1. Introduction

Understanding interannual and future changes in the hydrological cycle is of great importance to society. This is true for both planning the management of water resources and also for the mitigation of natural hazards, such as floods, landslides, and avalanches. In the case of water resources, it may be seasonal mean precipitation that is most important, while in the case of hazards, it is typically the occurrence of heavy or extremely heavy precipitation that matters. Depending on the application, the complete statistical distribution of precipitation frequency and intensity is of interest. The shape of the precipitation distribution is also a function of climate state, changing throughout the annual cycle as wintertime drizzle transitions to springtime showers to summertime storms. How are such factors manifested in the observational record of interannual variability and in model projections of climate change?

Understanding the dynamic and thermodynamic controls on precipitation remains a challenge in climate science. General circulation models (GCMs) struggle to successfully simulate the observed distribution of precipitation intensity (Sun et al. 2006; Wilcox and Donner 2007; Allan and Soden 2007) and the satellite-derived precipitation response to sea surface temperature (SST) variability (Wentz et al. 2007; Allan and Soden 2008). Convective parameterization in models certainly plays a role in the discrepancy between observed and simulated precipitation. For example, Wilcox and Donner (2007) show that the choice of model convective parameterization has a larger impact on the statistics of heavy precipitation than a 2-K warming. Nor are the statistics of stratiform precipitation adequately resolved (e.g., Zhou et al. 2007). In light of these challenges, it is clearly worthwhile to characterize the observed precipitation distributions as carefully as possible, to evaluate the skill of models used to predict future changes.

Recent studies have made impressive strides in understanding expected changes in global mean and extreme precipitation in a warmer climate, largely based on considerations of moisture availability and the global energy budget. While atmospheric water vapor content increases by close to 7 percent per degree of global mean temperature increase (i.e., 7% K⁻¹) in accordance with Clausius–Clapeyron scaling and assuming constant relative humidity, coupled climate models predict an increase in global mean precipitation of approximately 2% K⁻¹, consistent with energy balance constraints (Allen and Ingram 2002). The intensity of extreme precipitation events is expected to be broadly constrained by moisture availability and hence increase faster than global mean precipitation (Trenberth et al. 2003). However, several studies argue that increases in intense precipitation should not scale exactly with Clausius-Clapeyron because of the additional effects of latent heat release, changes in circulation strength, and the difference between local mean temperature and the temperature at which precipitation extremes occur, although observations remain debated (Pall et al. 2007; O’Gorman and Schneider 2009; Lorenz and DeWeaver 2007). For example, in a series of idealized GCM experiments, O’Gorman and Schneider (2009) show that fractional changes in precipitation extremes are less than changes in water vapor content, except at the highest latitudes, where the local temperature effect dominates.

Progress has also been made in understanding the regional patterns of predicted precipitation changes. Strengthening of tropospheric moisture fluxes, as predicted in a warmer climate, is expected to lead to an enhancement of the geographic distribution of evaporation and precipitation (Held and Soden 2006; Lorenz and DeWeaver 2007). In other words, wet regions are expected to become wetter and dry regions drier. This pattern is simulated in the Intergovernmental Panel of Climate Change (IPCC) Fourth Assessment Report multimodel ensemble projections, which indicate a general increase in mean precipitation in the tropics and midlatitudes and a decrease in the already arid subtropics. Furthermore, climate models suggest that a wetter climate for a given region is one in which heavy precipitation is more intense and more frequent (Sun et al. 2007; Kharin et al. 2007). This is consistent with the theoretical argument for a shift in the precipitation distribution toward extremes under global warming. Given the predicted response of global- and regional-mean precipitation to warming and the suggestion that increases in precipitation are accomplished by intense precipitation events, there remains a need to consider the full range of expected changes in the statistical precipitation distribution.

Impacts pertaining to these projected precipitation changes are likely to be far reaching and significant. As discussed above, percent increases in intense precipitation per degree warming are generally expected to be larger than percent increases in the mean. Moreover, all evidence, from observations to simulations, suggests that warmer climates lead to more intense precipitation events—even in regions where the total annual precipitation is reduced slightly—and with the possibility for correspondingly larger increases in intensity where the total amount of precipitation also increases (Solomon et al. 2007) This is meaningful because extremes in precipitation arguably matter more than the mean for erosion and natural hazards, such as floods and landslides. From a geological and land surface processes perspective, interesting questions thus arise concerning the sensitivity of erosion to changes in precipitation intensity.

We seek to understand how dynamical changes in the hydrological cycle affect the statistical distribution of precipitation. A natural starting point, and the inspiration for the present study, is to understand how large-scale atmospheric circulation patterns control the shape of the daily precipitation distribution in the modern record. An observational analysis also provides a target for model evaluation. Our approach is to consider the natural variability of the precipitation response in the American West attributed to El Niño–Southern Oscillation (ENSO). ENSO is generally considered to be the dominant pattern of global interannual climate variability. It is associated with hemisphere-wide precipitation and temperature anomalies that are consistent with a meridional shift in the position of the midlatitude tropospheric jet and Pacific storm track. Wintertime precipitation anomalies associated with ENSO have been extensively discussed in the scientific literature, and numerous studies have demonstrated enhanced seasonal precipitation in the Southwest and suppressed precipitation in the Northwest during El Niño events, and vice versa during La Niña (e.g., Mo and Higgins 1998; Schonher and Nicholson 1989; Kahya and Dracup 1994; Dettinger et al. 1998). Hence, it is clear that ENSO in the American West is a natural setting for probing further into the dynamical controls on large-scale precipitation patterns.

Wintertime daily statistics follow the general theme of seasonal precipitation, with enhanced daily precipitation expected in the Southwest during El Niño and the Northwest during La Niña. The importance of understanding the shape of the statistical distribution of precipitation, and the manner by which changes in mean translate into probabilities of extreme events, has been noted in other studies but with emphasis ultimately placed on the higher percentiles rather than the full distribution. For example, Higgins et al. (2007, 2008) demonstrate wintertime increases in the mean frequency of daily precipitation and in the amount of accumulated precipitation from heavy precipitation events (greater than the 90th percentile) in the Southwest during El Niño and the Northwest during La Niña. In addition, Cayan et al. (1999) find increases during El Niño in the frequency of heavy precipitation days (greater than the 50th and 90th percentiles) and an amplified and lagged streamflow response in the Southwest, and likewise during La Niña in the Northwest. Similar patterns in precipitation are also observed for the frequency of greater than 75th percentile events, for ENSO relative to the climatological mean (Gershunov and Barnett 1998; Gershunov 1998).

An alternative to comparing the means and extremes of precipitation is to evaluate the shape of the full statistical distribution of precipitation. For example, Sardeshmukh et al. (2000) apply statistical tests to identify regions (globally) of changes in the shape of the seasonal mean precipitation distribution for ENSO winters, using GCM ensembles and monthly observations. The authors also identify regions of changes in the probability of extreme values and evaluate whether these changes are due to shifts in the mean or changes in shape. They find that along the Pacific coast of North America, changes in the shape of seasonal precipitation indeed occur during ENSO events and in turn affect the probability of extreme events. By evaluating the shape of daily wintertime precipitation during ENSO events, our study effectively fills the gap between a global shape analysis of the seasonal distribution of precipitation (e.g., Sardeshmukh et al. 2000) and a consideration of only the higher percentile ranks for regional daily precipitation (e.g., Cayan et al. 1999). In the same vein, a recent study by Becker et al. (2009) analyzes the effect of ENSO on the parameters of a theoretical distribution function fit to daily rainfall.

ENSO is also of interest because its associated precipitation anomaly pattern in the American West straddles the dry subtropical zone of the desert Southwest and wet midlatitude zone of the Pacific Northwest. These zones are projected to have different precipitation responses under global warming scenarios, hence defining a border region of high sensitivity to a changing climate. It is also important to remember that the response of ENSO itself to a warmer climate is by no means clear. Whereas mean tropical Pacific SSTs are expected to shift toward more “El Niño like” conditions in a warmer climate (with no agreement on change in interannual variability or event amplitude) (van Oldenborgh et al. 2005; Solomon et al. 2007), the zonal mean atmospheric circulation response to global warming suggests a weakening and expansion of the Hadley cell and a poleward shift of the midlatitude jet, consistent with La Niña—rather than El Niño—processes (Lu et al. 2008; Chen et al. 2008). Given these apparently conflicting responses, we emphasize that we do not consider ENSO to be an analog for the future climate. Rather, we are concerned with how a rearrangement of the patterns of heating and circulation in the atmosphere influences the statistical distribution of precipitation, and we recognize that understanding these processes may have implications for projections of future climate. In addition, while any of the many identified modes of atmospheric circulation could be used to investigate the natural variability of the precipitation distribution, we choose ENSO in the western United States as a natural case study with large societal impacts. However, the same analysis framework can be readily applied to any mode of natural variability.

2. Data, methods, and the meaning of “wetter”

We use the Climate Prediction Center (CPC) Unified Raingauge Database (URD) of gridded (0.25° × 0.25°) daily station data for 1948–98 (Higgins et al. 2000) to evaluate wintertime [defined here as November–March (NDJFM)] precipitation in the American West as a function of ENSO. On a typical day, the URD includes approximately 13 000–15 000 reporting stations across the United States. We choose the URD because it represents the best available source of daily, high-resolution, multidecadal, and station-based precipitation data for the region. Statistical significance of differences in the mean and shape of daily precipitation distributions are evaluated for El Niño relative to La Niña winters. Strong ENSO events are selected based on whether the wintertime mean SST anomaly within the Niño-3.4 region in the tropical Pacific (5°N–5°S, 170°–120°W) (Trenberth 1997) exceeds a threshold of ±1 K (Table 1). No statistical comparison is made to the mean state or neutral ENSO years, although an inspection of mean-state ENSO conditions (not shown) confirms that the precipitation distribution lies between that of strong El Niño and La Niña winters.

Table 1.

Warm- and cold-event years (corresponding to the January months) during 1950–2008. The year is considered warm (cold) when the NDJFM average of the Niño-3.4 SST anomaly index exceeds 1 K (−1 K). Recall that the precipitation dataset only extends through 1998.

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Figure 1 shows the wintertime mean daily precipitation time series averaged over the Southwest (SW; 30.5°–40°N, 110°–126.25°W) and Northwest (NW; 40°–49.5°N, 110°–126.25°W) regions. These regions are selected because they exhibit coherent spatial precipitation patterns during ENSO events. In addition, we halved the region to consider only precipitation west of 116°W and found the results to be consistent. Several features are striking in this figure. First, according to the Student’s t statistic, there is no trend in the precipitation time series at the 5% significance level in either region (allowing for only a 5% chance of incorrectly rejecting the null hypothesis). We note that, for the entire United States and during the full twentieth century, other studies have identified significant trends (Groisman et al. 2004). However, the important point here is that any trend at the regional level in our data is swamped by the interannual variability. Hence, we are not concerned with a sampling bias with respect to the selected ENSO years, which might arise from the predominance of strong La Niñas in the early half of the record and strong El Niños in the latter half. Second, the time series serves as an excellent reminder that the ENSO phenomenon only explains some of the precipitation variability in the western United States. Not all wet years are strong ENSO years, and there exists quite a bit of scatter in the amount of precipitation during strong ENSO events. However, overall we see that in the SW, the wintertime mean precipitation averaged over El Niño winters is greater than during La Niña winters, whereas in the NW the wintertime mean precipitation is greater during La Niña, consistent with the canonical picture of wintertime ENSO precipitation impacts in the American West. This is confirmed in statistical tests presented in the next section.

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Wintertime mean daily precipitation time series averaged over the (top) SW and (bottom) NW regions. Filled diamonds indicate strong La Niña events; open circles indicate strong El Niño events. Dashed (dotted) lines represent the mean wintertime precipitation for all El Niño (La Niña) winters averaged over each region.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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It is also necessary to carefully define what is meant by “wetter” and “drier,” as there are several different ways of characterizing changes in precipitation. Figure 2a shows the density distribution of daily precipitation averaged over the NW, and Fig. 2b shows the same information represented as a cumulative distribution. Broadly speaking, we might imagine a shift in the mean of the statistical distribution of precipitation (the mean is indicated by the dashed lines in Fig. 2), or a change in the shape of the distribution. In addition, changes in the precipitation distribution may be indicated by a change in the frequency of precipitation events or in the amount of rain per event. In other words, a wetter climate may be one in which precipitation either occurs more often or is more intense, or a combination of both. When considering the latter, we weight the frequency of events by the amount of precipitation per event, such that the distribution, when plotted, gives the fraction of total rain as a function of daily rainfall rate (Fig. 2c). The histogram of the weighted case deemphasizes the drizzle and emphasizes the heavy precipitation events in the tail of the distribution (cf. Figs. 2b and 2c).

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Climatological wintertime mean daily precipitation in the NW during NDJFM (40°–49.5°N, 110°–126.25°W), presented as a (a) density distribution of regionally averaged precipitation, (b) cumulative distribution of fraction of rainy days, and (c) cumulative distribution of fraction of total rain amount, all as a function of rainfall rate.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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It is easy to appreciate that for a small—or even no—shift in the mean precipitation, there is the possibility for a large change in the contribution from intense events to the precipitation total. For example, previous studies have used the two-parameter gamma distribution to model daily precipitation amounts and have demonstrated that modest changes in mean precipitation tend to be accomplished by a larger proportion derived from heavy rainfall events (Groisman et al. 1999; Wilby and Wigley 2002; Becker et al. 2009). This is attributed to changes in the scale parameter, which essentially controls the spread of the gamma distribution. We choose to characterize the general shape of the daily precipitation data, rather than fitting it to the parameters of a theoretical function, such as the gamma distribution. While the gamma function is an efficient descriptor and facilitates comparison of distributions, the value of our approach is that it allows for a complete characterization of changes in the distribution and, in addition, it avoids possibly underfitting the data with a prescribed mathematical function.

3. Analysis

Distributions of daily precipitation during El Niño and La Niña winters are evaluated and compared using two standard statistical tests: the two-sample t test for mean and the nonparametric Kolmogorov–Smirnov (K–S) test for distribution shape (Massey 1951; Stephens 1979). Statistical significance is established by allowing for only a 5% chance of incorrectly rejecting the null hypothesis (α = 0.05). The null hypothesis states that the means and shapes of El Niño and La Niña precipitation are equal for the t test and K–S test, respectively. The t test in principle involves two assumptions: normality and data independence. Daily precipitation, however, has a highly skewed distribution and exhibits large day-to-day correlation. As elegantly shown by Boneau (1960), the t test is functionally robust to non-Gaussian distributions, particularly for large sample sizes. This is true even for the extreme case of the exponential distribution. The second assumption—serial correlation, for which we correct—is described in sections 3a and 3b.

In regard to the K–S test, it is noteworthy that because the distributions are cumulative, once a significant separation occurs anywhere between the distributions, the null hypothesis is rejected and the distributions are statistically different, regardless of the behavior elsewhere within the distributions. The K–S test searches for the maximum in the vertical separation between two cumulative distributions, f(x) and g(x), given by

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and determines based on this spread whether the data are from the same or different distributions. In the analyses that follow, we evaluate both the spatial patterns of mean precipitation as a function of ENSO (section 3a), as well as the shape of the precipitation distributions in regional averages (section 3b). Absolute changes in extreme precipitation are discussed in section 3c. In particular, we focus on the SW and the NW regions of the American West, as defined in section 2.

a. Change in mean

We begin by evaluating how mean daily wintertime precipitation varies with ENSO phase, and we address the canonical picture of ENSO precipitation impacts (e.g., Mo and Higgins 1998; Schonher and Nicholson 1989; Kahya and Dracup 1994; Dettinger et al. 1998). Figure 3 shows mean daily wintertime precipitation when raining, or mean daily intensity, in the study region for El Niño–minus–La Niña events. We refer to El Niño as warm ENSO events and La Niña as cold ENSO events. Across the western United States, we find that, when raining, the maximum difference between daily rainfall rates in warm and cold ENSO events is greater than 3 mm day⁻¹ (Fig. 3a). As in the regional average (Fig. 1), this variability is sufficiently large with respect to observed or projected trends that we can be confident our analysis is not polluted by sampling biases. In addition, there is an increase in mean daily precipitation intensity in the SW during warm events (up to 87%), in the NW during cold events (up to 56%), and a striking nodal line in the differenced precipitation field at roughly 40°N, indicating a zone of little-to-no change in mean intensity associated with ENSO (Fig. 3b). Overall, there is a clear difference in mean daily precipitation intensity during warm and cold ENSO events, and these features are generally consistent with previous studies of ENSO precipitation impacts, as discussed in section 1.

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Wintertime precipitation differences for warm-minus-cold ENSO events: (a) difference in mean daily precipitation when raining (mm), (b) percent difference in mean daily precipitation when raining, (c) percent difference in number of rainy days, and (d) percent difference in number of rainy days with precipitation ≥5 mm day⁻¹.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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We now evaluate the statistical significance of these observations, and in section 3b we identify how changes in mean are accomplished by changes in the frequency and intensity of precipitation. A discussion of how degrees of freedom were estimated in attributing significance follows at the end of this section. Applying the t test to each grid cell reveals a widespread pattern of statistically significant increases in mean (i.e., averaged across all days) daily intensity during warm (cold) events across the SW (NW) relative to cold (warm) events at the 5% significance level (Fig. 4), confirming the canonical picture of ENSO precipitation impacts in the mean. In addition, applying a more rigorous significance level (e.g., 1%) has only a minimal effect on the spatial pattern of statistical significance. This increase in mean daily precipitation intensity appears to be a robust result and is supported by several lines of evidence: It is evident in the spatial maps of observed precipitation differences and confirmed by t tests applied at the gridcell level. It is also supported by t tests applied to the NW and SW aggregate data (section 3c), providing a consistent story in all cases tested.

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Results of t test showing regions of statistically significant change in mean daily precipitation intensity during ENSO events, after correcting for temporal correlation at each grid cell. Shading indicates the p value for the left-tail test. In other words, p = 0.95 represents an increase in intensity during warm (relative to cold) events at the 5% significance level, and p = 0.05 represents an increase during cold (relative to warm) events, also at the 5% significance level. The significance level is the probability of incorrectly rejecting the null hypothesis.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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There are also interesting regional variations in the effect of ENSO phase on precipitation. In particular, we consider a range of precipitation thresholds to understand the frequency signal as a function of daily rainfall rate. For example, we find that the frequency of drizzle in the NW is relatively unaffected by cold ENSO events. Figure 3c shows that changes in the fractional number of rainy days are small across much of the NW (less than 10%), whereas in considering only precipitation greater than 5 mm day⁻¹, there is a much more obvious increase in the fractional number of rainy days during warm events in the SW and cold events in the NW, particularly along the coast (Fig. 3d). This suggests that in the NW, the total number of rainy days is dominated by drizzle and is less sensitive to ENSO phase, consistent with the finding by Cayan et al. (1999), that the fractional increase in precipitation frequency associated with ENSO is larger in the SW than the NW. Applying the t test, after correcting for spatial and temporal correlation, to the frequency of precipitation events (not shown) reveals an increase in the mean number of rainy days during warm events in both the SW and NW at the 5% significance level. This is evidenced in Fig. 3c by the increases in warm-event precipitation frequency northward of 40°N. If even a 1 mm day⁻¹ precipitation threshold is imposed (ignoring all precipitation less than 1 mm day⁻¹ and thereby removing the drizzle effect), then we do indeed see a significant increase in the number of rainy days in the NW during cold events. This result holds true for every precipitation threshold greater than and including 1 mm day⁻¹.

Adjustment for temporal correlation of data

Serial correlation arises as an issue when applying the t test to climatological data, and we detour briefly to discuss this subject here. The conventional t test assumes statistically independent data, which is generally not the case for daily precipitation. The effect of serial correlation is that the test will too frequently return a significant difference in means where no difference exists. In other words, the actual significance level is higher than the specified significance level. This behavior is occasionally referred to as liberal, to differentiate it from a conservative test. A standard approach is to compute the effective degrees of freedom, sometimes referred to as the equivalent sample size in time series analysis. The ensuing reduction in degrees of freedom accounts for the information loss due to serial correlation. We apply this technique throughout our analysis, after von Storch and Zwiers (1999), by calculating the decorrelation time and effective degrees of freedom at each grid cell from wintertime climatology. On average, this amounts to a 10% reduction in the degrees of freedom. In section 3c, we extend this treatment to account for effective spatial degrees of freedom as well.

b. Change in shape

We now focus in more detail on how the shape of the precipitation distribution changes as a function of ENSO phase. We apply the K–S test to identify differences in the shape of the distributions between warm and cold events, both in terms of the fraction of rainy days and the fraction of total rain amount. These analyses illuminate how the changes in mean precipitation shown in the previous section are accomplished by changes in the frequency or intensity of precipitation. To evaluate fractional differences in the amount of precipitation, we weight the distributions by the daily rainfall rate, as discussed in section 2.

Figures 5a and 5b show the spatial patterns of the K–S test applied to the distributions of the fraction of rainy days as a function of daily rainfall rate. The geographic regions of statistical significance correspond well with those identified in the previous section for changes in mean daily intensity according to the t test (Fig. 4). However, when the K–S test is applied to the weighted distributions representing the fraction of total rain, there are notable differences. In particular, the pattern of significance becomes less regionally concentrated and more diffuse. Figure 5c shows that a shift in the weighted precipitation distribution toward more intense daily rainfall rates during warm events is still largely confined to the SW. In contrast, in Fig. 5d we see that a significant shift in the weighted distribution toward more intense precipitation occurs across an extended region of the western United States during cold events. Recalling the cumulative nature of the test, it is important to emphasize that these maps are best interpreted as providing a geographic overview of where the shapes of the distributions differ, rather than indicating the relative importance of cold or warm events for a particular rainfall rate. Interestingly, Fig. 5d hints at an influence of cold-event weather systems that extends farther south than expected. This topic is addressed in detail in Feldl and Roe (2010).

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Results of K–S test applied to distributions of the (a),(b) fraction of rainy days and the (c),(d) fraction of total rain. Shading in (a) and (c) reveals regions of significant shifts in the warm ENSO event distribution toward more intense daily rainfall rates, relative to the cold-event distribution (5% significance level). Shading in (b) and (d) is as in (a) and (c) for cold events relative to warm events. At some grid cells, primarily in the SW, the K–S test returns a significant result in both cases [cf. (c) and (d)]. This can only occur when the cumulative distributions intersect in the middle of the distribution, meaning that warm-event precipitation significantly exceeds cold-event precipitation at one point [f(x₁) > g(x₁) in Eq. (1)], and vice versa at another [f(x₂) < g(x₂)].

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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The coherent spatial patterns evident in Fig. 3 lead us to consider daily regional averages of the precipitation data, where raining. Given this approach, the area over which we average may change depending on the number of rainy grid cells. The regional averages consist of 1120 cold-event rainy days and 1209 warm-event rainy days. We first focus on the cumulative distributions of daily precipitation frequency for warm and cold events. The nature of the K–S test effectively normalizes the distributions and ensures that the influence of ENSO on the frequency of precipitation is not obscured by the differing amounts of total seasonal precipitation in our two regions. Figures 6a and 6b present a comparison of the cumulative distributions of regionally averaged daily precipitation frequency for warm and cold events in the SW and NW, respectively. We conclude from the K–S test that the shapes of the distributions are indeed statistically different. Moreover, we find a significant increase in the fraction of total rainy days that are heavy rainy days (heavy-rainy-day fraction) during warm (cold) events relative to cold (warm) events in the SW (NW). This result is apparent from a shift in the warm-event distribution toward more intense daily rainfall rates in the SW, and likewise for cold events in the NW.

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Distributions of regional-mean precipitation for warm (solid) and cold (dashed) ENSO events, including mean daily precipitation intensity (vertical lines) and 95% confidence limits (gray envelope) for the K–S test. A shift in the distribution toward more intense daily rainfall rates implies an increase in the fraction of rainy days or total rain contributed by heavy precipitation. The D_ks between distributions for (a)–(d) is 0.116, 0.095, 0.099, and 0.103, respectively; all are significant.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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This and subsequent results are based on the interpretation of the cumulative distributions and hence a brief discussion is warranted. Focusing on Fig. 6a for the SW, a shift in the warm-event distribution toward the right implies that for every daily rainfall rate, the warm-event distribution has achieved a smaller percentile of its total rainy days than the cold-event distribution, which means a larger fraction is available to occur at more intense daily rainfall rates (i.e., imagine taking a vertical slice through the distributions). This shift is accompanied by an increase in mean daily precipitation intensity (as indicated by the dashed lines) during warm events in the SW, once again corroborating the robustness of our t test result in the mean on both a gridcell level (Fig. 4) and in the regional mean. An alternate perspective follows that for every percentile rank, the warm-event distribution occurs at a higher daily rainfall rate than the cold-event distribution (imagine a horizontal slice). For example, 10% of all rainy days (greater than the 90th percentile) occur at regionally averaged rainfall rates of greater than 6.3 mm day⁻¹ for warm events and greater than 4.9 mm day⁻¹ for cold events in the SW. Similarly, in the NW (Fig. 6b), 10% of all rainy days occur at regionally averaged rainfall rates of greater than 6.2 mm day⁻¹ for warm events and 7.0 mm day⁻¹ for cold events.

In these plots, the gray shading centered on the warm-event distribution represents the 95% confidence limits [100 × (1 − α), where α is the significance level]. If the cold-event distribution lies anywhere outside this gray envelope, then we may conclude, with 95% confidence, that the distributions are statistically different using the K–S test. Because of the integrative nature of cumulative distributions, which must converge at the upper and lower limits, the distributions are required to be contained within the 95% confidence interval at the highest and lowest rainfall rates. In other words, it is important not to construe that the distributions differ only at the rainfall rates where a separation is observed because differences may occur in the tails. Separation of the cumulative distributions at any given daily rainfall rate simply means that differences across all rainfall rates up to that point have accumulated to become statistically significant. Recall that the test statistic D_ks indicates the maximum separation between the cumulative distributions and is the metric for distinguishing whether the warm- and cold-event precipitation distributions are statistically different.

Turning now to the weighted case, a statistically significant change in shape due to an increase in the fraction of total rain contributed by heavy precipitation (heavy rain fraction) is observed during warm events relative to cold events in the SW (Fig. 6c) and during cold events relative to warm events in the NW (Fig. 6d). Hence, when considering the full distributions, we find both increases in the frequency and intensity of heavy precipitation in the SW during warm events and in the NW during cold events. This result is consistent with previous work (e.g., Higgins et al. 2007; Cayan et al. 1999). In addition, a recent study by Becker et al. (2009) finds that the Southwest is scale dominated during warm events (referring to the scale parameter of the gamma distribution), which the authors interpret as an increase in the relative frequency of intense precipitation days.

Figure 6c further hints at an intriguing result: at the very highest rainfall rates in the SW (greater than the 99th percentile), the heavy rain fraction from cold events actually exceeds that from warm events. That is, the daily rainfall rates for the top 1% of precipitation are higher during La Niña than during El Niño in the SW. Note that this is in line with our expectation that shifts in the cold-event distribution toward more intense daily rainfall rates are widespread across much of the American West and not limited to the NW (Fig. 5d). We cannot conclude as to the significance of this result directly from the cumulative distributions; instead, we apply a different technique in section 3c to search for the significance in the tail of the distributions.

The comparison of the distributions for frequency and intensity presented in this section supports our earlier conclusion that the precipitation response is nuanced and dependent on the particular question being asked. In what follows, we explore this idea further by identifying changes in the shape of the precipitation distributions independent of shifts in the mean. Namely, we normalize the x axis for each distribution, such that a value of 1 equals the mean daily rainfall rate (and a value of 2 is twice the mean daily rainfall rate). One benefit of this approach is that it allows one to compare the “flashiness” of the distribution or, in other words, the probability of extreme excursions far from the mean.

Figure 7 shows the adjusted cumulative distributions of warm- and cold-event precipitation in the SW and NW. We find no significant change in the frequency distribution of rainy days relative to the mean in the NW (Fig. 7b). This is not surprising, given our earlier result showing that the frequency of drizzle in the NW is relatively unaffected by ENSO state and tends to damp the frequency response in the full distribution. In the SW, there is a small but significant departure between the distributions, suggesting 1) an increase in the fraction of rainy days that are moderate rainy days during warm events and 2) an increase in the heavy-rainy-day fraction (greater than the 87th percentile) during cold events (Fig. 7a). This redistribution of the number of rainy days is indicated by the intersection of the distributions near twice the mean daily rainfall rate.

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Normalized distributions of regionally averaged precipitation for warm (solid) and cold (dashed) ENSO events, and 95% confidence limits (gray envelope) for the K–S test. The D_ks between distributions for (a)–(d) is 0.076, 0.035, 0.128, and 0.070, respectively. All but (b) are significant. We normalize the x axis for each distribution (see text for details).

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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Figures 7c and 7d allow us to characterize the flashiness of the precipitation, or how closely the distribution clusters near the mean. We see a statistically significant increase in the fraction of total rain contributed by above-mean events during cold (warm) events relative to warm (cold) events in the SW (NW). In other words, during warm events in the SW, the distribution is steeper at moderate rainfall rates, indicating that a larger portion of the precipitation distribution clusters near the mean daily regional-mean intensity. In contrast, precipitation is flashier (has a lower kurtosis) during cold events in the SW. Combining the results for the SW from Figs. 6c and 7c, we find an increase for warm events in the heavy rain fraction (in an absolute millimeters-per-day sense) but also an increase in the kurtosis, or a narrowing of the distribution.

Several additional points are striking and worth emphasizing. First, in the SW we see significant changes in both the frequency of events (albeit small) and intensity of precipitation relative to the mean, whereas in the NW only changes in intensity are significant. In other words, there do not appear to be significant changes in the relative distribution of the number of rainy days between warm and cold events in the NW. Second, these results demonstrate a fundamental difference in the shape of the weighted distributions independent of shifts in the mean during warm and cold events. The differences between warm and cold events cannot simply be explained by a shift in the mean daily intensity—an actual redistribution of the relative proportions of regional-mean precipitation is necessary.

Finally, in all cases we see that the increases in the fraction of total rain contributed by the heaviest precipitation occur during cold events rather than warm events (Figs. 6c and 6d and 7c and 7d). This is true for both geographic regions. However, we emphasize that this result is specific to the intensity of heavy precipitation only. When the full range of precipitation is considered, as is clear from several figures, mean El Niño precipitation still exceeds La Niña in the SW. In the next section, we further explore the intense cold-event precipitation signal inferred from the tails of the distributions.

c. Change in extremes

Cumulative distributions of total rainfall amount suggest that the intensity for the top 1% of precipitation events is enhanced during La Niña relative to El Niño in the SW regional average. This finding is particularly relevant to weather extremes and their associated impacts. What strategies can we use to evaluate the tails of the distributions statistically? Our preferred approach is to consider only the individual heavy precipitation events and to search for the local rainfall threshold above which cold events demonstrate an increased mean according to the t test. This picks out the intense, but possibly isolated, events and does not necessarily speak to a regional picture. Conversely, it is relevant to local and damaging severe-weather phenomena, such as landslides and flash floods.

As a brief aside, a second approach is to focus on all precipitation concurrent with heavy precipitation events, in essence, applying a regional-mean threshold. With this approach we find that, as suggested by the tail of the cumulative distributions in Fig. 6c, for regional-mean thresholds of at least 11 mm day⁻¹, cold events demonstrate an increase in mean daily regional-mean intensity in the SW. Recalling from section 3b that the average is taken over rainy grid cells only, these regional means represent extraordinarily high rainfall rates and only a handful of events exist for regional-mean precipitation of at least 11 mm day⁻¹. As such, there is not enough statistical power to declare significance. Hence, we conclude that this result is more of a curiosity than a convincing climatic signal.

Returning to the local threshold analysis, we construct an aggregate dataset for each threshold, without prior averaging. Thus, each precipitation event represents a single time and place. The t test is then applied to search for differences in mean daily rainfall rate for the thresholded data. A drawback of the above-mentioned regional threshold analysis is that, because it is the averaged data (again, only over rainy cells) to which the threshold is applied, one rainy grid cell on an otherwise dry day will have as much of an effect as 1000 rainy grid cells during a widespread precipitation event. This effect is particularly troublesome at high thresholds, where precipitation is sparse. In contrast, in using the local threshold and aggregate dataset, a widespread dry day will contribute few rain events and a widespread rainy day will contribute many events. Precipitation is in essence weighted by the spatial extent of the storm, simply by nature of the aggregate. An additional benefit of this technique is that we retain more data, hence increasing the statistical power of the test to obtain significant results. For instance, for no threshold, we have more than 2 000 000 pooled precipitation events across the SW region, decreasing to 1671 for a 70 mm day⁻¹ threshold; likewise, for the NW, more than 4 000 000, decreasing to 3159.

Figure 8 shows the difference in mean precipitation rate as a function of threshold for the SW and NW. A discussion of how degrees of freedom were estimated for the regional aggregate follows at the end of this section. As must be the case from prior analysis, for no threshold applied (i.e., a 0 mm day⁻¹ threshold), the mean daily precipitation is significantly increased during warm events relative to cold ENSO events in the SW, and vice versa in the NW. In addition, for all thresholds considered, the NW conforms to the expected picture, with cold-event precipitation increased over warm-event precipitation (Fig. 8a). However, beyond thresholds of 6 mm day⁻¹, the spread between means is not large enough to be assessed as significant. In stark contrast is the signal in the SW (Fig. 8b). As the threshold is raised to even 1 mm day⁻¹, the result that warm-event precipitation is greater than cold-event precipitation falls below the 95% confidence level. And for thresholds exceeding about 20 mm day⁻¹, we instead find that mean precipitation rates during cold events actually exceed those during warm events. The mean of the aggregate precipitation given a 20 mm day⁻¹ threshold represents the approximately 99th percentile rainfall rate. The synoptic conditions associated with these intense local precipitation events in the SW are explored in Feldl and Roe (2010). In summary, in both regions precipitation follows the canonical picture of increases in the SW during El Niño and in the NW during La Niña when considering the full range of precipitation, whereas for intense precipitation, rainfall rates in the SW are in fact higher during La Niña.

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Mean daily aggregate rainfall rate for warm-minus-cold ENSO events as a function of threshold for the (a) NW and (b) SW. This aggregate reflects an integrative measure of precipitation rates in the tail of the distributions beyond the specified threshold. We run t tests on categories of daily rainfall rates, testing every precipitation threshold in increments of 1 mm day⁻¹. The gray envelope indicates 95% confidence limits for the two-sample t test, after correcting for spatial and temporal correlation. The dashed envelope represents our most conservative estimate, assuming perfect spatial correlation. For thresholds greater than ~20 mm day⁻¹, cold events show a significant increase in mean daily intensity relative to warm events in the SW regional average.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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We emphasize that our result is an intensity signal not a frequency signal, and there is no significant increase in the number of rainy days during cold events in the SW for precipitation of at least 20 mm day⁻¹ (see the appendix for further details). Rather, we find that although heavy precipitation in the SW is more intense during cold events, it is more frequent during warm events. In other words, our results suggest that, for the SW, La Niña winters experience more locally intense precipitation (relevant to landslide hazards), whereas El Niño winters experience enhanced precipitation across the entire region and more frequent heavy rains (relevant to reservoir management). Localized regions of significant increases in mean daily intensity during warm ENSO events persist over the southern coast ranges of California for thresholded precipitation but do not survive spatial averaging.

Adjustment for spatial correlation of data

As discussed earlier, applying the t test to daily precipitation, which is correlated in both time and space, requires an adjustment accounting for data dependencies. In Fig. 8 we use a bracketing approach to constrain the upper and lower limits on the effective degrees of freedom, and we translate these bounds into the acceptable range of spread allowed by the t test. Note that as the threshold is raised to include increasingly extreme events, we lose observations and hence degrees of freedom (as indicated by the widening of the confidence intervals). Likewise, we also lose degrees of freedom by correcting for serial correlation. The lower bound (dashed line in Fig. 8) is obtained by assuming perfect spatial correlation, or in other words, 1 degree of freedom per day and then reducing this further to account for temporal correlation following our method in section 3a. The upper bound (gray envelope) is obtained by calculating the effective spatial degrees of freedom from the precipitation data after Bretherton et al. (1999)—which explicitly considers non-Gaussian precipitation data—and multiplying this by our lower bound. Because of assumptions inherent in the adjustment, this may still represent an overestimate of the actual degrees of freedom.

4. Discussion and conclusions

In this study we characterized how the daily distribution of precipitation is linked to a major mode of climate variability. Using ENSO as a case study for changes in midlatitude circulation patterns, we evaluated 50 yr of wintertime precipitation during El Niño and La Niña winters in the American West, based on a comprehensive, high-resolution, station-based dataset. Our major results are as follows:

• Increase in mean daily precipitation intensity is confirmed across the SW during warm ENSO events and across the NW during cold ENSO events.

• Change in mean is accomplished by a shift in the distributions of daily precipitation frequency and amount toward more intense daily rainfall rates.

• Frequency of drizzle (<1 mm day⁻¹) in the NW is largely unaffected by ENSO state.

• Fundamental changes in the shape of the precipitation distributions are observed, independent of shifts in the mean.

• For heavy precipitation, cold events show an increase in mean daily intensity across the SW.

For all cases applied to the full range of daily rainfall rates in the SW, we find that both local- and regional-mean precipitation is larger during warm events than cold ENSO events. However, in considering extreme precipitation, cold ENSO events demonstrate a significant increase in mean daily intensity when aggregated over the entire region. In map view, the spatial pattern of intense cold-event precipitation is diffuse (Fig. 9a). We find that approximately half of all grid cells that experience intense (≥20 mm day⁻¹) precipitation in the SW region show an increase in mean cold-event precipitation over warm-event precipitation. However, less than 1% of the intensely precipitating grid cells in the SW have a sufficient number of temporally uncorrelated observations to distinguish statistically between warm and cold ENSO means. This speaks to our earlier point and provides motivation for using the regional aggregate. As the threshold is raised to consider increasingly extreme precipitation, we lose degrees of freedom and statistical power. As a result, the statistics are severely hampered at the gridcell level, whereas in the regional aggregate we retain adequate information to address the extremes statistically.

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Wintertime precipitation differences for warm-minus-cold ENSO events: (a) percent difference in mean daily precipitation intensity and (b) percent difference in number of rainy days. All precipitation events <20 mm day⁻¹ per grid cell have been excluded. In general, as the precipitation threshold is raised, there are increasingly larger regions for which no heavy precipitation is observed during ENSO. Thus, we note that for precipitation ≥20 mm day⁻¹, the difference in mean daily intensity cannot be calculated for portions of the western U.S. interior.

Citation: Journal of Climate 24, 10; 10.1175/2010JCLI3555.1

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The richness of the spatial pattern emphasizes one of the strengths of our analysis, that by considering both regional and local effects, we gain a deeper understanding of how patterns of climate variability affect precipitation. The diffuse pattern of intense precipitation is expected because of the well-known low degree of spatial correlation in precipitation, compared to other climatological variables. In addition, we have already remarked on the high variability evidenced in the time series of regionally averaged ENSO precipitation (Fig. 1). Not only is it true that not all strong warm-event years are wet in the SW but we see that some strong cold events are in fact very wet in the SW. Finally, we also note that the western United States is characterized by complex topography, including two major north–south-oriented mountain ranges. Local and orographic effects are expected to lead to enhanced spatial variability across the region.

We find that distinct perspectives are gained by evaluating both the spatial patterns and regional aggregates of precipitation differences. Figure 9 shows the spatial extent of wintertime differences in the intensity and frequency of heavy precipitation that comprise the regional-mean picture. That intense cold-event precipitation matters on a local scale across the SW is indicated by the diffuse spatial pattern, combined with the significant increase for the region as a whole. From a composite analysis of several climate variables, these intense cold-event precipitation days in the Southwest arise from the presence of a persistent offshore trough and the simultaneous emplacement of a strong source of subtropical water vapor (Feldl and Roe 2010). While La Niña winters experience more locally intense precipitation in the SW, El Niño winters experience enhanced regional-mean precipitation and more frequent heavy rains (Fig. 9b). Thus, depending on the impact of interest, be it landslides or reservoir management, either El Niño or La Niña conditions may have the stronger signal. In addition, from Fig. 9 we can identify areas of Southern California that are particularly sensitive to El Niño, in that they exhibit increased intensity and frequency of heavy precipitation during warm events.

Our goal in this study was to investigate the link between large-scale atmospheric circulation and daily precipitation statistics, in the context of our two climatic regions: the Northwest and Southwest of the United States. While for most metrics the choice of the 40°N demarcation between climate zones is a good approximation to the patterns of precipitation variability, there are two notable exceptions: 1) El Niño weather influences the NW in the frequency of drizzle (<1 mm day⁻¹) (Fig. 3c) and 2) La Niña weather influences the SW in the intensity of heavy precipitation (≥20 mm day⁻¹) (Fig. 9a). We speculate that this observation may represent a difference in character between the northward extension of drizzly warm-front precipitation and the southward extension of intense cold-front precipitation. The main lesson here is that we cannot simply describe the response to changing patterns of circulation as a shift in the climatic zones, but that a more nuanced view is necessary, at least when considering the full spectrum of precipitation.

An abiding theme of this analysis is that extreme local events do not have to behave according to the regional mean. This point illustrates important subtleties in regional-scale climate predictability. It is interesting to consider whether the details of the daily precipitation distribution provide a benchmark for establishing confidence in climate prediction (e.g., Allan and Soden 2008). It seems a natural requirement that models have skill in reproducing observed precipitation statistics, particularly for impacts-related projections of extreme precipitation. More broadly speaking, how well do we have to understand the SST and circulation forcings to have skill in predicting the precipitation response for a given climate, be it past, current, or future? Some studies have employed statistical–dynamical methods toward this end (e.g., Gershunov and Cayan 2003). That we have found important differences depending on whether one considers frequency, intensity, or extremes suggests that it may be worthwhile to revisit the shape of the precipitation distribution for other circulation regimes—in addition to the midlatitude and largely maritime scenario presented here. Such considerations are highly relevant to the weather experienced under a changing climate.