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  • View in gallery

    Eastern Hemisphere study domain, inclusive of a TWP subdomain where event-specific rainfall statistics were compiled (after LC).

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    TWP SST distributions (%): dashed red line is for ocean background and black dashed line is the pdf distribution of the individual onset events (gray dots). Companion LSSTc data plotted at 49 monthly median onset locations [°C (100 km2)−1]. Thick black line is the least squares fit to the median onset values of LSSTc. This curve is shifted downward to best overlay background LSSTc data (thin red line). In each case, monthly LSSTc medians are plotted at monthly mean SSTs. Based on the least squared fit to background medians (not shown), the average onset-to-background ratio of median LSSTc varies from about 1.7 to 1.8.

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    Temporal and zonal correlations between precipitation and (a),(b) SST, (c),(d) LSSTc, and (e),(f) |SSTG|. Statistical significance (t test, >95%) is marked by contours in (a),(c), and (e) and dashed lines in (b),(d), and (f). All correlations are approximately in quadrature with rain, where SST and LSSTc lead rain by 1–2 and 2–3 days, respectively, and |SSTG| lags rain by 3–4 days.

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    An example of temporal–spatial coherence of LSST for the period August and September 2008. Characteristic persistence is 6–14 days with zonal dimension 0.5°–1.5° longitude.

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    Unfiltered 2008 time series of (a),(c),(e) LSSTc and (b),(d),(f) rain at (left) the equator, (center) 7.5°N, and (right) 12.5°N. Qualitative inspection reveals persistent zonal asymmetry in LSSTc at the equator, 15–90-day periods of asymmetry at 7.5°N, and seasonal variability at 12.5°N. Also note a general tendency for increased rainfall in periods of asymmetry biased toward LSSTc.

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    The 2008 Eastern Hemisphere rainfall in the MJO passband at 5°N. Positive (negative) anomalies are outlined in red (black) at 95th-percentile confidence. The active phase propagates eastward flanked by periods of significant suppression. Thick contours indicate the active MJO periods (days with MJO amplitude greater than 1).

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    Dispersion relation for (a) CMORPH precipitation, (b) SST, and (c) LSST. Rain exhibits MJO maximum for 20–80-day period and wavenumbers 1–6. SST exhibits MJO maximum, monotonically increasing power for 40–96-day period, and approximately symmetric about wavenumber 0 (nearly stationary). LSST exhibits MJO maximum for 30–60-day period and wavenumbers 1–7.

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    Rainfall and anomaly rainfall by phase of the MJO, averaged over 15°N–15°S. (a) Unfiltered CMORPH rain data exhibiting eastward progression and considerable disruption in the Maritime Continent region. (b) Eastward progression of rain anomaly in MJO passband. Contours of rain anomaly after MJO bandpass are superimposed. Anomaly magnitude is maintained in Maritime Continent region, suggesting that leading and lagging MJO phases (above and below anomaly) are similarly suppressed.

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    Temporal and zonal correlation between precipitation and (a),(b),(c) LSSTc and (d),(e),(f) SST at MJO phases 1, 4, and 7. Note that correlation maximum of LSSTc tracks the phase progression of MJO active phase across the Eastern Hemisphere. The correlation between precipitation and SST, while uniformly strong, exhibits no specific relationship to MJO active phase.

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    Correlation of filtered LSSTc with rain: (a) 0–20 days before rain and (b) 0–20 days after rain. Disruption of LSSTc within the Maritime Continent is especially evident in (b). Rain anomaly contours are thick lines. Statistical significance at 95th percentile is denoted by thin black lines.

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    (a) SST and (b) LSSTc anomalies by phase of the MJO and longitude. Both quantities lead precipitation (background contours) by approximately 10 and 11 days, respectively. Magnitude of the LSSTc anomaly is somewhat diminished in Maritime Continent region.

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    Leading and lagging variables in MJO passband. Leading variables are (a) LSSTc, (b) SST, and (c) number of rain events; lagging variables are (d) SSTG, (e) rain anomaly, and (f) average precipitation per event. Unlike other variables, number of events and precipitation per event are not bandpass filtered.

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Tropical Oceanic Rainfall and Sea Surface Temperature Structure: Parsing Causation from Correlation in the MJO

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  • 1 National Center for Atmospheric Research,* Boulder, Colorado
  • 2 University of Saskatchewan, Saskatoon, Saskatchewan, Canada
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Abstract

Based upon on the findings of Y. Li and R. E. Carbone, the association of tropical rainfall with SST structure is further explored, with emphasis on the MJO passband. Analyses include the tropical Indian Ocean, Maritime Continent, and tropical western Pacific regions. The authors examine the anomalies of and correlations between SST structure, the frequency of rainfall events, and rainfall amount. Based on detailed examination of a 49-month time series, all findings are statistical inferences and interpretations consistent with established theory.

The statistical inferences are broadly consistent with a pivotal role played by the convergent Laplacian of SST together with an expected, but somewhat indirect, role of SST itself. The main role of SST in the MJO passband appears limited to production of moist static energy, which is highly correlated with cumulative precipitation, yet bears a decidedly conditional relationship to the occurrence of rainfall. If rain occurs, then more rain is likely over warmer SST. The convergent Laplacian of SST is strongly associated with the onset of rainfall, apparently through its capacity to induce vertical air motion with sufficient kinetic energy to overcome convective inhibition in a conditionally unstable troposphere. The convergent Laplacian of SST is directly associated with the location and the variability of rainfall event frequency while having a less direct relationship to cumulative rainfall. These nuanced interpretations of rainfall forcing by the Laplacian of SST, and conditional modulation of cumulative rainfall by SST, may underlie systematic errors in highly parameterized models as a consequence of variable asymmetry in the field of Laplacian anomalies.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Richard. E. Carbone, National Center for Atmospheric Research, 1850 Table Mesa Dr., Boulder, CO 80305. E-mail: carbone@ucar.edu

Abstract

Based upon on the findings of Y. Li and R. E. Carbone, the association of tropical rainfall with SST structure is further explored, with emphasis on the MJO passband. Analyses include the tropical Indian Ocean, Maritime Continent, and tropical western Pacific regions. The authors examine the anomalies of and correlations between SST structure, the frequency of rainfall events, and rainfall amount. Based on detailed examination of a 49-month time series, all findings are statistical inferences and interpretations consistent with established theory.

The statistical inferences are broadly consistent with a pivotal role played by the convergent Laplacian of SST together with an expected, but somewhat indirect, role of SST itself. The main role of SST in the MJO passband appears limited to production of moist static energy, which is highly correlated with cumulative precipitation, yet bears a decidedly conditional relationship to the occurrence of rainfall. If rain occurs, then more rain is likely over warmer SST. The convergent Laplacian of SST is strongly associated with the onset of rainfall, apparently through its capacity to induce vertical air motion with sufficient kinetic energy to overcome convective inhibition in a conditionally unstable troposphere. The convergent Laplacian of SST is directly associated with the location and the variability of rainfall event frequency while having a less direct relationship to cumulative rainfall. These nuanced interpretations of rainfall forcing by the Laplacian of SST, and conditional modulation of cumulative rainfall by SST, may underlie systematic errors in highly parameterized models as a consequence of variable asymmetry in the field of Laplacian anomalies.

The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author address: Richard. E. Carbone, National Center for Atmospheric Research, 1850 Table Mesa Dr., Boulder, CO 80305. E-mail: carbone@ucar.edu

1. Introduction

The main objective of this paper is to clarify the specific roles of mesoscale sea surface temperature (SST) structure in the production and distribution of tropical oceanic rainfall. The warm waters of the tropical Eastern Hemisphere, including the Indian Ocean, Maritime Continent, and western Pacific, are widely associated with convective precipitation. These regions are commonly under the influence of the Hadley and Walker circulations and various tropical waves, though not uniformly so (Webster and Lukas 1992). The Madden–Julian oscillation (MJO) modulates rainfall at the planetary scale, typically exhibiting eastward propagation of about 5 ms−1 and a period of 30–60 days (e.g., Madden and Julian 1972; Kiladis et al. 2009; Zhang 2005; Wang 2012; Zhang 2013). The active phase of the MJO produces extensive superclusters of convective rainfall on a scale that is rarely if ever equaled under other circumstances (e.g., Chen and Houze 1997). Global weather and climate models have a long and somewhat tortured history, attempting to simulate or forecast near-equatorial rainfall, including the active phase of the MJO. The influence of geostrophy is greatly diminished at the scale of individual convective rainfall events, especially at the onset of rainfall. Recent global model performance improvements, mainly resulting from increased resolution, assimilation of SST observations, and coupled ocean models, suggest that major breakthroughs are possible (de Boisséson et al. 2012).

Herein, the working definition of SST “structure” includes SST and its first two spatial derivatives as described by Li and Carbone (2012, hereafter LC). SST itself is an important correlate with tropical rainfall as established by numerous works (e.g., Gadgil et al. 1984; Neelin and Held 1987; Ramanathan and Collins 1991; Fu et al. 1994; Lau and Sui 1997) and is often implicitly or explicitly attributed a direct causal relationship. While systematic errors persist, the influence of prescribed SST on tropical rainfall has gradually improved model rainfall climatologies (Hendon 2000; Waliser 2012). It is unclear whether large systematic errors are related to lower-boundary representations, large-scale tropospheric dynamics, or both, or neither. Models have evolved to the point where higher resolution increasingly begs improved representation of SST fields at scales commensurate with deep moist convection (Chelton et al. 2004; Minobe et al. 2008; Small et al. 2008). Significant performance improvements have been reported from prescribed weekly and daily SST fields (de Boisséson et al. 2012; Toy and Johnson 2014) at scales from 25 to 100 km.

Tropical SST gradients (SSTG) are generally weaker and less persistent than gradients imposed by western boundary currents. The comparison is more favorable with the amplitude of breezes at the margins of tropical islands (Li and Smith 2010). Unlike islands and western boundary currents, tropical midocean SST gradients are ephemeral and relatively subtle, approximately 1°C, on scales of 50–200 km (LC). The Tiwi Islands, north of the Australian continent, are relatively flat and wet, with a virtual temperature contrast of 1°–1.5°C across breeze fronts (e.g., Carbone et al. 2000). In season, Tiwi breezes regularly trigger rainfall events that are among the strongest on Earth, in an environment similar to the tropical western Pacific (TWP) and the Indian Ocean (IO).

At larger scales, an alternative view of lower-boundary forcing was advanced by Lindzen and Nigam (1987), Raymond (1995), and recently revisited by Back and Bretherton (2009). They examined the effects of SSTG, concluding that such gradients could significantly strengthen horizontal convergence and ascent in the marine boundary layer, especially when accompanied by large-scale deep tropospheric ascent. In principle, the lower troposphere, once destabilized by elevated SST, may render the deep troposphere more vulnerable to the occurrence of deep moist convection, subject to the limitations imposed by intervening convective inhibition (CIN). While theory associated with SSTG has a solid theoretical foundation, it has not gained much traction in the literature, perhaps because of the aforementioned anomaly correlation between rainfall and SST. Since correlation and cause are not synonymous, the authors have pursued the current line of research based on a renewed application of existing theory that emphasizes mesoscale dynamics together with sensitivity to low-frequency variations in the MJO passband.

LC examined the role of observed mesoscale SSTG (50–200 km), specifically in relation to the triggering of rainfall events in the TWP. Their working hypothesis assumed that transient mesoscale SSTGs, of order 1°C, could force boundary layer convergence sufficient to excite convective precipitation events. Established theory (Lindzen and Nigam 1987) proves that convergence can result from hydrostatic pressure gradients, where mesoscale atmospheric boundary layer temperature structure conforms to that of SST under conditions of slow mean flow. Specifically, convergence can occur near the maximum of the negative SST Laplacian (i.e., the convex curvature of SST), typically located in the warm half of a gradient. Based on observed atmosphere–ocean properties in the TWP, LC showed that local (~100 km) forcing of this type can be 10–20 times that of the average background Hadley–Walker circulations in the marine atmospheric boundary layer. Therefore, it seems plausible that SSTGs could increase the frequency of deep moist convection when and where the overlying troposphere supports it.

LC found that onset of rainfall is strongly preferred near the mode of the SST distribution (~28.9°–29.9°C), that the existence of large-amplitude SSTGs alone is insufficient to trigger rainfall, and that 75% of 104 rainfall events in the TWP were triggered at convergent anomalies of the SST Laplacian (LSSTc, signed positive). The background distribution of LSST, averaged over a period of years, is quite symmetric, exhibiting a dipole structure that is evenly divided between convergent and divergent anomalies of similar amplitude (LC). The tendency toward onset of rainfall near the SST mode, together with strong bias toward LSSTc, raises fundamental questions about the physical–dynamical relationship between SST structure and rainfall occurrence. Does the relationship between SST or one or more of its derivatives constitute a direct cause of rainfall? Are these properties cooperative in some manner, or are they merely coincidental or otherwise covariant?

In this paper, clarification is provided on lower-boundary forcing and how it varies with apparent stability of the overlying lower troposphere. The focus is subsequently directed toward rainfall in the MJO passband across the Eastern Hemisphere. Section 2 briefly summarizes the datasets and calculations therefrom. Section 3 examines anomaly correlations of local SST structure and rainfall in the (unfiltered) mesosynoptic passband, including events with a duration of 3 h or longer. Section 3 also reveals the existence of larger-scale, lower-frequency variations in SST structure, which constitute a basis for exploration of relevance to the MJO. Section 4 focuses on the MJO active-phase passband, including wave dispersion analysis (e.g., Wheeler and Kiladis 1999; Kiladis et al. 2009). SST structure, rainfall anomalies, and their covariances are examined across the Eastern Hemisphere, including the IO, the Maritime Continent (MC), and the TWP. Section 5 briefly summarizes major findings and advances plausible interpretations of same, leading to prescribed directions of and hypotheses for future research.

2. Observations and calculations

After LC, we rely on two satellite composite datasets that span a 49-month period, beginning in March 2006. Climate Prediction Center (CPC) morphing technique (CMORPH; Joyce et al. 2004), produced by the NCEP Climate Prediction Center, provides time-resolved rainfall estimates from a combination of geostationary infrared data and low-orbit microwave data. For daily averaged SST structure, we employ a composite dataset, OSTIA, produced by the international Group for High Resolution SST (GHRSST; Donlon et al. 2007).

a. Rainfall data (CMORPH; Joyce et al. 2004)

Quantitative precipitation estimates from CMORPH data rely exclusively on low-orbit microwave observations, the features of which are temporally interpolated and positioned based on geostationary IR imagery data. Typical microwave instruments in these orbits have footprints approximately 20–25 km in dimension. Multiple instruments sample the same region each day, from polar and other inclined orbits. Rainfall is gridded at 0.258° with a 3-h interval as obtained from the CPC morphing technique. Within a TWP subdomain, bounded by 0°–15°N, 130°–160°E (Fig. 1), rainfall statistics were calculated by LC at the individual storm scale for about 104 events spanning the 49-month period. Events were tracked from rainfall onset to dissipation, where onset was defined as a central maximum of 1 mm h−1 or greater from a minimum of five grid points. Among other quantities, the tracking of events enabled compilation of event life-cycle statistics. Additional detail on use of event-level CMORPH data in conjunction with local SST structure is provided in appendix A of LC.

Fig. 1.
Fig. 1.

Eastern Hemisphere study domain, inclusive of a TWP subdomain where event-specific rainfall statistics were compiled (after LC).

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

Across the tropical Eastern Hemisphere, 15°N–15°S (Fig. 1), CMORPH data were employed to estimate the planetary phase and amplitude of precipitation within the MJO passband (inclusive of the 30–60-day period and wavenumbers 1–5). Only dates and corresponding locations of cumulative rainfall were retained for hemispheric statistical analyses in the MJO passband. Unlike LC, individual rainfall-event onset locations were neither identified nor correlated with SST structure. Land areas were masked, defined by boundaries of SST data.

b. High-resolution SST data (GHRSST; Donlon et al. 2007)

Products from GHRSST are coordinated internationally. The version used herein, OSTIA, is available in the United States from the NASA Jet Propulsion Laboratory, California Institute of Technology. It consists of daily averaged SST on a 5-km grid. Both microwave and infrared data are assimilated, as appropriate for conditions. Owing to cloudiness during an active phase of the MJO, infrared data have minimal impact on the merged product. LC showed that the resolved scales were most often limited to those consistent with the dimensions of microwave footprints. Sources of data include the National Oceanic and Atmospheric Administration (NOAA) series of Advanced Very High Resolution Radiometer (AVHRR) polar-orbiting satellites, NOAA series of Geostationary Operational Environmental Satellites (GOES), NASA’s Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board the Terra and Aqua Earth satellites, the European Advanced Along-Track Scanning Radiometer (AATSR) on board the Envisat satellite, the European geostationary Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board Meteosat, the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E), and the Japan Aerospace Exploration Agency’s (JAXA) Multifunctional Transport Satellite (MTSAT).

The advantage of this GHRSST dataset is the quality control exercised by international experts, permitting resolution of relatively small-scale SST features (Donlon et al. 2007). Temporal and spatial interpolation is employed when too many microwave estimates are disqualified near a grid cell on a given day. Uncertainty in the combined SST estimates is approximately 0.1°C, with typical rms variations from a single instrument being 0.3°C. In LC and herein, the principal sensitivity is not to SST per se but rather to the derivatives thereof, where variation in point-to-point bias is the greatest data-quality concern. The most sensitive SST calculations are performed up to the day before rain, followed by days after rain, not during the occurrence of rain itself. We estimate the noiselike variability at 0.05°–0.08°C, through which a 40-point, order-10 polynomial is applied to the 5-km grid. This is consistent with harmonic content at 50–200 km; however, half wavelengths less than 75 km are damped.

c. MJO phase data

The amplitude and phase of the MJO is calculated globally (after Wheeler and Hendon 2004) based on daily analyses and reanalyses from the major NWP centers. These data are primarily focused on wave-1 characteristics as inferred by the divergence fields associated with upper- and lower-tropospheric zonal winds. Eight sectors, centered on the Eastern Hemisphere, identify the active-phase location, which is typically flanked by suppressed regions. SST structure is examined for its phase and amplitude variations relative to the MJO active phase across the Eastern Hemisphere in our 49-month period of record. Furthermore, exclusively in the TWP subdomain, this information is also used during periods of active-phase residence to isolate covariances between rainfall, onset frequency, mean areal rainfall rate, and SST structure.

3. Rainfall activity and SST structure in the mesosynoptic passband

a. Characteristic thresholds associated with forcing of rainfall events

Based on the findings of LC, we modestly extend those results to include the amplitude of LSSTc forcing as a function of SST. For example, if the characteristic forcing required to excite rainfall is particularly large (small) for a given range of SST, a plausible inference could signal greater (lesser) static stability in the lower troposphere. If so, the expectation of a corresponding lower (higher) area-normalized frequency of rainfall excitation should result. Normalized SST pdf distributions in the TWP domain are shown for both the background ocean and the ocean locations corresponding to 7500 LSSTc rainfall onset events (Fig. 2). Rainfall onset frequency is significantly favored over the background from 28.9° to 29.9°C. Approximately 61% of rain events have their origin within 0.5°C of the background SST mode, exceeding the average background SST frequency by about 25%. Approximately 21% of rainfall events occur above 29.9°C, nearly in proportion to the background, and 18% of events occur below 29°C, at a rate markedly below the background. In boreal winter, seasonal cooling is a major factor between 10° and 15°N, where SST is below 28.5°C and surface trade winds prevail (LC). Stronger surface winds will generally decrease conformance to mesoscale SST structure despite increased interfacial fluxes.

Fig. 2.
Fig. 2.

TWP SST distributions (%): dashed red line is for ocean background and black dashed line is the pdf distribution of the individual onset events (gray dots). Companion LSSTc data plotted at 49 monthly median onset locations [°C (100 km2)−1]. Thick black line is the least squares fit to the median onset values of LSSTc. This curve is shifted downward to best overlay background LSSTc data (thin red line). In each case, monthly LSSTc medians are plotted at monthly mean SSTs. Based on the least squared fit to background medians (not shown), the average onset-to-background ratio of median LSSTc varies from about 1.7 to 1.8.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

Two identical quasi-horizontal curves appear in Fig. 2. The upper curve is the least squares fit to the bivariate distribution of median rainfall onset LSSTc, plotted at the monthly average of onset SST. Significantly, the minimum of median onset LSSTc is essentially coincident with the mode of the onset SST distribution. A plausible interpretation of this negative covariance is consistent with reduced CIN near the SST mode. The lower LSSTc curve is merely the upper curve shifted downward to pass through the median background LSSTc data. While not an exact fit, it illustrates a similar pattern. A nearly constant onset-to-background ratio between the two sets of data, approximately 1.75, applies. This ratio is equivalent to a factor of 3 in the characteristic vertical kinetic energy (VKE) that would be required to overcome elevated potential energy (i.e., lower-tropospheric CIN), thereby possessing sufficient energy to reach a level of free convection. Above and below about 29.5°C, the characteristic value of onset LSSTc increases significantly while maintaining a similar VKE ratio over the background. The highest inferred VKE in this analysis is at the coolest SST, consistent with static stability in boreal winter trade winds at 10°–15°N. It should be noted that the authors have no direct knowledge of vertical air motions, so what we have stated here should be viewed as statistically inferred VKE. Established theory says that LSSTc should be linearly proportional to vertical velocity, other factors considered equal. While our reasoning is fully consistent with this theory, unrelated coincident or covariant forcings could be active.

Why might excitation of rainfall be easier near the SST mode? Active periods are often preceded by suppressed periods. Suppressed periods typically pass a high fraction of incoming shortwave radiation, resulting in storage of upper-ocean heat content prior to an active period. Following an active period, LC show that SST is cooler, owing to convectively generated winds, evaporation, and deposition of freshwater. While not necessarily the case, these processes can lead to a more stable marine atmospheric boundary layer (MABL). The summation of these leading (warm) and trailing (cool) periods of increased stability could well lead to the maximum of rainfall onset frequency near the SST mode. This pattern can and probably should be viewed as an aspect of convective–radiative equilibrium.

b. Anomaly correlations between rain and SST structure in the TWP

The correlation between rain and SST in the TWP (Figs. 3a,b) is in quadrature phase, with warm SST leading rain by 1–2 days. While some periodicity in longitude is indicated, there is no obvious zonal trend. Zonally averaged correlation (~0.1) is statistically significant in the 1–2-day period (Fig. 3b) as determined by a Pearson t test, where 95th percentile confidence is about 0.06 (see appendix for details). The quadrature phase relationship is expected given freshwater flux and convectively driven winds to cool the surface ocean (Elsaesser and Kummerow 2013). The period of SST–rain correlation averages about 6–7 days.

Fig. 3.
Fig. 3.

Temporal and zonal correlations between precipitation and (a),(b) SST, (c),(d) LSSTc, and (e),(f) |SSTG|. Statistical significance (t test, >95%) is marked by contours in (a),(c), and (e) and dashed lines in (b),(d), and (f). All correlations are approximately in quadrature with rain, where SST and LSSTc lead rain by 1–2 and 2–3 days, respectively, and |SSTG| lags rain by 3–4 days.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

Correlation between rain and LSSTc in the tropical Pacific (Figs. 3c,d) slightly leads quadrature phase, exhibiting a somewhat stronger and broader phase lead of 1–4 days at the 95th percentile, with correlation of about 0.17. We attribute the increased lead time to LSSTc’s primary association with excitation of rainfall in contrast to the full duration of rain events. As reported in LC, the curvature of gradients reverses polarity in response to the deposition of rain. The LSST–rain correlation period averages about 8 days. This period corresponds favorably with the characteristic longevity of LSST dipoles, which is 6–12 days as determined from inspection of Fig. 4. The longevity of these dipoles, to some extent, speaks to the frequency at which SST data should be assimilated in forecast models, where and when lower-boundary forcing is influential. In the domains examined here, weekly averages of SST would appear to be sufficient. Recent hindcast experiments (de Boisséson et al. 2012) at ECMWF may have relevance to the coherence exhibited in Fig. 4. They assimilated daily SST, weekly running averages, and monthly average SST data. The model employed had the resolution and compatible physics sufficient to capture the dynamics of an atmospheric mesoscale divergence field. The highest skill in capturing persistence of the MJO was achieved with weekly, as opposed to daily, SST fields. These results offer promise of improved MJO forecasts by demonstrating what may be an optimal match between the frequency of lower-boundary variations and the assimilation of SST data.

Fig. 4.
Fig. 4.

An example of temporal–spatial coherence of LSST for the period August and September 2008. Characteristic persistence is 6–14 days with zonal dimension 0.5°–1.5° longitude.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

Correlation between rain and SSTG amplitude (|SSTG|; Figs. 3e,f) is also in quadrature phase; however, the polarity is reversed. The strongest positive correlation (0.19) lags rainfall by 1–6 days, with a correlation period of about 13 days. This is broadly consistent with effects of freshwater flux and convectively generated winds that are likely associated with upper-ocean mixing and elevated eddy fluxes. There is irony in the association of gradient curvature with the excitation of rainfall on one hand, while also observing the strongest SSTG amplitudes to be a consequence of such disturbance. A plausible explanation for this is related to asymmetry in the field of LSST, which is discussed next.

c. Annual time series of LSST and rainfall in the TWP

When the time series of LSST is averaged, its pdf exhibits symmetry about zero between convergent and divergent LSST maxima (LC, their Fig. 10). If such symmetry is persistent over long periods, say from annual to decadal or more, it is unclear what difference, if any, LSST structure would make in the global redistribution of oceanic rainfall. A LSST time series with relatively constant amplitude, scale, and zero mean value implies quasi stationarity in lower-boundary forcing of this type. Any variability in regional rainfall would likely result from other forcings; however, LSST itself would seem to have little if any prognostic or diagnostic value beyond specific dipole locations. While the location of individual LSST dipoles could continually evolve, amplify, and dissipate at roughly 100-km scale, the net impact on regional/seasonal/interannual distributions of rainfall likely would be minimal. For this reason, the time series of SST structure was examined for evidence of low-frequency and regional-spatial variability, including LSST dipole asymmetry.

Unfiltered time series of daily LSST and rainfall in annual Hovmöller diagrams (Fig. 5) are informative because they illustrate low-frequency variability in the LSST field at three latitudes: the equator, 7.5°N, and 12.5°N. Simple inspection reveals temporal and zonal variability on scales from 2 weeks to 4 months and from 500- to 2000-km zonal extent. LSSTc variability is evident in dipole asymmetry and/or amplitude. Periods of variation are inclusive of, but not limited to 30–60 days, characteristic of the MJO. Upon further inspection, qualitative intercomparisons with rainfall reveal a noticeable degree of covariance between zonal–temporal patches of net field convergent LSST (〈LSSTc〉) and rainfall and diminished rainfall where net divergent 〈LSST〉 prevails. While far from a 1:1 match, these associations hint at a statistical relationship between the regional LSST field asymmetry and rainfall variability at low frequencies. Quantitative calculations, in the form of bivariate anomaly correlations, are presented in section 4, with emphasis on the MJO passband.

Fig. 5.
Fig. 5.

Unfiltered 2008 time series of (a),(c),(e) LSSTc and (b),(d),(f) rain at (left) the equator, (center) 7.5°N, and (right) 12.5°N. Qualitative inspection reveals persistent zonal asymmetry in LSSTc at the equator, 15–90-day periods of asymmetry at 7.5°N, and seasonal variability at 12.5°N. Also note a general tendency for increased rainfall in periods of asymmetry biased toward LSSTc.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

In summary, the mesosynoptic properties of TWP rainfall, as presented with respect to daily SST and its derivatives, are consistent with previous findings, where SST leads in quadrature. Added insight is provided by a stronger and longer leading phase of LSSTc compared to SST, from which a cooperative LSST–SST (forcing–production) of rainfall could emerge. Qualitative inspection of annual Hovmöller diagrams provides hints of an association between the larger scales and lower frequencies of LSSTc asymmetry with rainfall variability.

4. MJO passband characteristics

a. Rainfall distribution and wave dispersion analysis

The MJO typically exhibits a well-defined active phase flanked by relatively strong suppression. All subsequent analyses are across the Eastern Hemisphere domain (15°N–15°S; Fig. 1), or within as otherwise noted.

An example of activity in the MJO passband is illustrated by the 2008 Eastern Hemisphere precipitation at 5°N (Fig. 6). Unfiltered CMORPH data (mm h−1) are presented together with eastward-propagating, filtered rainfall anomaly contours in the 30–96-day passband and wavenumbers 1–5. Thick contours indicate the active MJO periods (days with MJO amplitude greater than 1) based on RMM (Wheeler and Hendon (2004). Contours in thin black and red lines are days with MJO amplitude less than 1. The MJO amplitude of each day is exactly from the Wheeler MJO index. For year 2008, there are 256 days with MJO amplitude greater than 1 (after Wheeler and Kiladis 1999, hereafter WK99). The passband anomaly contours are distinct from observed rainfall, capturing the general field of weaker and stronger rainfall periods as positive (red) and negative (black) anomalies. As is typical, the pattern is best developed from the IO to the date line.

Fig. 6.
Fig. 6.

The 2008 Eastern Hemisphere rainfall in the MJO passband at 5°N. Positive (negative) anomalies are outlined in red (black) at 95th-percentile confidence. The active phase propagates eastward flanked by periods of significant suppression. Thick contours indicate the active MJO periods (days with MJO amplitude greater than 1).

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

For wave dispersion analyses, we follow methodology in the works of Takayabu (1994), WK99, Masunaga et al. (2006), and the comprehensive review of Kiladis et al. (2009, their Fig. 1a). As previously, we identify rainfall from CMORPH data, since these estimates are somewhat more direct than those inferred solely from infrared outgoing long wave radiation. The dispersion space in Fig. 7a includes wavenumbers ±15 and periods from 2 to 96 days. The analysis yields a substantially similar pattern of symmetric power to Kiladis et al. (2009). Power is distributed for each of the major wave types including MJO, Kelvin, and eastward- and westward-propagating inertia–gravity waves and equatorial Rossby waves. At least in this realization, the MJO and Kelvin waves are prominent. We note that the asymmetric part of the energy spectrum was quite weak in the MJO passband for this time series, which may not be the case in other instances. Given that the RMM index winds are restricted to the zonal component, all remaining figures remain compatible with the symmetric component of the precipitation field.

Fig. 7.
Fig. 7.

Dispersion relation for (a) CMORPH precipitation, (b) SST, and (c) LSST. Rain exhibits MJO maximum for 20–80-day period and wavenumbers 1–6. SST exhibits MJO maximum, monotonically increasing power for 40–96-day period, and approximately symmetric about wavenumber 0 (nearly stationary). LSST exhibits MJO maximum for 30–60-day period and wavenumbers 1–7.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

This analysis was also applied to SST structure, including SST and LSST (Figs. 7b and 7c, respectively), where only the symmetric MJO-related low-frequency power is displayed. All land area perturbations were set to zero for computational convenience. In the MJO region, symmetric SST power surrounding wavenumber 0 extends from about 40 days, increasing power to the 96-day computational limit. Symmetry about wavenumber 0 is consistent with a quasi-stationary wave. LSST exhibits power centered on a period of about 20–80 days and wavenumbers 1–7.

b. Rainfall distribution and anomaly correlations in the Eastern Hemisphere

As previously described in association with Fig. 6, phase space is defined by the two-component RMM index, Wheeler and Hendon (2004), where analysis of the MJO is typically expressed in eight zonal sectors that span the Eastern Hemisphere (sectors 2–7) and also include adjacent portions of the Western Hemisphere (sectors 1 and 8). The Indian Ocean is mainly associated with active phases 2 and 3, the Maritime Continent is mainly with active phases 4 and 5, and the western Pacific is mainly with active phases 6 and 7. In addition to a high concentration of convective precipitation systems, the active phase is characterized by large-scale lower-tropospheric convergence and upper-level divergence (Hendon and Salby 1994). The deep tropospheric circulation is typically flanked in the zonal dimension by a reversal of the horizontal divergence field and relatively suppressed conditions. The analysis as performed herein is confined to the oceanic portions of the Eastern Hemisphere (where up to eight sectors have some impact) between 15°S and 15°N. Given our focus on the influence of SST structure, all results are limited to the oceanic portions thereof.

We begin by examining oceanic rainfall distribution as a function of MJO phase and longitude with unfiltered CMORPH data (Fig. 8a). Eastward progression of rainfall in the IO (~60°–90°E) is mainly in phases 2 and 3, followed by a perturbed rainfall pattern in the MC (~100°–140°E), where average rainfall rate is diminished in phases 3–5. Progression to the TWP (~130°E–180°) occurs mainly in phases 5–7. The MJO passband filter is subsequently applied to the original rainfall data (Fig. 8b), the anomaly exhibiting a steady eastward progression as in the original data. Unlike the appearance of original data, the anomaly maintains relatively constant amplitude in the MC despite considerable disruption from mountainous islands comingled with intervening seas. The correlation maintains both strength and phase progression in the TWP through 150°E, with a somewhat diminished amplitude near the date line. Identical line contours of the anomaly appear in Figs. 8a and 8b for direct reference to original data.

Fig. 8.
Fig. 8.

Rainfall and anomaly rainfall by phase of the MJO, averaged over 15°N–15°S. (a) Unfiltered CMORPH rain data exhibiting eastward progression and considerable disruption in the Maritime Continent region. (b) Eastward progression of rain anomaly in MJO passband. Contours of rain anomaly after MJO bandpass are superimposed. Anomaly magnitude is maintained in Maritime Continent region, suggesting that leading and lagging MJO phases (above and below anomaly) are similarly suppressed.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

c. Zonal distributions of SST and LSSTc correlations with rain in active phases of the MJO

The longitudinal distributions of LSSTc and SST correlations with rain were calculated (after Wheeler and Hendon 2004) for MJO phases 1–8 in the period of record, including the IO, MC, and tropical Pacific from 15°N to 15°S. LSSTc (Figs. 9a–c) and SST (Figs. 9d–f) exhibit correlation at phases 1, 4, and 7, which are both in quadrature and leading by about 11 and 10 days, respectively. SST correlation is consistent with numerous studies, including DYNAMO observations (Xu and Rutledge 2014). Unique to this study are zonal maxima of LSSTc–rain correlation specific to the longitude bands of all active phases 1–7. Phases 1, 4, and 7 (Figs. 9a–c) illustrate the LSSTc correlation maxima at longitudes corresponding to the rain anomaly in Figs. 8. While subject to various interpretations, the LSSTc–rain correlation pattern easily lends itself to the suggestion of a causal relationship between LSSTc and heavy rainfall in the MJO active phase (to be discussed in section 5).

Fig. 9.
Fig. 9.

Temporal and zonal correlation between precipitation and (a),(b),(c) LSSTc and (d),(e),(f) SST at MJO phases 1, 4, and 7. Note that correlation maximum of LSSTc tracks the phase progression of MJO active phase across the Eastern Hemisphere. The correlation between precipitation and SST, while uniformly strong, exhibits no specific relationship to MJO active phase.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

Surprisingly, no significant change in SST–rain correlation is evident with eastward progression of the active phase (Figs. 9d–f). The SST positive anomaly, while very strong, persistent, and zonally extensive, is nearly invariant for all phases of the MJO in the Eastern Hemisphere. Active or suppressed, SST–rain correlation exhibits stationarity in quadrature spanning the 49-month period, from the IO to the date line, and for phases 1–8. This pattern serves to question the interpretation of an invariant correlation with a causal relationship, especially when stationarity is implied by wave dispersion power (Fig. 7b).

By reason of it being the basis for the existence of finite LSST, SSTG itself remains indirectly relevant to the causes of rainfall. Recall, in Fig. 3, unfiltered SST correlation with rain is in reverse polarity and in quadrature, lagging rain. The largest gradient amplitudes are generated in response to occurrence of rain, thereby obviating direct causal relationship. In the MJO passband, a similar pattern prevails at low frequency, with a correlation period of about 45 days.

Correlations in the MJO passband between LSSTc and rainfall (Fig. 10) also mirror the sense of anomalies shown in the unfiltered mesosynoptic data (Fig. 3). Within the MJO passband, low frequency of variation necessarily prevails, with correspondingly broader lead and lag times that are in quadrature with a 40–45-day period. The LSSTc positive anomaly leads rain by about 0–20 days (Fig. 10a) with the lagging negative anomaly being more variable and somewhat weaker (Fig. 10b).

Fig. 10.
Fig. 10.

Correlation of filtered LSSTc with rain: (a) 0–20 days before rain and (b) 0–20 days after rain. Disruption of LSSTc within the Maritime Continent is especially evident in (b). Rain anomaly contours are thick lines. Statistical significance at 95th percentile is denoted by thin black lines.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

The bivariate distribution of SST and LSST anomalies with MJO phase and longitude (Figs. 11; 60°E–180°) further illustrate correlations evident in previous figures. The LSSTc positive anomaly leads precipitation slightly more than SST but over a narrower longitudinal band and therefore a shorter residence time. A markedly deeper and somewhat broader negative LSSTc, compared to the SST anomaly, lags precipitation, which is likely a consequence of LSSTc specificity to the active phase.

Fig. 11.
Fig. 11.

(a) SST and (b) LSSTc anomalies by phase of the MJO and longitude. Both quantities lead precipitation (background contours) by approximately 10 and 11 days, respectively. Magnitude of the LSSTc anomaly is somewhat diminished in Maritime Continent region.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

Within the TWP domain (Figs. 12), event-based rainfall calculations permit examination of SST and LSSTc given three rainfall properties for all phases of the MJO in the period of record. The TWP domain is approximately centered on phase 6. Figures 12a–c constitute the “leading” variables: LSSTc, SST, and number of rain events. Figures 12d–f are the in-phase variables: |SSTG|, rain anomaly, and average rain per event, each of which lag the onset of rainfall. Specifically, we draw the reader’s attention to Figs. 12e and 12f, which embody the preferred definition of MJO active phase by rain anomaly and precipitation rate per event. The area-mean values of SST, LSSTc, and rainfall rate are specific to the MJO passband. The curves showing frequency of rain events (Fig. 12c) and rain per event (Fig. 12f) are unfiltered data from LC. Phase 6 is clearly the center of the active phase, defined by maxima in rainfall anomaly and rain per event. SST, LSSTc, and rain event frequency each precede maximum rainfall by approximately one MJO phase. These phase characteristics are consistent with the statistical inferences previously discussed. The coevolution of event frequency and rain per event tends to support the notion of an increased presence of organized convection (MCSs, superclusters), which facilitates greater rainfall production. An important attribute of SST, LSSTc, and the frequency of events is their strongly positive phase covariance. This covariance tends to obfuscate distinctions between “correlations with” and “causes of” rainfall in the context of SST structure, to be discussed in section 5. Such obfuscation may have contributed to the history of divergent conclusions among distinguished investigators in the relevant literature (e.g., Neelin and Held 1987; Ramanathan and Collins 1991; Lindzen and Nigam 1987; Back and Bretherton 2009).

Fig. 12.
Fig. 12.

Leading and lagging variables in MJO passband. Leading variables are (a) LSSTc, (b) SST, and (c) number of rain events; lagging variables are (d) SSTG, (e) rain anomaly, and (f) average precipitation per event. Unlike other variables, number of events and precipitation per event are not bandpass filtered.

Citation: Journal of the Atmospheric Sciences 72, 7; 10.1175/JAS-D-14-0226.1

5. Conclusions and interpretations from statistical inferences

Our conclusions are based on statistical inferences and consistency with established theory. As such, these fall short of proof and the establishment of cause, though the authors find the evidence compelling. The statistical inferences point toward a nuanced interpretation of causality and correlation between rainfall and SST structure. The leading variables are SST and its convergent Laplacian, the latter of which requires SST gradients of significant amplitude. The large majority of rain events have origin near the regional mode of SST distribution, where convective inhibition appears to be weakest. The apparent convective inhibition increases at both cooler and warmer SST, where the normalized event frequency is lower and the fraction of ocean is smaller.

Moist static energy production appears to be the main role of SST, which is sufficient to explain its high correlation with the cumulative aspect of oceanic rainfall climatology. While SST tends to be strongly correlated with cumulative rainfall, we conclude that its relationship is primarily conditional: i.e., if a rain event occurs, then more rain is likely when SST is elevated. A graphic example of this is SST’s apparent “blindness” to the active phase of the MJO, as exhibited in Fig. 9. Unlike LSSTc, SST maintains a similar correlation with rainfall from the most active to the most suppressed phases. LSSTc correlation with rainfall strengthens within the MJO active phase, while markedly decreasing in both leading and lagging periods of suppression. We argue that this result is likely evidence of a distinction between causality and correlation. The convergent Laplacian, consistent with established theory on forcing of vertical air motion, is strongly associated with increased frequency of rain events, given a conditionally unstable atmosphere and low surface wind speed.

LSST is highly symmetric when averaged over sufficient space and time. However, the time series reveals substantial asymmetry over periods from weeks to months—for example, in the MJO passband. Many of these periods are associated with rainfall anomalies of corresponding sign to the net LSST field asymmetry, convergent or divergent. While a quantitative pan-oceanic analysis has yet to be performed, such asymmetry may prove to be more important to the ultimate distribution of rainfall than the amplitude of individual LSST dipoles. One of our working hypotheses for ongoing research is motivated by systematic rainfall errors in global models, which may be related to Laplacian asymmetry.

While global models have traditionally operated at resolutions incapable of explicit representation at the convective mesoscale, recent MJO hindcast experiments (de Boisséson et al. 2012) at ECMWF may have relevance to issues raised herein. They assimilated daily OSTIA SST data for daily SST fields and running weekly averages thereof. The ECMWF global model employed had resolution (~15 km) sufficient to capture the essential dynamics of an atmospheric mesoscale divergence field. We are encouraged by these results, where correlation with the MJO exceeded 0.7 over 32 days and was consistent with, but not necessarily related to, weekly coherence of LSST fields, as illustrated herein (Fig. 4).

Covariance between SST and LSSTc is pervasive in our analysis, but not uniformly so. Potential causes of such covariance are numerous and therefore subject to speculation. In suppressed conditions, incoming shortwave radiation tends to warm the upper ocean over depths influenced by temperature, salinity, and biota profiles, as well as variation in surface winds and mesoscale ocean dynamics (Soloviev and Lukas 1996; Johnson et al. 2001). Owing to one or more of these factors, even under cloud-free skies, it is likely that SST warming (cooling) will be nonuniform, being less pronounced in oceanic patches where a larger heat flux is required for a similar SST increase (decrease). Under suppressed conditions, SST warming could assume the thermal shape of “bubbling up” (LSSTc) where surface heating is strongest and upper-ocean mixing is inhibited, thereby potentially assuming a net regional convergent bias. Similarly, in active MJO periods of ocean surface cooling, a net divergent LSST field, “cratering down,” could emerge. The most common temporal sequence of SST–LSST evolution in our time series exhibits a marked tendency toward these trends, but not uniformly so.

A few comments are in order with respect to characterizations of one fluid driving the other in the MJO. Evidence in the established literature weighs heavily toward the atmosphere driving the ocean. Much of our thinking is influenced by the pendulum of convective–radiative equilibrium. A key to our findings here is the critical importance of a leading, warming, suppressed phase and its apparent role in amplifying LSSTc. While we give partial credit to the MJO for helping to sow the seeds for future rainfall excitation, fundamentally, this is the influence of incoming shortwave radiation. While arguable, the authors perceive the evolution of LSST structure (at the leading suppressed phase) to be as likely or more likely determined by influences within the upper ocean (including static and dynamic stability factors), not necessarily the MJO per se. It is obvious that rainfall activity near the highest SSTs under these conditions is quite minimal in the pdf of total rainfall despite the buildup of 〈LSSTc〉. A high frequency of activity near the SST mode suggests that onset of significant rainfall awaits relaxation of CIN as moistening of the middle troposphere develops in eastward propagation where LSSTc amplification has occurred. During this transition from suppression to the active phase, with the assistance of LSSTc mesoscale convergence, the MJO directly and fully occupies the driver’s seat. The atmosphere not only controls the active phase but also helps to reset the convective–radiative pendulum for both fluids, requiring a substantial period for recovery. With respect to the SST structure, recovery is a combination of dissipative processes in the upper ocean (SST gradients diminish) and the reestablishment of a well-mixed MABL in the wake of moist convection. Our summary perspective is one of a time-shared driver’s seat, where the atmospheric component accounts for the bulk of energy exchange.

The significance of our findings may become directly associated with systematic rainfall errors in highly parameterized global models, especially in regions where the average covariance between SST and LSSTc is unusually weak or negative. In such regions, large overestimates of rainfall are likely, given a diminished capacity to excite events in regions of elevated SST, and thereby more clearly expose the conditional relationship of SST to rainfall. Our future research will focus on oceanic regions historically most prone to systematic overprediction of rainfall. That investigation will proceed on the hypothesis that SST–LSSTc covariance is diminished where there is substantial overprediction of rainfall. Regions where systematic underprediction of rainfall occurs may be similarly sensitive to Laplacian asymmetry or other SST field influences.

Acknowledgments

CIRA, Colorado State University, and NCAR’s Earth Observing Laboratory postdoctoral programs jointly supported the efforts of Y. Li, as has the Global Institute of Water Security at University of Saskatchewan. The authors gratefully acknowledge Drs. Tom Schroeder and Mark Merrifield, Directors, Joint Institute for Marine and Atmospheric Sciences (JIMAR), University of Hawaii, for their encouragement and assistance through NOAA Grant NA0OAR4320075. The authors are deeply appreciative for consultations and advice provided by professors Roger Lukas and Bin Wang, University of Hawai‘i at Mānoa; Dr. Frank Bryan, NCAR; and Drs. Harry Hendon and Matt Wheeler, Australian Bureau of Meteorology and Centre for Australian Weather and Climate Research. Thanks are due to Dr. George Kiladis and an anonymous reviewer for their constructively critical reviews of an earlier manuscript. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

APPENDIX

The Test of Correlation Significance

Covariance is one of the most commonly used measures of the relationship between two random variables. The correlation coefficient represents the measure of linear relationship (i.e., strength of the association) between two variables; in this case, precipitation and SST/LSST.

We seek to determine whether two variables, precipitation and SST/LSST, are independent. Under the assumption of bivariate normal, independence is defined as zero correlation (r = 0).

For a finite number of samples n, the test statistic
eq1
with n − 2 degrees of freedom, follows a Pearson–Student’s t distribution and can be used in the test of our hypothesis.

Our null hypothesis H0 is as follows: The correlation coefficient r = 0.1 is statistically significant at 95% confidence level.

To satisfy H0, the condition t < tmin or t > tmax must be satisfied. Given 1491 days in the time series,
eq2
where qt (percent, degrees of freedom) is the quantile function of the t distribution. The quantile function is also called the percent point function or inverse cumulative distribution function. It provides the value at which the probability of the random variable will be less than or equal to that probability (Gilchrist 2000):
eq3
Since t > tmax, we accept our H0 and conclude that the correlation coefficient r = 0.1 is statistically significant at 95% confidence level and r ≈ 0.06 is the minimum value to satisfy the 95% confidence level.

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