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  • View in gallery

    The correlation of hourly precipitation at 0.25° resolution is given every 5° for (top) DJF and (bottom) JJA for 1989–2013 for 60°N–60°S.

  • View in gallery

    CMORPH hourly precipitation correlation averaged for the four points ±0.5° from the center of each grid point, as given by R2 (see appendix) for (top) DJF and (bottom) JJA.

  • View in gallery

    The angle of the major axis each correlation ellipse makes with the east–west direction is plotted for points 0.5° away from the center of the ellipse for (top) DJF and (bottom) JJA. Owing to symmetry, values range only from −90° to +90° and wrap around (i.e., −90° = +90°) so that the color bar is circular.

  • View in gallery

    The major (blue) and minor (red) axes of each correlation ellipse for distances 0.5° from the center point for (top) DJF and (bottom) JJA. Owing to crowding, only every second point is plotted. The scale of each vector is given in the inset.

  • View in gallery

    The eccentricity of each correlation ellipse at 0.5° radius from the center is plotted for (top) DJF and (bottom) JJA.

  • View in gallery

    Composites of correlations for land areas within each box, as identified for (top) DJF and (bottom) JJA. Each rectangle depicts a 10° × 10° domain (±5° from the center point) as shown by small tick marks. The areas used are North, Central, and South America; Africa; Australia; Europe, north and south Asia; and the Maritime Continent.

  • View in gallery

    For the various regions selected for composites, based solely on the isotropic correlations 0.5° from the center, the rate of falloff for the correlations with distance in units of 0.25°. O1: correlation > 0.6, latitude > 22.5°; O2: correlation > 0.6, latitude < 22.5°; O3: correlation < 0.6; L1: 0.4 < correlation < 0.7; L2: correlation < 0.4.

  • View in gallery

    Composite regions used based on the classifications in Fig. 7 plus bands of latitude.

  • View in gallery

    Each of the main regions has the composite over all grid points of correlations for hourly precipitation. Ocean regions are framed in light blue and land regions in red. Each composite is for a 10° × 10° domain, and the color key is as for Fig. 1. The composites have been weighted east–west by cos(ϕ) to account for the convergence of the meridians. The number of points in each composite is in Table 1.

  • View in gallery

    For the three main ocean regions over the Northern Hemisphere, as given at top: composites for each region of the correlations as a function of time. The sequential rows depict 12 and 6 h before, time zero, and 6 and 12 h afterward. For each region, the left columns are for DJF and the right ones for JJA. A red star indicates the highest values, and tracking the red stars gives the speed (km h−1) at the bottom right of the time zero panels.

  • View in gallery

    As in Fig. 10, but for the three main ocean regions over the Southern Hemisphere.

  • View in gallery

    As in Fig. 10, but for the three main land regions over the Northern Hemisphere.

  • View in gallery

    As in Fig. 10, but for the two main land regions over the Southern Hemisphere.

  • View in gallery

    As in Fig. 10, but for the two ocean “desert” regions over the Southern Hemisphere.

  • View in gallery

    For the main ocean regions, as given at top: composites for each region of the correlations at time 0 plus the locations of the centroid (white star) at times −6, 0, and 6 h and, where feasible, −12 and +12 have also been added. For each region, the left columns are for DJF and the right ones for JJA. The speed (km h−1) is given at bottom of each panel, and the blue arrows show the direction and movement.

  • View in gallery

    For each composite region, the mean vector wind (kt; 1 kt = 0.51 m s−1) from ERA-Interim for 1989–2013 is plotted using conventional symbols: one full barb is 10 kt, a half barb is 5 kt, and the direction is toward the point. For clarity, each value is slightly offset in the vertical. Levels included are 850 (green), 700 (blue), and 500 (red) hPa, along with the vector movement of the rain over 12 h (black). The dashed lines indicate the composite zones with O1 and O2 grouped. The background blue indicates ocean, and brown is land.

  • View in gallery

    Schematic figures illustrating (a) the typical location of the surface low pressure system (orange outlined L) and associated rainfall (green) relative to the 500-hPa geopotential height contours (black lines) in midlatitudes. While the average mean flow (black arrow) is west–east, the steering of the surface low and associated precipitation ahead of the trough is northeastwards (orange arrow). (b) A typical low pressure system and associated cold front in midlatitudes of the Northern Hemisphere has a characteristic slope for the trough and front that produce poleward momentum fluxes aloft, but illustrated here by the u′ and υ′ covariability arising from the front orientation that applies between about 20° and 50°N (pink zone). The prime indicates the departure from the zonal mean. Red arrows indicate flow.

  • View in gallery

    The grid with points H, A, E, D, O, B, G, C, and F is shown along with the axes J1 and J2, the angle of the major axis α, and a schematic of the isotropic ratios M of the values on the diagonal vs those north–south plus east–west. For the given values of α, a schematic is given of the orientation of the ellipses (yellow) that result in each quadrant as J1 and J2 vary.

  • View in gallery

    The eccentricity ε is given for a number of ellipses. From left to right, the ratio of the minor axis to the major axis b/a is 1, 0.9, etc., and the orientation is −45°, 0°, and +45° for α.

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Near-Global Covariability of Hourly Precipitation in Space and Time

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Abstract

A detailed analysis of hourly precipitation from 60°N to 60°S for the covariability is performed at 0.25° resolution using the new CMORPH dataset. For all points, correlations are computed with surrounding points both concurrently and for various leads and lags up to a day. Results are more coherent over the oceans than land; the contours of constant correlation tend to be elliptical, oriented northeast–southwest in the northern extratropics and southeast–northwest in the southern extratropics. An ellipse is fitted to the correlation pattern, and major and minor axis vectors and eccentricity are mapped. Based upon both the isotropic correlations and ellipse, points are allocated to one of 20 clusters, and 16 are documented. Over the main extratropical ocean storm tracks, correlations exceed 0.8 for points 50 km distant and fall to about 0.3 at about 5° radius. In the tropics values drop to 0.65 within 50 km and 0.2 at 5° radius. Over land, values are lower in summer and drop to 0.1 at 5° radius. Decorrelation e-folding distances range from less than 50 km over land to 200 km over extratropical ocean storm tracks. The movement of precipitation is compared with mean atmospheric winds. The lead–lag relationships indicate movement of systems but reveal the relatively short lifetimes of precipitation, of less than 12 h, even taking movement into account. The orientation of the ellipse reflects the structures of rain phenomena (fronts, etc.) rather than movement. These statistics demonstrate that daily averages fail to capture the essential character of precipitation.

ORCID: 0000-0002-1445-1000.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kevin E. Trenberth, trenbert@ucar.edu

Abstract

A detailed analysis of hourly precipitation from 60°N to 60°S for the covariability is performed at 0.25° resolution using the new CMORPH dataset. For all points, correlations are computed with surrounding points both concurrently and for various leads and lags up to a day. Results are more coherent over the oceans than land; the contours of constant correlation tend to be elliptical, oriented northeast–southwest in the northern extratropics and southeast–northwest in the southern extratropics. An ellipse is fitted to the correlation pattern, and major and minor axis vectors and eccentricity are mapped. Based upon both the isotropic correlations and ellipse, points are allocated to one of 20 clusters, and 16 are documented. Over the main extratropical ocean storm tracks, correlations exceed 0.8 for points 50 km distant and fall to about 0.3 at about 5° radius. In the tropics values drop to 0.65 within 50 km and 0.2 at 5° radius. Over land, values are lower in summer and drop to 0.1 at 5° radius. Decorrelation e-folding distances range from less than 50 km over land to 200 km over extratropical ocean storm tracks. The movement of precipitation is compared with mean atmospheric winds. The lead–lag relationships indicate movement of systems but reveal the relatively short lifetimes of precipitation, of less than 12 h, even taking movement into account. The orientation of the ellipse reflects the structures of rain phenomena (fronts, etc.) rather than movement. These statistics demonstrate that daily averages fail to capture the essential character of precipitation.

ORCID: 0000-0002-1445-1000.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kevin E. Trenberth, trenbert@ucar.edu

1. Introduction

Precipitation varies greatly over short distances and is intermittent; most of the time it does not rain or snow, and even when it does the intensity varies greatly. Rain events arise from a wide variety of meteorological phenomena, from individual clouds and thunderstorms to large-scale stratiform rains, frontal systems, and extratropical and tropical storms. Even large-scale rain or snow systems have a lot of embedded fine structure that makes precipitation coherent only over modest distances. Over land, orographic features greatly influence precipitation and the structures that ensue. Weather forecasters track rain storms with radar and satellite imagery to enable predictions downstream, but the deterministic predictability is limited to minutes, or hours at best. Yet there is very little in the way of analysis of these aspects of precipitation available.

To properly deal with the character of precipitation and the processes involved requires detailed knowledge of the spatial and temporal characteristics and the frequency, intensity, duration, amount, and type. This is not possible using daily values that are the most widely available from rain gauges (Trenberth et al. 2017). There have been a number of analyses of radar imagery but usually from a synoptic or case study standpoint rather than for climate purposes. Examples of the latter include Kursinski and Mullen (2008), who analyzed hourly precipitation using Stage IV (radar) data for the eastern United States, and Paulat et al. (2008), who analyzed hourly radar data in Germany with a detection limit at 0.1 mm h−1 at 7-km resolution. However, there are substantial shortcomings in radar data alone, especially in complex terrain and for wintertime frozen conditions (e.g., Smalley et al. 2014). A major issue has been the availability of suitable calibrated datasets, especially over the oceans. Here, detailed analyses are made of near-global gridded hourly precipitation rates from an updated observational dataset [Climate Prediction Center morphing technique (CMORPH) version 1.0 bias corrected (CRT) hourly] at 0.25° resolution.

The questions posed are to determine the representativeness of a single point in terms of precipitation, how well it relates to and covaries with other points at the same time, and how much it persists and moves, producing covariability in time. In other words, what are the spatial and temporal scales associated with precipitation? Also, how representative are values at one location and time?

To generalize the results, it is desirable to produce composites over similar areas or regimes. This could mandate some remapping of the results onto a regular spatial grid that does not change with latitude. Various methods have been used for clustering results in the past, and here we use some simple methods to achieve this goal. There are strong diurnal and seasonal cycles in many places. Accordingly, we perform separate analyses for the winter and summer seasons as December–February (DJF) and June–August (JJA), but we mostly neglect the diurnal cycle except insofar as it mainly becomes a factor over land in summer.

2. Datasets and methods

The latest generation of CMORPH v1.0 CRT and Tropical Rainfall Measurement Mission (TRMM) 3B42v7 have all been bias corrected using ground-based stations or Global Precipitation Climatology Project (GPCP; Huffman et al. 2009) products, generally with great improvements (Maggioni et al. 2016; Gehne et al. 2016; Xie et al. 2017).

CMORPH capitalizes on high-frequency geostationary satellite observations and tracks propagating cloud features to infill gaps in data, thereby providing better continuity in space and time.

More specifically, CMORPH propagates high-quality passive microwave precipitation estimates both forward and backward in time, using cloud motion vectors derived from correlations of temporally/spatially lagged high-frequency geostationary satellite infrared observations. The cloud motion vectors were further adjusted to match the motion of precipitation patterns determined by temporal/spatial lag correlations of hourly radar precipitation over the continental United States (Joyce et al. 2004) and “morphed” by inversely weighting temporal distances of the estimation target time to the forward/backward scan times.

The new CMORPH near-global high-resolution precipitation estimates (Xie et al. 2017) begin in 1998, and we use them at hourly resolution for 60°N–60°S. Issues remain in winter over land because of snow, but careful evaluations show a consistently superior performance over the TRMM 3B42 dataset (Xie et al. 2017). High-elevation regions are also problematic (e.g., Romilly and Gebremichael 2011). We use the CMORPH data at 0.25° resolution (Trenberth et al. 2017; see acknowledgments for access information).

A trace is defined as less than 0.01 in. (= 0.25 mm), and values less than this are not measured in rain gauges. From space, a practical limit for detection of precipitation has proven to be 0.02 mm h−1 from instantaneous rates, which would be up to 0.5 mm day−1 if continuous at just below that threshold. Hence, we use this value as a threshold for determining whether there is precipitation or not, although light rates are not well measured (Trenberth et al. 2017).

We have computed statistics for all data together. Often the interest is only in the precipitation itself, and its coherence, but of equal or more importance is the coherence of dry spells, since most of the time it does not precipitate; Trenberth and Zhang (2018) show that near globally precipitation occurs 11% of the time. In a more detailed analysis, albeit with radar data, over the eastern United States, Kursinski and Mullen (2008) provided conditional precipitation results at 4-, 16-, and 32-km resolution and showed that the e-folding distances for 1 mm h−1 thresholds were up to about 160 km in winter and about half that in summer, and e-folding times were up to 3 h in winter and about half that in summer. Even at 32-km resolution, the domain-average e-folding times east of 105°W were only 2.1 h in winter and 1.7 h in summer.

3. Modeling the results

We have computed many statistics and attempted to composite many of them to make the numbers palatable. First, we have computed correlations for each grid point with all other grid points for distances up to 10° away. The main computations are for ±20 grid points, or ±5°, and the strongest relationships are for ±2.5°. Hence, by plotting contours of correlations for 5° squares, we can place the core patterns all on one map.

In terms of statistical significance, because we have so many hourly values—for a season from 1998 to 2013 (16 years of 90 days and 24 h)—the 5% significance level of correlations is less than 0.01, and even lower for the composites. However, in practical terms, the amount of variance accounted for is small at those values, and we do not focus on correlations of less than 0.1.

To help visualize the results, we have computed the correlations for ±2 points (±0.5°) in each direction (north, south, east, and west) and averaged them, then plotted that at the core point and mapped the result, called R2. We also did this for points ±10 points away (R10), but the values are very low in many areas. However, these assume isotropy.

The correlation isopleths tend to form some sort of elliptical shape, with values rapidly falling off in all directions but often with a distinct orientation for the least rapid falloff. To simply assess the orientation and the magnitude, the 8 points that are two grid squares (0.5°) distant (Fig. A1) have been used to compute several simple indices that can be related to the shape and magnitude of the pattern, as given in the appendix. Hence, we also consider the diagonal points and computed the metrics given in the appendix, based on the assumption that the correlations form a basic elliptical shape for the most part. These provide an easy way to see the changes in coherence geographically and further provide metrics for clustering the results as composites. For each ellipse, we compute the length of the major and minor axes a and b and the foci c, where c2 = a2b2; the eccentricity ε = c/a; and the orientation of the major axis α. Because the basic data resolution is in degrees, we use dy = rdϕ and dx = r cosϕdλ, where r is the radius of Earth, and λ and ϕ are longitude and latitude for assessing the orientation of the axis. Note that because we use a Robinson projection (e.g., Fig. 1), the orientation of north varies depending on where the points are, and accordingly, a background grid of latitude and longitude is indicated every 30° to indicate local north.

Fig. 1.
Fig. 1.

The correlation of hourly precipitation at 0.25° resolution is given every 5° for (top) DJF and (bottom) JJA for 1989–2013 for 60°N–60°S.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

4. Results

a. Correlations and ellipses

The maps of the correlation isopleths for every 5° of latitude and longitude over the ±10 points in each direction (north, south, east, and west) for DJF and JJA (Fig. 1) are fascinating, although difficult to read owing to the huge amount of detail included. The blue regions indicate where the correlation of the hourly data at zero lag falls to less than 0.1, as is frequent over land. In the white regions, there are no data or the values are all zero. In contrast, over the extratropical oceans in the major storm tracks in each hemisphere, distinctive elliptical-shaped patterns are evident with distinct orientations. The latter are mostly northeast–southwest (NE–SW) in the Northern Hemisphere and northwest–southeast (NW–SE) in the Southern Hemisphere. The tilt is somewhat less as the tropics are approached, and the ellipses are much smaller and more circular in the deep tropics. In the dry zones of the subtropics and downward branches of the Hadley and Walker circulations, where precipitation is often nonexistent or very light, or perhaps episodic with El Niño events, the correlation patterns are very small and sometimes incoherent, indicating very local thunderstorms with little organization or movement, or perhaps variations in the size of systems.

As a first summary of the characteristics of these patterns, the average correlation ±0.5° in both north–south and east–west directions (called R2) is mapped (Fig. 2), although with a very light smoother. This confirms what is visible in Fig. 1, that it is only over the extratropical oceans that values exceed 0.7, or even 0.8, in the major storm tracks. Over the tropical oceans and near land over the oceans, values lie mostly between 0.6 and 0.7, and over land values drop further. They are also much lower over the subtropical southeast Pacific and Atlantic Oceans in the Southern Hemisphere, where the subtropical anticyclones are most stable.

Fig. 2.
Fig. 2.

CMORPH hourly precipitation correlation averaged for the four points ±0.5° from the center of each grid point, as given by R2 (see appendix) for (top) DJF and (bottom) JJA.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Accordingly, Fig. 2 provides a first cut at classifying results as one metric for gathering and compositing results: (i) Ocean 1 (O1): R2 > 0.6 and latitude > 22.5°; (ii) Ocean 2 (O2): R2 > 0.6 and latitude < 22.5°; (iii) Ocean 3 (O3): R2 < 0.6; (iv) Land 1 (L1): R2 > 0.4; (v) Land 2 (L2): R2 < 0.4. In addition, separation by hemispheres is also essential.

The second classification relates to the anisotropic aspects of the elliptical shape of the correlation pattern, and in particular, the direction of the major axis of elongation of the ellipse. The elongation appears to relate mostly to the precipitation phenomena and the orientation of frontal systems: NE–SW in the Northern Hemisphere and NW–SE in the Southern Hemisphere, although cyclonic low pressure systems also move poleward of the main flow, since they form on the eastern side of the upper-level trough (see Fig. 17a, presented later).

The angle the major axis of the correlation ellipse makes with the east–west direction α (Fig. A1), ranges from −90° to +90°, and the color bar wraps in a circular fashion (Fig. 3). Another way to view the orientation is by plotting the major and minor ellipse axes (Fig. 4) to help pin down the impressions seen in Fig. 1. The measure of the degree the ellipse departs from a circle is the eccentricity ε, as given in Fig. 5. Here the east–west dimension includes a cosϕ factor to allow for the convergence of the meridians. To help interpret these values, Fig. A2 presents idealized ellipses for certain ratios of major to minor axes b/a and makes clear that values of b/a greater than about 0.7 are quite circular in shape.

Fig. 3.
Fig. 3.

The angle of the major axis each correlation ellipse makes with the east–west direction is plotted for points 0.5° away from the center of the ellipse for (top) DJF and (bottom) JJA. Owing to symmetry, values range only from −90° to +90° and wrap around (i.e., −90° = +90°) so that the color bar is circular.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 4.
Fig. 4.

The major (blue) and minor (red) axes of each correlation ellipse for distances 0.5° from the center point for (top) DJF and (bottom) JJA. Owing to crowding, only every second point is plotted. The scale of each vector is given in the inset.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 5.
Fig. 5.

The eccentricity of each correlation ellipse at 0.5° radius from the center is plotted for (top) DJF and (bottom) JJA.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Based on all of these parameters, it is evident that the orientation and characteristics of the ellipses are primarily a function of latitude. Accordingly, the second metric we use to classify the ellipses is simply latitude bands, about every 4 points in Fig. 1 or 2 points in Fig. 5. Hence, we stratify as 60°–40°S, 40°–20°S, 20°S–0°, 0°–20°N, 20°–40°N, and 40°–60°N. However, as we previously split out the tropics, 22.5° is used instead of 20° for the main ocean regions. This has another advantage in that we simply aggregate the values without worrying about remapping to accommodate the convergence of the meridians. In this way, we have composited over a number of relatively homogenous clusters.

b. Composites

However, we first simply composited over broad land areas (Fig. 6). The regions selected are shown but only land points were used for the composites, and all results shown here are for the same size domain of ±5°, but some are simply blown up to a larger size. As can be seen in Fig. 1, these land regions are not homogenous; for instance, the Intermountain West over North America has rather different character results versus the Southeast. In all cases, the summer ellipses are somewhat smaller than the winter ones (JJA in north and DJF in the south). Note also that the color scheme in Fig. 6 is quite different than in Fig. 1, and values tend to drop to correlations of <0.1 in less than 3°. In the extratropical land areas, the orientation is similar in summer and winter, but with somewhat stronger tilts NE–SW in winter in the north. Africa is clearly mixed, but the Southern Hemisphere dominates in JJA. The tilt is largely missing in the tropics.

Fig. 6.
Fig. 6.

Composites of correlations for land areas within each box, as identified for (top) DJF and (bottom) JJA. Each rectangle depicts a 10° × 10° domain (±5° from the center point) as shown by small tick marks. The areas used are North, Central, and South America; Africa; Australia; Europe, north and south Asia; and the Maritime Continent.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

To show how the rate of falloff at 0.5° distance relates to values at greater distances, out to 2.5°, Fig. 7 presents composites, based solely on the isotropic correlations 0.5° from the center, and the rate of falloff. The regions used here are ocean type O1, where the R2 correlation > 0.6, latitude > 22.5°; O2, where correlation > 0.6, latitude < 22.5°; O3, where correlation < 0.6; land type L1, where 0.4 < correlation < 0.7; and L2, where correlation < 0.4. This shows very well that choosing R2, as opposed to a greater distance, gives essentially the same classes and in most cases amazingly good agreement between the Northern and Southern Hemispheres. The exception is O1 over the Northern Hemisphere in summer (JJA), which has a faster falloff than in winter and in the Southern Hemisphere year-round. The highest values at 2.5° (10 points) radius are for O1 in southern winter, with an e-folding distance of 1.8° or about 130 km (100–160 km, depending on latitude). The O3 region, mainly in the eastern tropical and subtropical Pacific and Atlantic, has a much shorter e-folding decorrelation distance of less than 0.75° (80 km), as do nearly all land areas, with L2 regions having an e-folding decorrelation distance of only 0.5° (about 50 km).

Fig. 7.
Fig. 7.

For the various regions selected for composites, based solely on the isotropic correlations 0.5° from the center, the rate of falloff for the correlations with distance in units of 0.25°. O1: correlation > 0.6, latitude > 22.5°; O2: correlation > 0.6, latitude < 22.5°; O3: correlation < 0.6; L1: 0.4 < correlation < 0.7; L2: correlation < 0.4.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

The main composites are for the regions in Table 1, with the numbers of points included in each also given for DJF and JJA. Regions that are too fragmented or with fewer than about 150 points are not included. These regions are plotted in Fig. 8. Then the composites are plotted roughly on top of the regions (Fig. 9), and it is necessary to refer back to Fig. 8 to see the relationship.

Table 1.

For each region and latitude band (see Fig. 8), the number of points in each composite for DJF and JJA are given. Regions that are too fragmented or with fewer than about 150 points are not included.

Table 1.
Fig. 8.
Fig. 8.

Composite regions used based on the classifications in Fig. 7 plus bands of latitude.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 9.
Fig. 9.

Each of the main regions has the composite over all grid points of correlations for hourly precipitation. Ocean regions are framed in light blue and land regions in red. Each composite is for a 10° × 10° domain, and the color key is as for Fig. 1. The composites have been weighted east–west by cos(ϕ) to account for the convergence of the meridians. The number of points in each composite is in Table 1.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

For instance, the O1 composites placed over the North Pacific also apply to the North Atlantic, and similarly for the southern oceans. The three composites on the east side of the Pacific for DJF are for all of the three O3 domains, including those in the Atlantic. Similarly, the L1 and L2 regions typically have points over all continents—over North America, Asia, and Europe in the north and over Africa, Australia, and South America in the tropics and south—but each is plotted only once. Ocean regions are framed in light blue, and land regions in red. Each composite is for a 10° × 10° domain, and the color key is as for Fig. 1.

This Fig. 9 color key, as opposed to the one in Fig. 6, shows how small the composite values greater than 0.1 correlation are over many land areas, compared with the ocean regions. The symmetry for north versus south for the oceans is quite striking, and patterns over land are quite similar to those over the ocean at the same latitude, except smaller in size. From 40° to 60° latitude the ellipses are quite round or elongated north–south, with eccentricities over 0.7. In contrast, from 20° to 40°, the orientation is strongly SW–NE in the Northern Hemisphere and NW–SE in the Southern Hemisphere. In low latitudes over the ocean, the winter orientation is in the same direction as for the higher latitudes but not quite as tilted, but in summer they tend to be oriented largely east–west, consistent with an ITCZ or monsoon structure. In the tropics, the fairly circular pattern of correlation does not necessarily mean that the precipitating systems are isolated or unorganized. Rather, squall lines in the tropics are mostly linear but can be oriented in any direction.

c. Time sequences

The in situ correlations do not provide information about the direction of movement or speed. Although organized precipitation phenomena may be trackable for days, the individual rainfall events are relatively short-lived. The same kind of correlation patterns have been computed for times from 6 to 24 h leads and lags. We have also used larger domains (±20 grid points) for some computations, but what we show are the time sequences from 12 h before (−12 h) to 6 h before, time zero, and 6 and 12 h afterward. The main results are shown in Figs. 1015; each figure is for different composite regions.

Fig. 10.
Fig. 10.

For the three main ocean regions over the Northern Hemisphere, as given at top: composites for each region of the correlations as a function of time. The sequential rows depict 12 and 6 h before, time zero, and 6 and 12 h afterward. For each region, the left columns are for DJF and the right ones for JJA. A red star indicates the highest values, and tracking the red stars gives the speed (km h−1) at the bottom right of the time zero panels.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 11.
Fig. 11.

As in Fig. 10, but for the three main ocean regions over the Southern Hemisphere.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 12.
Fig. 12.

As in Fig. 10, but for the three main land regions over the Northern Hemisphere.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 13.
Fig. 13.

As in Fig. 10, but for the two main land regions over the Southern Hemisphere.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 14.
Fig. 14.

As in Fig. 10, but for the two ocean “desert” regions over the Southern Hemisphere.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 15.
Fig. 15.

For the main ocean regions, as given at top: composites for each region of the correlations at time 0 plus the locations of the centroid (white star) at times −6, 0, and 6 h and, where feasible, −12 and +12 have also been added. For each region, the left columns are for DJF and the right ones for JJA. The speed (km h−1) is given at bottom of each panel, and the blue arrows show the direction and movement.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

The strongest correlations are over the oceans in the O1 and O2 regions (Figs. 10, 11) and the Southern Hemisphere composites (Fig. 11) mirror those in the north quite strongly (Fig. 10). The systematic differences with latitude are clear in each, relatively modest departures from isotropy in the higher latitudes and some east–west extended covariability in the tropics (recall that the panels have to be weighted east–west by cosϕ). The strong NE–SW in the north and NW–SE in the south orientation of the ellipses is reflected at all times. Even the summer versus winter patterns are quite similar, although the correlations fall off more rapidly with distance in summer in the Northern Hemisphere. The movement (see also Fig. 15) is fastest and slightly poleward in the high southern latitudes (over 50 km h−1) in both seasons, and the direction is similar to the elongation in the spatial correlations. In the midlatitudes 22.5°–42.5°, the movement is slightly poleward but does not match the structure in the correlation pattern. The mean movement is typically more west to east in the extratropics than the elongation axis. The northern summer movement is a lot slower. In the low latitudes over the oceans, the movement is small or slightly westward in northern summer. These figures (Figs. 10, 11) also show how rapidly the correlations fall off with time, and by ±12 h the peak values in the tropics are down to 0.15 or so.

Over land, in the L1 domains where the correlations are strongest (Figs. 12, 13), similar comments apply except that all correlations are smaller and fade in time much quicker, to the point where it is not possible to track them even for 12 h at high latitudes, and the values in the tropics indicate irregularity of movement. This is in part because there is a strong diurnal cycle over land so that lagged correlations can be higher for 24 h than for 12 h. However, the mirroring of the north (Fig. 12) and the south (Fig. 13) still pertains to a large degree, and the land orientation in midlatitudes is much the same as over the oceans. Here we see much stronger evidence in the tropics of westward movement in both seasons. In high northern latitudes in DJF (Fig. 12), the values are likely compromised by the fact that the precipitation is likely in the form of snow and is poorly represented in this dataset.

For L2, where the spatial correlations fall to less than 0.4 within 0.5°, in all zones (not shown) the time sequences are fairly chaotic. From 40° to 60°N there is no movement, signifying the dominance of orography. From 20° to 40°N and from 20° to 40°S, there is clear eastward movement in winter but no movement in summer. In JJA from 0° to 20°N and from 0° to 20°S, there is evidence of westward movement, but not in DJF; instead, the movement is inconsistent for 6 h before versus after. For L2, the maximum correlations at ±6 h are mostly less than 0.1 and the patterns are incoherent, signifying a lack of consistency among the grid points and the strong role of either local convection and/or topography. In the latter case, upslope orographic rains may persist in the same location, for instance.

For the ocean “desert” regions over the Southern Hemisphere (Fig. 14), the correlation patterns for 0°–20°S are largely circular, as for O2, but the values are much smaller. Westward movement is indicated for the O3 0°–20°S region. Farther south, the O3 ellipses tile NW–SE and move slightly eastward.

To further show how the movement of the rain systems, summarized in Fig. 15, relates to the mean winds, we have computed the mean wind from ERA-Interim reanalyses at 850, 700, and 500 hPa for each season and every point, and then averaged over all points within each composite region (Fig. 16). Of course, the mean flow is not the same for all locations within these large composite regions, and precipitation occurs preferentially when the atmospheric circulation is cyclonic. It is not surprising then that differences exist. Nonetheless, overall in the extratropics, especially over oceans, there is quite a good relationship with wind speed between 700 and 500 hPa, and the direction of movement is distinctly poleward of the mean wind. This is expected for cyclonic weather systems, which tend to propagate poleward of the wind direction and also especially because the low pressure systems occur ahead of troughs (Fig. 17a). The movement of the precipitation is a bit slower than the winds over land, suggesting a topographic component. In the tropics, the mean steering currents are generally much weaker. For instance, for O2 in both seasons the general flow tends to be light easterly, but in DJF the movement tends to be from the west. This would be the case for precipitation associated with the Madden–Julian oscillation, for instance. Hence, the correspondence between actual movement and the climatological winds is quite good, and the differences are largely as expected from the propagation characteristics of the weather systems.

Fig. 16.
Fig. 16.

For each composite region, the mean vector wind (kt; 1 kt = 0.51 m s−1) from ERA-Interim for 1989–2013 is plotted using conventional symbols: one full barb is 10 kt, a half barb is 5 kt, and the direction is toward the point. For clarity, each value is slightly offset in the vertical. Levels included are 850 (green), 700 (blue), and 500 (red) hPa, along with the vector movement of the rain over 12 h (black). The dashed lines indicate the composite zones with O1 and O2 grouped. The background blue indicates ocean, and brown is land.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Fig. 17.
Fig. 17.

Schematic figures illustrating (a) the typical location of the surface low pressure system (orange outlined L) and associated rainfall (green) relative to the 500-hPa geopotential height contours (black lines) in midlatitudes. While the average mean flow (black arrow) is west–east, the steering of the surface low and associated precipitation ahead of the trough is northeastwards (orange arrow). (b) A typical low pressure system and associated cold front in midlatitudes of the Northern Hemisphere has a characteristic slope for the trough and front that produce poleward momentum fluxes aloft, but illustrated here by the u′ and υ′ covariability arising from the front orientation that applies between about 20° and 50°N (pink zone). The prime indicates the departure from the zonal mean. Red arrows indicate flow.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

In terms of an e-folding time for decay of correlations, for the O1 and O2 regions, the values range from 6–7 h in the tropics and JJA in northern midlatitudes to 7.5–9 h in the other extratropics regions. For L1 it is closer to 3 h in the tropics and northern midlatitudes, up to 4 h for 20°–40° in DJF, and strongest—nearly 5 h—from 20° to 40°S in JJA (winter). For L2 regions, the e-folding time is less than 2.5 h.

5. Discussion and conclusions

In this paper, we have documented the covariability of hourly precipitation at 0.25° resolution mainly through determining correlation patterns both at leads and lags as well as contemporaneously. Hence, we have achieved the goal of determining the representativeness of a single point in terms of precipitation, how well precipitation relates to and covaries with other points at the same time, and how much it persists and moves. The patterns are striking in their variations spatially and especially with latitude and season. The correlations fall off with distance quite quickly and the highest values at 2.5° (10 points) radius are for the O1 region in southern winter, with an e-folding distance of 1.8° or about 130 km (100–160 km; depending on latitude). The O3 region, mainly in the eastern tropical and subtropical Pacific and Atlantic has much shorter e-folding decorrelation of less than 0.75° (80 km), as do nearly all land areas, with the L2 regions having an e-folding decorrelation of only 0.5° (about 50 km).

In terms of the covariability in time, the previous section documented the results showing an e-folding time for decay of correlations ranging from 6 to 9 h over the oceans but only from 2 to 5 h over land. Together, the spatial and temporal scales provide answers to the questions about how representative values are at one location and time.

One interesting result is the elliptical shape of the correlation patterns, which is striking, and the degree of elongation varies strongly with latitude. In midlatitudes, the orientation is distinctly NE–SW in the north and NW–SE in the south. This is consistent with expectations from the extensive work on storm tracks. It relates directly to poleward transports of moisture, heat, and equatorward transport of momentum by transient eddies (Fig. 17b). In particular, an equatorward transport of momentum requires a correlation between u and υ, so that in the Northern Hemisphere, stronger eastward flow coincides with northward flow while weaker eastward flow coincides with southerly flow, and this mandates a trough that slopes to the southwest toward lower latitudes, as shown schematically in Fig. 17b; see Trenberth (1991) for a Southern Hemisphere schematic and an extensive review of the many statistics associated with storm tracks identified by a bandpass-filtered (2–8 day) variables. The same argument applies in the Southern Hemisphere, where poleward transport of momentum in the upper troposphere at about 40°S in January and July results in a maximum in (negative), (negative), and (positive) a few degrees equatorward of the storm track in association with the Eliassen–Palm flux (Trenberth 1991). South of the storm track in the Southern Hemisphere, the flux of weakly reverses, and so does the orientation of the trough and elongation of the precipitation correlation pattern. These earlier studies used vertical motion and moisture fields to deduce aspects of diabatic heating, both from clouds and latent heating, the latter being associated with the precipitation detailed here.

Lau and Lau (1990) documented the three dimensional structure and propagation characteristics of tropical synoptic-scale disturbances for summer, which are dominated by 3–8-day time scales. The disturbances remain coherent over several days and tend to travel west or northwestward. Lau and Crane (1995, 1997) analyzed cloud properties associated with the passage of synoptic-scale circulation systems in middle and low latitudes. In midlatitudes, these progressed eastward in association with the advective effects from westerly winds in the upper troposphere. In Lau and Crane (1997), they plotted “propagation vectors” for cloud episodes in winter midlatitudes, primarily in western ocean regions. These moved primarily eastward, or slightly north of eastward, in the main storm tracks. They also present various composites of winds and geopotential heights associated with various kinds of clouds, and their “high-top thick” clouds most likely correspond to the main precipitation and were shown to exhibit shapes compatible with those found here. They further show patterns over North America (land) that are more irregular in shape. Although based on coarse resolution in space and time analyses, these studies show that the primary characteristics of the precipitation are likely associated with baroclinic synoptic weather systems and the corresponding winds and geopotential heights often involved. Catto et al. (2012) related precipitation to atmospheric fronts and were able to distinguish between cold, warm, and quasi-stationary fronts. They found over 90% of rainfall to be associated with fronts, and over the ocean it is mainly cold fronts. Accordingly, the contemporary precipitation is apt to be oriented as for cold fronts over the ocean, but over land there is a larger warm front component. They further noted the problematic identification of fronts in regions of high orography.

An alternative approach may be one based on objects or events. White et al. (2017) tracked events, defined as rainfalls over 24 mm day−1, in space and time using TRMM data for 40°N–40°S. The average event lifetime was 4.1 h. Dias et al. (2012) tracked tropical convection, using an object-based approach, and found that “contiguous cloud regions” mostly propagate westward at about 15 m s−1 and have lifetimes of less than 2 days and zonal widths of less than 800 km. The disadvantage of these approaches is the dependency on thresholds.

Hence, the elongations featured in our precipitation correlation patterns are also what are seen on a day-to-day basis in terms of the orientation of cold fronts, or atmospheric rivers, throughout the midlatitudes, terminating in a low pressure trough at higher latitudes: the circumpolar trough in the Southern Hemisphere or the Aleutian and Icelandic lows in the Northern Hemisphere. In the northern summer, these features retreat farther north and the relationships are not as strong. Of course, these are very dynamic features and change daily. Nevertheless, the main features we have documented arise from synoptic disturbances, and the orientation and movement are mainly governed by the advection and propagation of frontal-like features. Even so, the lifetimes of the individual rain events are short and the spatial coherence is also quite limited, highlighting that the evolution is likely governed by the embedded convection and stratiform rain systems.

The results shown here reveal previously undocumented characteristics of precipitation. The dataset used has known flaws over land in winter associated with the detection of snowfall, but the results are reasonable and consistent with the previously documented movement and development of precipitation-producing weather systems, especially fronts. We have been able to document the average lifetime of the features, their covariability as a function of distance, and their movement. However, these statistics demonstrate characteristics that are not available from daily averages, which fail to capture the essential character of precipitation.

Acknowledgments

This research is partially sponsored by DOE Grant DE-SC0012711. The datasets are discussed in section 2, and those used are public domain and available online. The CMORPH data are described at http://www.cpc.ncep.noaa.gov/products/janowiak/cmorph_description.html and the high resolution data are described at http://ftp.cpc.ncep.noaa.gov/precip/CMORPH_V1.0/REF/EGU_1104_Xie_bias-CMORPH.pdf and downloadable at ftp://ftp.cpc.ncep.noaa.gov/precip/global_CMORPH/30min_8km. NCAR is sponsored by the National Science Foundation.

APPENDIX

Fitting Ellipses to Correlations

To explore as simply as possible the orientation and rate of falloff of the correlation isopleths, we consider grid points 0.5° in each direction of the central point O; see the grid in Fig. A1. We choose the grid points adjacent to O. The points A, B, C, and D form a square centered on the origin O. So do points E, F, G, and H, except they are farther away along the diagonals.

Fig. A1.
Fig. A1.

The grid with points H, A, E, D, O, B, G, C, and F is shown along with the axes J1 and J2, the angle of the major axis α, and a schematic of the isotropic ratios M of the values on the diagonal vs those north–south plus east–west. For the given values of α, a schematic is given of the orientation of the ellipses (yellow) that result in each quadrant as J1 and J2 vary.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

We compute the quantities J1 and J2. J1 tells us all about the elongation east–west, while J2 tells us about the orientation NE–SW. Because the points are farther away from the center for J2, there is a need to normalize to get a direction to combine with J1. R2 provides an isotropic metric as the average correlation 2 points (0.5°) from the center point. The magnitude and how rapidly it falls off is given by M (values M1, M2, and M3), expressed as a percentage decrease. Some ellipses are plotted in yellow to suggest what the orientation looks like when J1 and J2 are compared. The angle of orientation of the major axis = 0.5 tan−1(J2/J1). The vector (M, ) could be plotted to indicate the major axis of the ellipse and its decay; however, we prefer to use the major and minor axes instead, as given below.

The general equation for an ellipse, rotated through an angle , is
ea1
where a is the major axis and b is the minor axis. The distance of the foci from the origin is c2 = a2b2, and the eccentricity is ε = c/a. Fig. A2 illustrates how the eccentricity varies with a and b.
Fig. A2.
Fig. A2.

The eccentricity ε is given for a number of ellipses. From left to right, the ratio of the minor axis to the major axis b/a is 1, 0.9, etc., and the orientation is −45°, 0°, and +45° for α.

Citation: Journal of Hydrometeorology 19, 4; 10.1175/JHM-D-17-0238.1

Given that we can find the points A, B, C, and D, we assume symmetry and at x = 0, Y = 0.5(A + C), and at y = 0, X = 0.5(B + D). From (A1), we can solve for a and b,
eaa2a
eab2b
where s = and c = . In the figures we plot the vectors (a, α) and (b, α) in polar coordinates.

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