most warm ENSO phases aligned with AM precipitation events and cold phases aligned with BM precipitation events, neutral ENSO accounted for 33%-49% of total ENSO phases for the SWUS spatial units for the various winter months combinations (appendix 4(c)). This finding emphasizes that the predictability of SWUS precipitation must consider the effect of other modes when neutral ENSO events are occurring. This study analyzed non-ENSO indices alongside neutral ENSO seasons, but no consistent trends were established. An opportunity lies in unlocking the circumstances, statistical relationships, and governing large-scale dynamics that could explain how neutral events, in concert with other modes, lead to positive and negative precipitation anomalies. Across all ENSO indices and spatial units, most neutral events for the study period resulted in BM precipitation. We assume that non-ENSO indices may increase in importance during neutral ENSO events, although the statistical inference could not be established in this study. We also speculate that the criteria for determining neutral ENSO and the long-term mean could influence the classification of seasons as neutral or otherwise. Since the    Despite the established scientific consensus that warm ENSO translates to more precipitation, while cold ENSO results in reduced precipitation, departures from this norm were observed for SWUS. For all spatial units, almost one-third of warm ENSO were BM, and one-third of cold ENSO were AM. However, there was a higher chance of a warm ENSO being BM than a cold ENSO being AM; this is attributable to a higher frequency of the cold PDO phase. An analysis of non-ENSO and ENSO indices did not offer consistent conclusions for understanding these departures. For example, in CO, the DJF combination had fewer warm Niño 3.4 phases AM than BM across all ENSO indices. Failing to account for these departures, and the large-scale dynamics during neutral ENSO conditions undermines the understanding of the relationships between climate indices and precipitation, which is crucial for SWUS precipitation prediction. We could not determine the best winter month combination, the best ENSO metric, or the ideal spatial configuration for defining SWUS precipitation. Moreover, our analysis could not establish the consistent criteria for neutral ENSO, the definite criteria for computation of long-term mean, and the guidelines for selection of study period, which are crucial considerations for analyzing SWUS precipitation. Studies should communicate all these methodological choices-that is, inform the readership of all detailed metadata-to allow for the understanding of similarities and differences in outputs across studies.

Non-ENSO indices
Across all spatial units and various winter month combinations, the frequency of seasons with BM precipitation was greater than AM precipitation. The AM precipitation events ranged between 38.2% to 45%, with the lowest frequency in combination 4 and the highest frequency in combination 3 and UT (appendix 4(c)). Similarly, the highest frequency for the BM seasons ranged between 55% and 62% for the mentioned spatial units. Arguments persist that we have had two cold phases of PDOs between 1950present (65% of the time), which influenced low precipitation for all SWUS spatial units. The analysis of cold and warm PDO phase frequencies resulted in nearly similar percentage frequencies across all SWUS spatial units. However, this study interrogated beyond frequency similarities and explored seasonby-season PDO phase alignments with precipitation patterns.
Periodicities of warm PDO-AM precipitation had little difference from periodicities of warm PDO-BM precipitation, even for spatial units where a higher frequency of warm PDO events aligned with AM precipitation events. These findings indicate that warm PDO phases do not translate to increased precipitation events for all SWUS spatial units, and some other climate modes may be the dominant determinant of SWUS precipitation. However, our findings show that cold PDO phase frequencies were relatively greater for BM precipitation seasons than AM. Therefore, the choice of spatial unit and winter month combinations affect the precipitation-PDO relationships. An emerging argument from this conclusion is whether influences of PDO should be based on season-to-season phase shift or the general PDO phase for a given multidecadal period regardless of seasonal phase variations. This study argues that the inconsistencies of PDO-precipitation relationships may be explained by the determination of the long-term mean value and the study duration. A long-term mean determines the baseline value, which subsequently affects the classification of AM and BM precipitation events. Furthermore, we are not able to establish the circumstances that defined warm PDO-AM precipitation or cold PDO-BM precipitation and exemptions from these patterns, which will be handy in explaining SWUS PDO-precipitation interactions. Given these observations, the PDO phases in isolation are insufficient to explain SWUS precipitation outcomes.
The AMO phase shifts did not have consistent patterns with precipitation for SWUS spatial units. However, the general trend across all spatial units was a higher frequency of cold phases than warm phases, with cold phases accounting for approximately 56%-58% of all seasons. The higher prevalence of cold AMO phases should have translated to more precipitation AM, but this trend was not apparent, as the SWUS spatial units had more seasons below the mean precipitation value. Another observation was that there were more warm AMO phases BM than AM for most spatial units, a conventional trend determined by previous studies. Similarly, there were more cold phases for BM seasons than AM, which differed from established conventional trends, translating to an inconsistent conclusion regarding the effects of AMO phases on SWUS precipitation trends. Variations from this general trend were observed in C2, C3, NV, and CA, and attributed to the choice of winter month combinations. The analysis of the AMO resulted in four conclusions: (1) AMO phase shifts are not adequate and consistent in determining precipitation for SWUS spatial units; (2) the choice of winter month combinations for each spatial unit has a bearing on the AMO-precipitation relationships for SWUS; (3) the AMO in isolation is not a standard climate index for determining SWUS precipitation patterns; (4) interactions between the AMO and other climate signals displayed no consistent patterns in their influence on SWUS precipitation.
The warm NAO phases had a higher frequency than the cold NAO phases, with warm seasons ranging between 54%-60% across all spatial units and winter month combinations. This study did not establish consistent patterns between NAO phase shifts and SWUS precipitation. However, the general trend was that there were more warm phases BM than AM. The cold phases did not have a discernible trend with AM or BM precipitation seasons for SWUS. Our findings indicate that the NAO is not a reliable index for determining the trends of SWUS precipitation.
The SWUS spatial units experienced more cold PNA seasons than warm across all winter month combinations. No consistent trends were observed between precipitation patterns and PNA phase shifts for all SWUS spatial units. More so, there were no consistent trends between PNA and other climate modes for the study period. This study concluded that the non-ENSO indices (PDO, AMO, PNA, NAO) when evaluated on a seasonal basis against precipitation yield inconsistent phase alignments with AM/BM precipitation events. However, the PNA and PDO have high correlations with ENSO indices and precipitation. This study is unable to determine how the ENSO and non-ENSO climate indices interact to affect SWUS precipitation and recommends the application of numerical modeling that systematically varies all appropriate parameters of interest to objectively compare simulated outputs. For example, skillful multi-decadal simulations of the historical past, with water vapor tracers (Insua-Costa and Miguez-Macho 2018), could provide mechanistic information that characterizes the source region of precipitation that falls over a given area. Dynamical assessment of water vapor transport and comparison among anomalous precipitation years can provide insight into why, as one illustration, the winter of 2022-2023 resulted in excessive western US precipitation even though ongoing La Nina conditions suggested otherwise. A strategically designed modeling campaign could reveal whether the conditions specific to the winter of 2022-2023 are generalizable with previous La Nina events leading to anomalously positive precipitation.

Phases of climate modes and extreme precipitation events
The phase of the ENSO index was the dominant determinant of the extremely low or high precipitation events in SWUS, although the ENSO-extreme precipitation phase alignments were inconsistent across winter month combinations and spatial units (appendix 4(d)). For seasons below the 15th percentile, neutral and cold ENSO phases largely accounted for these events. On the contrary, for seasons above the 85th percentile, neutral and warm ENSO phases accounted for these events. Although the influences of cold and warm ENSO phases are well established, a few exemptions were observed, such as in NV and UT, where all winter combinations had at least two warm seasons for the 15th percentile. The physical mechanisms explaining the incongruence between extreme precipitation events and ENSO phases should be investigated. Our work, aligned with previous research, speculates that non-ENSO metrics could sway neutral ENSO conditions to either spectrum of extreme SWUS precipitation. However, no consistent trends could be attributed to non-ENSO indices for any SWUS spatial unit. Studies should investigate the physical mechanisms or statistical relationships that account for neutral ENSO events and warm/cold ENSO phases that do not conform to established scientific conventions.

Conclusion
The SWUS is approaching the limits of water resource use with adverse implications on social, economic, and ecosystem sustainability, compounded by population growth and increasing demand. The principal objective of this systematic review was to improve the understanding of SWUS precipitation trends, the patterns of the teleconnections impacting precipitation, the statistical relationships underpinning precipitation, and the climate indices that could help explain precipitation predictability. Our review revealed that a suite of decision criteria, including the definition of SWUS winter months, determination of geographical extent, the selection of the temporal scale, computation of the long-term mean, means of analysis, the selection of ENSO and non-ENSO indices, and the temporal extent of the study period, precluded a robust determination characterizing the relationship between certain modes of natural climate variability and SWUS precipitation outcomes. Motivated by this systematic review and the research gaps identified, we then varied these decision criteria to improve the understanding of precipitation predictability and the associated implications on long-term water resource planning for the SWUS.
Our results demonstrate that none of the ENSO metrics provided a conclusive characterization of spatial and temporal variability in precipitation for the SWUS. This finding is compounded by the imprecise criteria for the determination of the mean state upon which ENSO phases are determined and the computation of extreme precipitation seasons. The mean state is likely changing as a result of natural and anthropogenic signals and standard mechanisms for its determination will improve the understanding of SWUS precipitation predictability. Despite these shortcomings, ENSO indices were the primary determinants of SWUS precipitation, although inconsistencies persisted depending on the choice of ENSO index, selection of spatial unit, and the winter month combinations. However, the inconsistent and indeterminate thresholds for the determination of ENSO phases impair the cross-validation of studies' outputs and understanding of the interactions with the various climate modes. Subsequent studies should evaluate how the selection of ENSO metrics and phase threshold values impact the prediction of precipitation magnitude and trends through statistical and numerical modeling approaches. In addition, shifts in ENSO types (i.e. CP El Niño, EP Niño, and commingled Niño) should be considered to ascertain associated precipitation variability. The adequacy of purely statistical associations should be interrogated to gauge whether it is a sufficient analytical framework to determine ENSOprecipitation associations. Furthermore, precipitation events deviating from the already established warm/cold ENSO-precipitation associations could offer new knowledge regarding SWUS precipitation predictability, while understanding the neutral ENSO phase could offer new opportunities for precipitation prediction.
The non-ENSO indices in isolation were found inadequate to explain SWUS precipitation outcomes.
Studies should explore whether PDO modulates or forces similar conditions as ENSO and the cumulative variance it explains for precipitation events. Additionally, whether the PDO is an independent deterministic mode, a low-frequency ENSO signal, a modulator of ENSO, or a consequence of atmospheric noise and how it influences SWUS precipitation across geographies at different temporal periods remains unclear. The drivers of its recent inconsistent phase change also require examination. Furthermore, the non-ENSO indices had temporal incongruence with the ENSO metrics as they operated at decadal to multidecadal scales while ENSO operated at interannual scales. Future studies could explore how the influence of the non-ENSO metrics varies with the ENSO phase and El Niño type. A modeling campaign targeting the simulation of multiple phase combinations of ENSO and non-ENSO metrics is required to determine the individual and cumulative influences of the climate modes on SWUS precipitation.
Other key findings included: (1) there were no statistically significant changes in SWUS precipitation when considering the whole study period and when considering PDO phase shifts; (2) the choice of study period influenced the persistent change patterns of the teleconnections as revealed through application of the MK test; (3) the predictability of SWUS precipitation must examine precipitation predictability during neutral ENSO events, which accounted for one-third to one-half of the ENSO phase frequency across SWUS spatial units; (4) the choice of spatial and temporal scales, winter month combinations, ENSO metric, computation of the long-term mean, and the choice of temporal extent of the study period all influenced statistical associations between precipitation and the climate indices.
We recommend future studies to combine traditional statistical analysis and numerical modeling approaches to determine the individual and cumulative reliability of the climate modes, which are important for understanding SWUS precipitation predictability.

Data availability statement
No new data were created or analysed in this study.

Acknowledgments
This work was supported by The Joint Research Program (JRP), a cooperative effort between the Salt River Project and Arizona State University. The authors thank Dr Erinanne Saffell, the Arizona State Climatologist, for providing historical precipitation data (available from NOAA's National Centers for Environmental Information statewide mapping website) for all the states analyzed. We are grateful to Dr Antonios Mamalakis who provided data for the NZI index. (Mann et al 2021).

Appendix 1. Definitions, data sources, and additional methodological details Appendix 1(a). Definitions Atlantic multidecadal oscillation (AMO): AMO is a multidecadal (65-70 years) climate mode with hemispheric scale impacts that is centered in the North
El Niño and southern oscillation (ENSO): refers to equatorial SST anomalies in the EP, comprising the leading mode of interannual (2-7 years cycle) precipitation variability in SWUS (Brown and Comrie 2004). Several indices are used to characterize anomalies in the tropical Pacific including; Niño 1 and 2 (0 • -10 • S, 90 • W-80 • W), Niño 3 (5 • N-5 • S, 150 • W-90 • W), Niño 3.4 (5 • N-5 • S, 170 • W-120 • W), ONI (The same region as Niño 3.4 but with a 3 month running mean rather than a 5 month running mean, and Niño 4 (5 • N-5 • S, 160 • E-150 • W) (Trenberth et al 2020). Apart from the indices above, the NZI, BEST, and SOI are considered measures of the same climatic mode. Pacific-North American teleconnection pattern (PNA): a mode of variation in mid-latitudes occurring during winter months. The pattern consists of a deeper than-usual Aleutian low-pressure center and high pressure over western North America (Redmond and Koch 1991).

North Atlantic oscillation (NAO): a meridional oscillation between Iceland and Azores constituting quasi-biennial (decadal) characteristics. It is associated with changes in the Atlantic
Southern oscillation index (SOI): normalized difference in monthly mean pressure anomalies between Tahiti (5 • N-5 • S, 80 • W-130 • W) and Darwin Australia ((5 • N-5 • S, 90 • E-140 • E). It is positive if pressure is higher than normal in the southeast Pacific and lower than Normal in the North of Australia (Andrade andSellers 1988, Tootle et al 2005).
BEST: a combination of the SOI and standardized Niño 3.4 meant to incorporate atmospheric processes (Smith and Sardeshmukh 2000).
Teleconnection: refers to a statistically significant remote response, either concurrent with or timelagged, from a forcing region (Yeh et al 2018). The relationships between climate modes and precipitation were determined through a series of computations: (1) determination of the phase of each climate mode for all the 10 SWUS spatial units, and for each of the winter month combinations (DJF, DJFM, and NDJFM); (2) computation of the longterm mean between 1950-2018 for each spatial unit and winter month combination and identification of AM and BM winter years; (3) computation of extreme precipitation events (below 15th and above the 85th percentiles) for each SWUS spatial unit and winter month combinations; (4) determination of the frequency of each climate mode (counts and percentages) for AM and BM years, and for below the 15th and above the 85th percentiles for the SWUS spatial units and for the winter month combinations; (5) establishing associations for ENSO and non-ENSO indices with precipitation for each spatial unit and winter month combinations for AM, BM, below the 15th, and above the 85th percentiles. Arizona (Svoma and Balling, 2007) Primarily focuses on Phoenix metropolitan area (Andrade and Sellers 1988) Arizona and western New Mexico; Spring (March-May), Autumn (September-November), winter (DJF), summer (JJA) (Galambosi et al 1999) Statewide AZ. (Goodrich and Ellis 2008) Winter (December-February), Salt and Verde watershed (Goodrich 2004) Statewide AZ; Winter DJFM. (Jacobs et al 2005) Drought Planning in AZ. (Pagano et al 1999) Survey-based article for AZ water management Western USA (Jiang et al 2013) Focuses on the 11 westernmost states; warm period (June-September). (Redmond and Koch 1991) Western USA consists of 11 western-most states: Montana, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada, California, Idaho, Oregon, and Washington (Wang et al 2009) Intermountain region (Between the Cascade-Sierra range and the Rocky Mountains (Yang et al 2018) The 11 western-most states (Zhang et al 2012) Cold season (October-March). Modeled the 11 westernmost states. (Brown and Comrie 2004) Focuses on the 11 westernmost states. Winter DJF (Cayan et al 1998) Western North America; 100 • W to the Pacific Coast and 30 • to 60 • N. (Cayan et al 1999) Studies the 11 western-most states; Cool season October-April  Defined as the 11 western-most states. Review article about interdecadal climate regime dynamics in the North Pacific. (Newman et al 2003) North Pacific, studies PDO (Paek et al 2017) Explores the differences between CP and EP El Nino. Winter is defined as October-March, and Summer (June-August). Studies the Contiguous USA only. (Ryu et al 2010) Focuses on ENSO and hydrologic variability for the conterminous USA. (Tootle et al 2005) Studies influences of PDO, AMO, ENSO & NAO for contiguous USA stream flow. Cool season is defined as October-March, although acknowledges December-February as the traditional winter months (Wise et al 2015) Warm season (May-October), Cold (November-April). Studies five atmospheric-based teleconnections for the contiguous USA  The contiguous USA. CP and EP El Niño events (Zhong et al 2011) The contiguous USA is divided into 6 climate regions. Impacts of global ocean on US precipitation (Dai et al 2020) The contiguous US. Winter DJF. Precipitation frequency and intensity under the influence of greenhouse gases (Gershunov and Barnett 1998) North America. Influences of NPO and ENSO on climate variability (Higgins et al 2000) USA precipitation variations are explained by ENSO and Arctic oscillation (Higgins et al 1999) Relationship between monsoon and ENSO in AZ-NM, NW Mexico, and SW Mexico (Kurtzman and Scanlon 2007) Southern Review article about decadal and multidecadal circulations.  (Zhong et al 2011(Zhong et al ) 1950(Zhong et al -1999. Oceanic influences on ENSO for the USA (Anderson et al 2010) 1931-2000. Regional variation in summertime precipitation (Andrade and Sellers 1988) 1900-1985. Effects of ENSO on seasonal and annual precipitation (Bamston et al 1997(Bamston et al ) 1950(Bamston et al -1997. Highly ENSO-related SST region (Brown and Comrie 2002) 1950-2000. Precipitation variability in SWUS and the SOI and PDO teleconnections (Brown and Comrie 2004) 1925-1995. PDO and ENSO and western USA precipitation (Pascolini-Campbell et al 2015 1928-2012. Correlations of streamflow with precipitation for the Gila River area (Cañón et al 2007) 1900-2003. Correlations of PDO and ENSO for Colorado river basin (Cayan et al 1998) 1880-1994. Decadal variability of precipitation over Western North America (Cayan et al 1999) 1948-1995. ENSO and hydrological extremes (Cayan et al 2010) 1950-2100. Future dryness in the SWUS (Chylek et al 2014) 1895   Historical period 1968, future 2038-2070(Galambosi et al 1999) 1949-1989. Compares fuzzy rule-based model (FBRM) and multiple linear regression model (MLRM) for ENSO in AZ (Gao et al 2011(Gao et al ) 1970(Gao et al -1999. Evaluate climate change in the CRB using RCMs. Future 2040-2069 (Gao et al 2012) 1970. Future 2040-2069. Moisture convergence in RCMs and GCMs for SWUS (Gershunov and Barnett 1998) 1933-1993. ENSO and PDO influences on the contiguous US (Goodrich and Ellis 2008) 1896-2006. Examines large winter climate reversals (Goodrich 2007(Goodrich ) 1925(Goodrich -1998. PDO on western USA precipitation (Goodrich 2004(Goodrich ) 1925(Goodrich -1998. PDO on AZ precipitation (Guan et al 2005) 1955-2003. PDO-ENSO relationship for the mountainous region (Gutzler and Robbins 2011) 1976-2000, future 2076-2100. Climate variability and projected change for A1B scenario (Gutzler et al 2002(Gutzler et al ) 1950(Gutzler et al -1997 1000-1800. Forced and unforced drivers of AMO (Meehl and Hu 2006) A 1360 year analysis of drought in the SWUS and Indian monsoon region  1000-2100. Determines future warming from greenhouse gas (GHG)-induced perspective Appendix 2(c). Modeling approaches for the cited articles, classified as whether statistical or dynamic. The column titled Description/Model type provides additional details about the study and the choice of the model type.

Statistical
Dynamic Description/Model type Erb et al (2020) Analyzes results from community earth system model (CESM) Rajagopalan et al (2000) Compares ENSO and PDSI. Also, check for influences of NAO and PDO in the ENSO-PDSI relationship Arriaga-Ramrez and Cavazos (2010) Determines how ENSO and PDO affect extreme precipitation for winter and summer months Redmond and Koch (1991) Studies correlations between temperature and precipitation with SOI and PNA in the western USA Rockel et al (2008) Compares CLM (climate version of the local model) to RAMS (regional atmospheric modeling system) Ryu et al (2010) Uses PCA/ empirical orthogonal function (EOF) using multivariate ENSO index Scanlon et al (2005) Vegetated and non-vegetated areas respond to interannual climate variability and influences on the water cycle. Seager and Vecchi (2010) Uses 15 coupled climate models to study anthropogenic-induced drying of SW USA Seager et al (2007) Examines future drying in SW North America by analyzing 19 models participating in AR4 Shakun and Shaman (2009) Identifies a southern hemisphere equivalent of PDO which is strongly related to its Northern hemisphere equivalent Sheppard et al (2002) Provides a general understanding of the SW climate patterns for the period 1700-2000. Incorporates reconstructed records. Ting et al (2011) Studies AMO using climate model intercomparison project (CMIP3) simulations for the 20th, 21st , and pre-industrial eras with 23 IPCC models. Tootle et al (2005) Studies ENSO, PDO, AMO, and NAO for the contiguous USA Wang and Kumar (2015) Coupled GCMs specifically National Center for Environmental Prediction (NCEP) model together with observational data Wang et al (2009) Uses six RCMs of the North American Regional Climate Change Assessment Program (NARCCAP) Wise et al (2015) Studies composites of teleconnections and how they impact US climate variability Yang et al (2018) Explores the 2015/16 El Nino dynamics. Winter is defined as DJF Yang et al (2019) Explores impacts of IPO & AMO on SWUS and North China Yu et al (2017) Studies CP and EP El Nino events Zhang et al (2012) ENSO anomalies for the western US. Uses three weather research and forecasting (WRF) regional models and three global models and compares their outputs Anderson et al (2010) Studies summer precipitation characteristics in the SWUS Andrade and Sellers (1988) Uses Mann-Whitney U-test to determine the relationship between precipitation and El Nino Bamston et al (1997) Determines region within the Pacific that reliably represents ENSO Brown and Comrie (2002) ENSO and PDO and how they correlate to SWUS precipitation Brown and Comrie (2004) ENSO and PDO and western USA precipitation Pascolini-Campbell et al (2015) Explores decadal variability of streamflow using PDSI & standardized precipitation index (SPI) Cañón et al (2007) Uses PCA to explore precipitation in the Colorado river basin and associations with PDO and ENSO Cayan et al (1998) Used PCA to regionalize western North America and then correlations to determine the decadal variability of precipitation (Continued.)  Cayan et al (1999) Uses SOI index to correlate with extreme precipitation Cayan et al (2010) Uses 12 GCMs used in IPCC AR4 using statistical downscaling Chylek et al (2014) MLR using multiple predictor variables of future SWUS climate Dai et al (2020) Uses WRF models to study contiguous USA precipitation DeFlorio et al (2013) Uses community climate system model (CCSM4) model for 150 years simulation period Delsole et al (2011) Uses multiple model ensembles to separate forced and unforced components in the global climate system Dominguez et al (2010) Compares IPCC AR4 model runs to observations Dominguez et al (2012) Uses eight climate ensemble models for IPCC AR4 on western US precipitation Ni et al (2002) Linear and non-linear techniques for climate reconstruction Fleming and Anchukaitis (2016) Uses CMIP5 for reconstruction Fosser et al (2017) Compares outputs of CPMs and RCMs in SW Germany Galambosi et al (1999) Fuzzy-based rule model (FBRM) vs multiple linear regression model (MLRM) Gao et al (2011) Uses 11 different models to investigate Climate Change in the Colorado River Basin Gao et al (2012) Had 4 GCMs and 4 RCMs Gershunov and Barnett (1998) Determines how ENSO and NPO influence North American climate Goodrich and Ellis (2008) Examines precipitation reversals in AZ Goodrich (2007) Examines PDO and ENSO Goodrich (2004) PDO and ENSO on AZ's winter precipitation Guan et al (2005) PDO and ENSO relationship for mountainous areas Gutzler and Robbins (2011) Simulations were done for A1B radiative forcing scenario Gutzler et al (2002) ENSO and PDO on SW winter precipitation Higgins et al (2000) Uses PCA to determine dominant factors of seasonal predictability Astel et al (2004) Derives tree ring indices to detect PDO and ENSO signals Hereford et al (2006) Determines multidecadal precipitation variability in the Mojave Desert Hidalgo and Dracup (2003) Relies on correlational analysis when studying PDO and ENSO effects on Upper Colorado River Basin (UCRB) hydroclimate variability Higgins and Shi (2000) Studies interannual variability of the summer monsoon for SWUS Higgins et al (1999) Relationship between monsoon behavior and ENSO  Liu et al (2017b) Uses regression and correlations for oxygen isotopic reconstruction Liu et al (2017b) Uses WRF CPM models to simulate future N. American climate. Uses RCP 8.5 scenario Luong et al (2017) Simulates NAM in SWUS using CPM McCabe and Clark (2006) Uses PCA and correlations to determine the shifting relationship between summer monsoon and winter precipitation in SW McCabe and Dettinger (2002) Relies on PCA to determine leading modes of variability of snowpack Mamalakis et al (2018) Explores correlations between ENSO indices & NZI Mann et al (2021) Uses models to study forced AMO variations Mantua et al (1997) Explores leading variability modes for the Pacific McAfee and Russell (2008) Correlates NAM and spring precipitation McCabe and Dettinger (1999) Uses multiple ENSO indices and correlates with western US precipitation McCabe et al (2004) Uses PCA and regression analysis to determine leading modes of drought frequency McPhaden (2015) Monitors SST in the Pacific to explain the 2014/15 El Nino Meehl and Hu (2006) Uses the parallel climate Model (GCM) for multidecadal analysis  Uses 6 multi-model ensembles, 3 with decreasing El Nino amplitudes and 3 with Increasing  Uses PCM, a GCM to simulate future US extremes Meehl et al (2009) Uses PCM to study the 1970s climate shift Mo et al (2009) Uses different models and 9 combinations of Pacific and Atlantic SST anomalies together with observational data Newman et al (2003) Uses EOF to determine relationships between ENSO & PDO Paek et al (2017) Uses reanalysis data and primarily uses EOF analysis Pal et al (2019) Illustrates advantages of CPM over RCM Piechota et al (1997) Uses PCA, cluster analysis, and Jackknife Prein et al (2020) Uses WRF model Quiring and Goodrich (2008) Explores interactions between multi-year La Ninas and El Ninos with PDO, AMO, and EPO. Cook et al (2015) Simulates 2006-2099 warming under RCP 8.5 (17 models) & 4.5 (15 models).

Appendix 2(d).
Publication outlets for the cited literature.

Appendix 3. Analysis of precipitation trends Appendix 3(a). Descriptive statistics
The tables provide general descriptive statistics for precipitation of the SWUS spatial units at two levels: one, considering all the seasons; two, considering four different winter month combinations (DJF, DJFM, JFM, and NDJFM).  (1950-1975, 1976-1995, and 1996-2018)

Appendix 4 Appendix 4(a)
Correlational analysis between SWUS precipitation and climate modes. The correlograms in appendix 4(a) show significant relationships between SWUS precipitation and the various climate modes for the entire dataset  while considering the various winter months combinations.

Appendix 4(b)
Correlational analysis for winter months combinations while considering PDO phase shifts. The correlograms in appendix 4(b) show significant correlations for the SWUS precipitation and climate modes while considering the PDO phase shifts (1950-1975, 1976-1995, 1996-2018) for the various winter month combinations.

Appendix 4(c)
Phases of climate modes and precipitation deviation from the mean. The tables in appendix 4(c) provide counts and percentage occurrence of warm, cold, and neutral phases between 1950-2018 for the Oceanic teleconnections and relate the counts and percentages to each SWUS spatial unit precipitation events above/ below the mean for the entire period of study.