1. Introduction
A number of previous studies of the climatology of precipitation over the United States have been motivated by the needs of water management or flood assessment concerns (Miller and Frederick 1966; ESSA 1968; Miller et al. 1973; Hansen et al. 1994). These studies focused on the spatial distribution of climatic annual or monthly precipitation, on return periods of various heavy precipitation amounts, and on probable maximum precipitation amounts. Many other climatic studies have focused on the diurnal distribution of precipitation, where a principal motivation was to improve understanding of causative mechanisms (Kincer 1916; Wallace 1975; Schwartz and Bosart 1979; Balling 1985; Landin and Bosart 1985, 1989; Winkler 1985; Riley et al. 1987; Winkler et al. 1988). Gridded analyses of monthly mean relative frequencies of various threshold precipitation amounts by Jorgensen (1967), Jensenius and Erickson (1987), and Higgins et al. (1996) were conducted largely to establish a climatic benchmark against which to evaluate numerical simulation and probabilistic precipitation forecasts.
The increased interest in the climatology of precipitation over the last 25 years has been driven largely by the need to improve forecasts of precipitation amount. This need was motivated in part by the occurrence of a number of tragic flooding episodes in this country during the 1970s, such as those associated with Hurricane Agnes in the northeastern United States (Bosart and Carr 1978); the Big Thompson Canyon, Colorado, and Rapid City, South Dakota, flash floods (Maddox et al. 1978); and the Johnstown, Pennsylvania, flash flood (Bosart and Sanders 1981). Extensive research on climatological and forecasting aspects of heavy rain ensued during subsequent years.
In recent years, the National Weather Service has begun to incorporate quantitative precipitation forecasts (QPFs) directly into hydrologic streamflow models. A critical requirement for these QPFs is that they have high spatial and temporal resolution, since many floods occur on small streams, where drainage basins might cover only 10–100 km2. Until recently, most QPF guidance products were issued for the synoptic scale. However, the recently implemented Eta Model (Black 1994; Rodgers et al. 1996) now provides QPFs with some mesoscale detail, especially that associated with orographic forcing during the cool season. However, this and other operational models still do not adequately forecast significant mesoscale convective systems. Such mesoscale detail is added manually to QPF guidance by forecasters at the Hydrometeorological Prediction Center (HPC) of the National Centers of Environmental Prediction (Olson et al. 1995).
Even though manually produced QPFs are usually superior to those generated by operational models, their accuracy is not sufficient for predicting many smaller-scale floods and flash floods. For example, the survey team for the great midwestern flood of 1993 (NWS 1994) found that HPC QPFs demonstrated considerable skill for scales down to about the size of a Midwestern state, but such scales do not delineate individual convective systems well. The report went on to state that limits in the spatial and temporal resolution of observations, in numerical modeling capabilities, and in scientific understanding of convective rainfall events make it impossible to provide highly specific QPFs. The findings support the need for increased understanding of the causes of the mesoscale structure of precipitation events. High temporal and spatial resolution climatological studies for various categorical precipitation amounts can help identify some of the causes of the mesoscale precipitation distribution. Also, such climatic data can be incorporated into operational QPF products through subjective judgements (Krzysztofowitz and Sigrest 1997). Alternatively, mesoscale climatology can be incorporated objectively in a post hoc sense into QPFs issued for widely separated points. Such a scheme, which applies the mesoscale precipitation climatology developed by Daley et al. (1994), is now being tested operationally in the western United States (Henkel and Peterson 1996).
Another development over the last decade has been the attempt to utilize high-resolution objective QPF guidance produced by statistically based models. In an initial effort, 0–6- and 3–9-h objective QPFs were produced operationally on an 80-km grid (National Weather Service 1987; Charba 1987). This model applied gridded monthly mean relative frequencies of various precipitation categories (Charba 1985) as a climatic predictor. Just recently, a new QPF model has been developed with higher spatial and temporal resolution; the QPFs are produced on a 20-km grid for 1-, 3-, and 6-h periods in the 1–22-h range. This model has an input requirement for analogous gridded monthly relative frequencies at commensurate temporal and spatial resolutions. Because such a gridded climatology was not available, an effort was undertaken for its development, and it is the subject of this article. As noted above, this type of climatic database should also have other applications, such as guidance for the preparation of operational QPFs, objective guidance for interpolating any type of precipitation data for widely separated points onto a fine mesh grid, verification of operational probabilistic precipitation forecasts, and verification of climatic forecasts of precipitation from regional numerical simulation models.
This work represents a significant extension of previous studies of gridded climatic relative frequencies of precipitation amount. For instance, such analyses by Jensenius and Erickson (1987) were conducted for large spatial scales based on a short sample (13 yr) of precipitation data. The gridded monthly frequencies developed for the initial higher-resolution statistical QPF model noted above were based on a longer sample (27 yr), but the analysis grid was relatively coarse (80 km) and the averaging period was restricted to 6 h (Charba 1985). In this study, the grid mesh (20 km) is one-quarter of that used previously, 1- and 3-h averaging periods supplement the previously used 6-h period, and the historical sample was extended to 33 yr.
This article was motivated by several specific objectives. One is to describe the method used to develop the precipitation climatology, with an emphasis on new procedures used to compute and smooth the frequency data. Another aim is to discuss some of the interesting climatic features that appear over the United States, a few newly uncovered by this analysis. A final aim is to note the availability of this digital database for other possible applications by the operational and scientific community.
2. Database
The precipitation database used for this study consisted of archived hourly precipitation measurements from the U.S. Cooperative Hourly Precipitation Network, available from the National Climatic Data Center (NCDC) in Asheville, North Carolina. Data were obtained for the 33-yr period spanning 1 January 1963–31 December 1995. During this period, the number of reporting stations over the conterminous 48 states ranged from almost 3100 during the early 1970s to about 2800 in the most recent years. Figure 1 shows the station network as it existed in 1975.
Prior to use in the frequency analysis, the precipitation data were subjected to a series of error checking procedures, as discussed in appendix A. The error checks resulted in very few rejections of station precipitation data (less than one per 1000 hourly reports), which attests to the rigor of the error checking already performed at NCDC.
3. Analysis procedure
The specific requirement for the gridded climatic database was the monthly mean relative frequency on a rectangular grid for five precipitation categories and three time durations. The grid is a 175 × 220 array on a polar stereographic map projection with a mesh length of 23.81 km at 60°N, about 20 km over the conterminous United States. Figure 2 shows an outline of the grid based on the plotted coordinate labels, and the subset of 19636 grid points where the analyzed frequency data were required. The precipitation categories are ≥0.10, ≥0.25, ≥0.50, ≥1.00, and ≥2.00 in. (equivalent amounts in mm are given in Table 1), and the time durations are 1, 3, and 6 h. The full set of precipitation category–time duration combinations totals 15, that is, five categories × three durations. The time periods for which frequencies were required consist of 24 1-h periods, eight 3-h periods, and four 6-h periods, where the beginning and ending times (in UTC) of the specific 3- and 6-h periods are evenly divisible by three and six, respectively.
The procedure used to develop the monthly relative frequency fields consisted of several steps. The first step involved the manner in which the hourly precipitation data were used to specify occurrences/nonoccurrences of the various precipitation categories within 20-km grid boxes, the second step consisted of the computation of the corresponding monthly relative frequencies for grid boxes with precipitation data, the third step involved the application of an objective analysis scheme to obtain initial gridded fields of the frequencies, and the final step consisted of the application of smoothing procedures that were necessary to instill spatial and temporal coherence to the frequency data.
a. Precipitation category specification
The first step in the procedure used to specify occurrences/nonoccurrences of the various precipitation categories from the hourly precipitation data entailed superimposing a grid array of square boxes 20 km on a side over the station network. The specification of an occurrence/nonoccurrence value for a given precipitation category was based on all precipitation observations in the box, though only one observation was required. The value was assigned to the centerpoint of the box. The centerpoints of all 20-km boxes over the conterminous United States coincide with the grid points shown in Fig. 2. A subset of 3641 boxes (Fig. 3) were found to contain one or more stations over all or part of the period spanning 1963–89. The occurrence/nonoccurrence values were specified and archived for this fixed set of boxes for the 1963–95 period of record available.
The values assigned for categorical occurrences/nonoccurrences was dependent on the number of stations (or precipitation measurements) in a box. In general, the values were computed as the fraction of stations within the box for which the precipitation equaled or exceeded the category breakpoint. Thus, for the vast majority of the 3641 boxes that contained only one station, the categorical value was 1 when the reported precipitation met the amount criterion and 0 when it did not. For instances when a box contained more than one station, the fractional value was somewhere in the range 0 to 1. For example, if the precipitation category is ≥0.25 in. and the box contained the three reports of 0.00, 0.10, and 0.50 in., the categorical value would be 1/3 or 0.33. It is worth noting that the overall mean number of stations per box for the 1963–89 period was only 1.06, the standard deviation was 0.25, and the maximum was 9.0. Clearly, only a very small fraction of the boxes had more than one station.
The above procedure for specifying categorical occurrence/nonoccurrence values for boxes with one or more precipitation measurements was chosen because of its efficiency and practicality. The method has the attribute of using all the available station precipitation measurements without the necessity of considering the history of each reporting station, which would have been burdensome with the large station network and the long period of data record involved. The use of all stations is desirable because this increases the sample size. The procedure results in two compromises, but these are quite minor. One is that the exact location of the station(s) within a 20-km box is not known. The maximum positioning error that could result is only 14 km, which is quite small in comparison to the 65-km average spacing of the precipitation stations. Another compromise is that when more than one precipitation report appears in a box, the ensuing categorical value becomes an average over such values at the individual stations involved. With a box size of 20 km, this too results in negligible error in the eventual gridded frequency analysis. For instance, while it is possible that climatic variations in station precipitation could occur within such boxes in a few locations, for example, where stations are clustered along the steep slopes of the front range of the Rocky Mountains in Colorado, near coastal southern California, and perhaps in a few locations along the slopes of the Sierra Nevada and Cascade Mountains (see Fig. 1), the retention of such isolated detail was not considered feasible for the gridded nationwide climatic analysis being attempted.
b. Frequency computation
Following archival over the 33-yr period of record, the categorical precipitation values for each box, daily time period, and month were initially summed over all days archived. The monthly mean relative frequency was then obtained by dividing the sum by the sample size, that is, the number of days the category was specified for the box. However, the frequency computation was limited to those boxes with a sample size of ≥530. This arbitrary sample criterion, which is slightly greater than half the maximum possible sample size of about 990, that is, 33 yr × 30 days per month, represents a trade-off between the likely appearance of random frequency variations due to sampling inadequacy when the criterion is too small and the undesirable loss of computed frequency values when the criterion is too high. With this sample criterion, the number of boxes over the nation that returned frequency values averaged about 2450, which is substantially less than the maximum possible number of 3641.
It should be noted that the precise meaning of the computed frequency values is inherently linked to the number of stations that were used to specify the precipitation categories. For boxes that contained only one station, the frequency value represents the percentage of times the precipitation category was observed at the station. Where the category value was specified from more than one station, the ensuing frequency value retains this definition, but it represents an average point frequency over all stations in the box. In either case, the frequency value is assigned to the center of the box. Because the vast majority of boxes had only one station, as noted above, the number of locations with average point frequencies over the United States is quite small. Further, even for locations with average point frequencies, the latter still approximate single point values when viewed in terms of the scale of the analysis being performed, also as noted above.
The fields of monthly mean relative frequency exhibited varying degrees of spatial and temporal coherence among the different precipitation categories and time durations. For the lightest precipitation category and longest duration, ≥0.10 in. and 6 h, the point frequency data showed relatively good spatial coherence, as shown in Fig. 4 (also see Fig. 6a later). At the other extreme, frequencies for the heaviest category and shortest time duration (≥2.00 in. and 1 h) showed very little spatial coherence, as nonzero values appear at only widely scattered points (Fig. 5, also see Fig. 7a later). The spatial coherence, as well as continuity in the month-to-month and period-to-period time domains, will be examined further following a discussion of the gridding of the frequencies, which was the immediate subsequent step in the analysis.
c. Frequency gridding
The gridding step of the analysis was intended to obtain initial gridded fields of frequency values at all points of the 20-km grid that are consistent with the point frequency data. First, it is important to recall that the positions of the frequency values coincide with a subset of the grid points composing the analysis grid. Thus, the function of the gridding procedure was to interpolate to the intervening grid points, while essentially preserving the frequency values for those grid points with data.
Because of its versatility and ease of application, a modified form of the objective analysis method described by Cressman (1959) was used to perform the gridding. The analysis method is similar to that described by Glahn et al. (1985), but the analysis correction scheme was extended to include an adjustment that results in a reduction of analysis error for grid points where the data points have an asymmetric spatial distribution about them (appendix B). The analysis scheme also included procedures that checked for and rejected possibly erroneous frequency values. The error checking scheme and the number of rejected frequency values are discussed in appendix A.
The objective analysis scheme was successful in accomplishing its intended functions. To illustrate this, Figs. 6a and 7a show contour maps of the gridded fields corresponding to the plotted point frequencies in Figs. 4 and 5, respectively. Note that the frequency peaks in Fig. 6a in most instances closely reflect the corresponding point values in Fig. 4. The closeness of the match is also evident in the highly spiked example of Figs. 5 and 7a, except where a frequency spike in the point plot is closely surrounded by zero values. It should also be noted that because the analysis largely retained the individual point frequencies, instances of error in the frequencies would be retained in the initial gridded fields. Thus, even though the number of point frequencies rejected during the objective analysis was quite small (see appendix A), their removal from the initial gridded frequency fields reduced the amount of smoothing that was ultimately required to obtain coherence in the final fields.
d. Temporal and spatial smoothing
The example of Fig. 7a illustrates an extreme case of the lack of spatial continuity in many of the initial gridded frequency fields. An analogous lack of continuity also appeared in the month-to-month and period-to-period frequency variations at any given point, as shown later in this section. The final step of the analysis addresses the application of smoothing procedures that were designed to filter such spatial and temporal irregularities.
As noted previously, the needed smoothing of the initial gridded frequencies was less for light precipitation categories and long time durations, which have frequent occurrences, than for heavy categories and short durations, which have rare occurrences. In essence, smoothing increases the sample size, and the number of occurrences, over which the frequency is evaluated. For instance, smoothing over space expands the averaging area beyond the 20-km box, and smoothing over consecutive periods of the day or over consecutive months of the year expands the averaging domain in each of these two time dimensions.
The smoothing in each of the two time dimensions was conducted by applying (1) and the smoothing over the grid was done by applying (2). The smoothing applied in each case was controlled in two ways. One control was through the values assigned to the smoothing parameters μ in (1) and b in (2). The other control was through the number of passes the smoothing operator was applied.
The smoothing applied for each of the 15 combinations of precipitation category and duration was determined largely on the basis of subjective examination of the frequency fields. To reduce the workload involved in making the individual smoothing choices, the smoothing was subjectively fine-tuned, through careful inspection of the fields, for only several of the category–duration combinations. Then, the smoothings for the remaining combinations were largely inferred using the smoothing controls for these combinations as guides. In particular, three precipitation category–duration combinations were chosen to serve as guides. The first combination was one where occurrences were most common (≥0.10 in. and 6 h, which was the first example above), the next was one where the occurrence frequency is in the intermediate range (≥0.10 in. and 1 h), and the third where the occurrence frequency is most rare (≥2.00 in. and 1 h, the second example above). The smoothing selections for the guide category–duration combinations are illustrated by examining the unsmoothed and smoothed frequency fields for each.
A contour map of the raw (unsmoothed) frequencies for the first category–duration combination (≥0.10 in. and 6 h) used as a guide is shown in Fig. 6a. The month of July was chosen for illustrating the smoothing for each combination because, during the course of the study, we observed the spatial and temporal variability in the frequency fields to be highest during the summer;thus, the summer months represent a worst-case scenario. For this category–duration combination, the raw frequencies for a cross section (SS) along line ACB in Fig. 6a are shown in Fig. 9a, and corresponding month-to-month (MM) and period-to-period (PP) time sections for point C in Fig. 6a are shown in Figs. 9b and 9c, respectively. Note that random variations in each of these frequency profiles are small, with the least randomness in the PP curve (Fig. 9c).
The smoothing parameters applied for this precipitation category–duration combination (as well as those ultimately chosen for all other combinations) are given in Table 2. In this table and in the subsequent text, the period-to-period smoother is referred to as the PP smoother, the month-to-month smoother as the MM smoother, and the spatial smoother as the SS smoother. The table includes the number of passes and the smoothing parameter for each of these smoothing types.
As a quantitative measure to express the smoothing resulting from the smoothing parameter and number of passes for each smoothing type, we used the centerpoint weight (W in Table 2). The centerpoint weight is the factor by which the center gridpoint frequency is multiplied during the smoothing application. Of course, the smoothing increases as the centerpoint weight decreases. The centerpoint weight for the one-dimensional smoother is μ for one smoothing pass, μ2 + 2a2 for two passes, and (μ3 + 6μa2) for three passes, where a = (1 − μ)/2. The centerpoint weight for the corresponding two-dimensional smoother is the square of that for the one-dimensional case. The overall centerpoint weight is the product among the centerpoint weights from the three smoothing types. Quantitative values for each of these four centerpoint weights are included in Table 2.
Note from Table 2 that for the ≥0.10 in. and 6-h combination, the smoothing (in terms of the centerpoint weight) was highest with the SS smoother and next highest with the MM smoother, while no smoothing was applied with the PP smoother. The relative smoothings are consistent with the subjective assessments noted above from Fig. 6a and the unsmoothed profiles in Fig. 9. The contour map for the smoothed frequencies for this combination (Fig. 6b) exhibits improved coherence, resulting from removal of random wiggles in the contours, with only a slight reduction of peak amplitudes. The smoothed SS, MM, and PP profiles shown in Fig. 9 reveal an analogous benefit.
The depictions of the raw and smoothed frequency fields for the category–duration combination with intermediate occurrence frequencies, that is, ≥0.10 in. and 1 h (the second guide), are shown in Fig. 10. The raw frequency field (Fig. 10a) and the corresponding spatial and temporal profiles in Fig. 11 reveal substantial random frequency variations in space and in both time domains. Table 2 shows that substantial smoothing was done, as the centerpoint weight was 0.76 for the PP smoother, 0.55 for the MM smoother, and 0.25 for the SS smoother. Thus, the smoothing was again greatest with the SS smoother and least with the PP smoother. Note that the smoothing for this combination was rather heavy, as the overall centerpoint weight was only 0.105. Nevertheless, Fig. 10b shows that the smoothed frequency field retained the coherent finescale detail evident in the unsmoothed field. The smoothed profiles in Fig. 11 also show the removal of the small-scale, random variability and a retention of the systematic larger-scale variations.
The depictions of the raw and smoothed frequencies for the category–duration combination with fewest occurrences, that is, ≥2.00 in. and 1 h (the third guide), are shown in Figs. 7 and 12. The raw frequency field (Fig. 7a) and the corresponding profiles in Fig. 12 show that very heavy smoothing would be needed to achieve acceptable spatial and temporal coherence. Table 2 shows that the smoothing parameters selected were indeed extreme, especially with the SS smoother, wherein the centerpoint weight was only 0.098. Also, the center gridpoint frequency retained only 0.02 of its original value following all three smoothing applications. Thus, it is not surprising that the smoothed field in Fig. 7b bears only a weak resemblance to its unsmoothed counterpart, and the same is true of the smoothed and raw frequency profiles in Fig. 12. Also, an extreme reduction in the frequency peak at point C from a value of 0.14 to 0.02 is evident from Figs. 7 and 12a.
The use of the above three precipitation category–duration combinations as guides was based on the assumption that the smoothing should increase with decreasing relative frequency of the category. Thus, the smoothing should increase with increasing precipitation category and decreasing duration. Adherence to this rule resulted in initial estimates of the required smoothing for all remaining combinations. Slight adjustments to the initial estimates were then made based on several control factors. One control was based on spot examinations of the frequency fields for selected category–duration combinations. Another control stemmed from a firm goal to preserve real diurnal variations in the period-to-period frequencies at a point. This goal placed a strong brake on the PP smoother, especially for the 3- and 6-h precipitation durations. A third factor was the insistence that the smoothing performed with each smoothing type, as expressed by the centerpoint weight, was to change in a consistent manner as the precipitation category and duration changed.
e. Discussion
As noted before, spatial and temporal coherence was an important requirement for the monthly frequency fields. Because of the excessive random variability in the raw gridded frequency fields, the smoothing treatment constituted a major part of the analysis procedure. A novel aspect of the smoothing methodology used in this study was the full flexibility to specify the smoothing individually for each of the 15 precipitation category–duration combinations. This allowed us to minimize the smoothing and thus maximize the spatial and temporal detail for each combination. On the other hand, a negative aspect of the smoothing is that the smoothed frequency fields are no longer true monthly means of the categorical precipitation occurrences, as originally specified. That is, a smoothed gridpoint frequency value is actually applicable to an area larger than a 20-km box, to a period longer than 1 month, and to durations longer than 1, 3, or 6 h. Also, the precise amount of expansion in the three dimensions is not known.
Two additional points bear emphasis. One is that a special attempt was made to retain the true period-to-period frequency variations. This was done by insisting that the PP smoothing applications be as light as possible, especially for the 6-h periods, and to a lesser extent the 3-h periods. Another point is that while it has been stated repeatedly that the spatial smoothing was heavier than the temporal smoothing, the former is artificially magnified by the fineness of the data in the spatial domain. In fact, a rigorous assessment of the true differences among the three smoothing types is beyond the scope of this study. It is permissible here to state only that the smoothing was kept to a minimum in both the space and time dimensions based on subjective assessment of the noisiness of the frequency data.
In view of the above considerations, the smoothed relative frequencies are approximations of true monthly means of the various precipitation categories. The approximation is good for the lighter precipitation categories and longer time periods, but it weakens with the heavier categories and shorter periods. This property of the frequency analysis should be considered in any application for which the database is used. One application is an examination and discussion of selected spatial and temporal climatic features in the frequency fields, which is considered next.
4. Climatic features in the monthly frequency fields
The monthly relative frequency fields for the various precipitation categories and durations exhibited a broad range of climatic features over the United States. At large scales, the features confirm those found in previous studies, but at small scales new features were found and others clarify those noted previously. In this section, selected climatic features are illustrated and compared with those documented, with emphasis on features that are new. Various physiographic factors, which include mountain ridges and valleys, ocean coasts, and large lakes, are linked to many of the climatic signals, and they are discussed in terms of their interaction with the diurnal heating/cooling cycle. Also, aspects of the climatic feature commonly termed the summertime nocturnal precipitation maximum of the Great Plains are discussed, again with an emphasis on small-scale features that were newly discovered in this study. Linkages between climatic features and the likely forcing factors are presented primarily to stimulate interest and/or further investigation. In the following sections, the climatic features are discussed according to the physiographic factor(s) to which they are believed primarily related.
a. Cool season orographic effects of mountains
The most pronounced features in the monthly frequency fields are elongated bands of high (low) frequencies along the western (eastern) slopes of the major mountain ranges in the western United States during cool season months. These are illustrated in Fig. 13, which shows January frequency patterns for ≥0.10 and ≥0.25 in. during 1800–2100 UTC. The positions of these bands relative to the mountain ranges is seen by comparing this figure to a smoothed topographical map for the area, which is shown in Fig. 14. (The smoothed topography for an individual 20-km box was specified initially as an arithmetic mean of a 7 × 7 subarray of point elevations within the box. Values at subarray points were interpolated from 30-s quadrangle mean elevations, as provided by the U.S. Geological Survey. Subsequently, the grid of such mean values was subjected to one pass of the nine-point smoother with a b value of 1.0.) Note that the north–south bands of peak frequencies in Fig. 13 are positioned along the western (windward) slopes of the Coastal Range, the Sierra Nevada and the Cascade Mountains, and the various ranges of the Rocky Mountains (Fig. 14). Also, pronounced frequency reductions appear along the eastern (leeward) slopes, especially for mountain ranges near the West Coast; the frequency reduction is moderate in conjunction with the modest Coastal Range in California and Washington, but very strong for the high Sierra Nevada and Cascade Mountains in California, Oregon, and Washington. Also note the small, but distinct, east–west-oriented minimum in the frequencies along the California–Oregon border, which is just north of the High Sierras in northern California.
It is hypothesized that the wintertime frequency maxima and minima noted above result from orographic effects associated with frequent moist, lower-tropospheric westerly currents traversing the various mountain ranges. It is noteworthy that many of the climatic features noted above were obtained from numerical simulations with a regional atmospheric model for the western United States by Giorgi et al. (1993). Even the small frequency minimum along the California–Oregon border might be a reflection of the upstream removal of valley-channeled, northward-bound moisture on the windward side of the High Sierras in northern California. The latter minimum was also evident in the hand-drawn atlas maps of January precipitation frequency in Miller and Frederick (1966) and for January precipitation amount in the ESSA Climatic Atlas (ESSA 1968). The feature did not appear in the simulated precipitation fields of Giorgi et al. (1993), probably because of the smooth topography used in their model.
An irregular north–south band of peak frequencies along the western slopes of the Rocky Mountains in Arizona, Utah, and Idaho is quite apparent for 3-h precipitation of ≥0.10 in. in Fig. 13a, but this band largely disappears when the precipitation intensity is only slightly higher: ≥0.25 in. in a 3-h period (Fig. 13b). This dramatic reduction in frequency with increasing precipitation intensity could be due to low moisture availability following upstream orographic depletion near the West Coast. Other interesting small-scale features include the frequency peak in northeast Oregon and southeast Washington; the peak near the point where the borders of Idaho, Montana, and Wyoming meet; and the peak just southeast of the Great Salt Lake. It is possible that the first peak is an orographic reflection of the Blue Mountains (Fig. 14); the second peak may be due to topographic lifting of moist westerly flow that is funneled along the Snake River Valley in southeastern Idaho toward the Windward Range to the northeast; and the last peak might be in part a reflection of the release of supplemental moisture from the Great Salt Lake by the Wasatch Range to the east. Each of these features were at least partially resolved in the hand-drawn maps in the ESSA Climatic Atlas (ESSA 1968) and Miller and Frederick (1966) and in the simulated precipitation fields of Giorgi et al. (1993), but they have improved definition here. On the other hand, neither the atlas maps for heavy precipitation intensity in Miller and Frederick (1966) nor the frequency map for moderate precipitation intensity in Fig. 13b show a pronounced maximum east of the Great Salt Lake, probably because the underlying precipitation episodes are generally light.
The seasonal and diurnal variations of the cool season frequencies for ≥0.10 in. in the western United States are illustrated in Figs. 15a and 15b for point A on the windward side of the Cascades in northern Oregon (Figs. 13a and 14). Seasonally, the peak frequencies at this point occur in November, December, and January (Fig. 15a) when the position of the principal storm track is present at this latitude (Reitan 1974). A deep frequency minimum occurs in midsummer, reflecting the retreat of the storm track to higher latitudes during the warm season (Reitan 1974). The diurnal frequency variation for this point in January is quite weak (Fig. 15b), with a weak maximum during late morning (1500–1800 UTC) and a minimum in late evening (0300–0600 UTC), similar to that found for the Sierra Nevada in California by Landin and Bosart (1989). The lack of a significant diurnal variation suggests that the precipitation processes are predominantly convectively stable.
In the eastern United States, cool season orographic forcing of precipitation by the Appalachian Mountains is also indicated in the climatic frequencies, but it is weaker than in the west (Fig. 16). One location in the east where the apparent orographic effect is strong is at the “Triple Point,” where the borders of Georgia, South Carolina, and North Carolina meet (point A in Fig. 16). Note that the January frequency pattern for ≥0.25 in. during 1800–2100 UTC shows a small, but steep, maximum centered on this point. The smoothed topographic field shown in Fig. 17 reveals that point A lies near the southern extension of the Appalachian Mountains. Although the figure shows that the areally averaged ground elevation at point A is well under 3000 ft (914 m), the maximum point elevation in the immediate area is about 4800 ft (1463 m), and it is about 6600 ft (2012 m) 50 km to the northeast (both point elevations not shown), the latter being near the highest elevation in the entire Appalachian range. Also, the January diurnal variation in the frequencies for this event (not shown) was quite weak, similar to that seen earlier for the western United States. Thus, it is hypothesized that this localized frequency maximum is due primarily to orographic lifting of moist flow from both the Gulf of Mexico and the Atlantic Ocean. Note that this location within the Appalachian range is unique in that only here are flows from these moisture sources undisturbed by intervening topographic features.
Interestingly, the localized maximum at the Triple Point was evident in the frequency fields throughout the year, as indicated in Fig. 18, which compares the monthly time series for ≥0.25 in. during 1800–2100 UTC at this point with a nearby point in central Tennessee (also see Fig. 16). However, in contrast to the very weak diurnal frequency variation for this point during the winter (noted above), Figs. 10 and 11c show that the peak during July exhibits a pronounced diurnal maximum during the afternoon. The afternoon maximum in summer is indicative of thermodynamic forcing from solar heating of the high terrain. Also, note that the monthly frequency profile for the Triple Point (Fig. 18) exhibits minima in April and October. If we postulate that the peak at this point during spring and fall is due to both orographic and thermodynamic forcing, the combined climatic effect is apparently weaker than that during the winter or summer when the localized maximum is believed to result from a singular mechanism. We should add that the year-round frequency maximum was also seen in the January atlas maps of Miller and Frederick (1966) and the ESSA Climatic Atlas (ESSA 1968), but it exhibits better spatial definition in Fig. 16.
b. Thermodynamic effects of mountains during the warm season
For mountainous locations with frequent summertime precipitation, the predominant forcing mechanism of the mountains on the climatic distribution of precipitation is the thermodynamic response to daytime heating and nighttime cooling of the elevated boundary layer. For instance, this forcing mechanism has been discussed in conjunction with thunderstorm genesis for the Rocky Mountains by Banta (1984, 1986), Banta and Schaaf (1987), and others. That is, daytime solar heating (nighttime radiational cooling) of the mountains results in elevated heat sources (heat sinks), which act to promote (inhibit) convective precipitation. Evidence of this cause-and-effect linkage is indicated for the southern Rocky Mountain region in Figs. 19 and 20. A careful comparison of the July frequency distribution for ≥0.10 in. during the early afternoon period of 2000–2100 UTC (Fig. 19) with the topographical map for the area (Fig. 20) reveals that virtually all locations with relatively high elevation exhibit high frequencies, and the opposite is true for locations with low elevations. In fact, even a small topographic feature such as the Black Hills in extreme western South Dakota appears as a distinct maximum in the frequency field (point E in Figs. 19 and 20). In a climatic analysis of cloud-to-ground lightning data—obviously related to precipitation occurrence—for the western United States, Reap (1986) found a pronounced increase in the frequency of lightning activity over high terrain. Banta and Schaaf (1987) found that leeside mountain slopes in New Mexico and Colorado were preferred locations for convective storm genesis, in agreement with the above findings. Also, in a detailed climatic analysis of lightning data for New Mexico by Fosdick and Watson (1995), the lightning frequency patterns were remarkably similar to those in Fig. 19.
The summertime precipitation–topographic linkage is further illustrated when frequency profiles for the mountainous points A, B, and C in New Mexico and Colorado are contrasted with a baseline location in the high plains (point D) near the Texas–New Mexico border (Figs. 19, 20, and 21a). The hourly frequency time series for the mountainous locations in Fig. 21a show a very sharp frequency maximum during early afternoon and a deep minimum during late night and early morning hours. This finding is similar to that found by Tucker (1993) based on her diurnal frequency analysis of 20 yr of hourly precipitation data in New Mexico. It is also similar to the variations in lightning activity found by Reap (1986) and Fosdick and Watson (1995). Also, the month-to-month frequency variation (Fig. 21b) for the afternoon frequency peak at 2100–2200 UTC for point B reveals a very sharp midsummer maximum. The coincidence of the frequency maxima for all three mountain locations with the times of maximum diurnal and seasonal heating supports the hypothesis that thermal instability is the dominant forcing mechanism. Similarly, the early morning frequency minimum is suggestive of the stabilizing effect of nocturnal cooling. In contrast to the mountainous points, note that the high plains location does not exhibit an afternoon maximum in the frequency profile. Instead, a moderate maximum appears in the evening (around 0300 UTC), similar to that found for lightning occurrence over the high plains by Reap and MacGorman (1989) and Fosdick and Watson (1995). Also, the morning minimum for this point is not as low as that seen for the mountainous points. Further, the monthly frequency profile for the 2100–2200 UTC (afternoon) period shows a weak maximum in May, in contrast to the July and August maximum for the mountains. Thus, if diurnal heating and cooling control summertime convection in the mountains, these results suggest that other forcing mechanisms are important for the neighboring high plains location. Possible mechanisms for high plains convective storms are discussed by Holton (1967), Banta (1984), and Benjamin and Carlson (1986).
An interesting temporal–spatial frequency shift is noteworthy for the three southern Rocky Mountain points (A, B, and C in Figs. 19, 20, and 21a). The diurnal frequency profiles for these points (Fig. 21a) reveal a pronounced south-to-north time lag in the afternoon frequency peak. In particular, the peak frequency in southern New Mexico precedes the corresponding peak in northern New Mexico by 2 h, and it precedes the peak in Colorado by 3 h. For the two New Mexico points, this result is similar to the space–time shift found in lightning data by Fosdick and Watson (1995). One possible explanation for this finding rests on the premise that atmospheric moisture is higher in southern New Mexico than points farther north. For instance, July mean upper-air charts shown in Maddox et al. (1995) suggest this to be true, and Fosdick and Watson’s (1995) climatic analysis of precipitation and lightning data show that summertime rainfall in southern New Mexico is higher than that in the northern part of the state even though the lightning counts are much higher in the latter area. Increased precipitation in southern New Mexico is also confirmed by our analysis; for instance, summertime frequencies for very intense precipitation, ≥1.00 in. h−1, were nonzero only in the southern part of the state (not shown). If the premise of increased moisture in southern New Mexico is true, then less solar heating would be required to initiate convection there and, thus, precipitation should begin earlier in the day. Another possibility is that there is a climatic difference in ridge-top winds at the neighboring locations, which, according to Banta (1984 1986) and Banta and Schaaf (1987) could affect the timing of leeside thunderstorm formation. A similar, though less pronounced, southwest-to-northeast time lag was also observed in successive hourly frequency patterns for the southern and central Appalachian Mountains (not shown). The northeastward extension of peak frequencies from the Triple Point is suggested from Fig. 10b.
c. Features of the nocturnal precipitation maximum of the central United States
Kincer (1916) and Balling (1985) found that in the central and southern plains states more than 60% of summer season rainfall occurs during nighttime hours. Also, in studies of heavy rains associated with flash floods, Maddox et al. (1979) and Crysler et al. (1982) have documented a strong nocturnal maximum in this area. Other studies have noted the contrast between the plains nocturnal precipitation maximum and the pronounced afternoon maximum in most other areas of the nation (Pitchford and London 1962; Wallace 1975; Schwartz and Bosart 1979; Easterling and Robinson 1985; Landin and Bosart 1985, 1989; Winkler 1985; Riley et al. 1987; Winkler et al. 1988). Because the nocturnal maximum is unique in many respects, and because it has been the subject of extensive scientific study, some of the more novel aspects of its structure and evolution found in this analysis are examined.
A number of previous studies have indicated a southern and central Rocky Mountain origin for nocturnal plains convective systems (e.g., Maddox et al. 1982; Cotton et al. 1983; Fosdick and Watson 1995). On the other hand, Riley et al. (1987) and Winkler et al. (1988) argued that the nocturnal precipitation maximum of the central plains cannot be explained solely on the basis of the eastward drift of afternoon convection that began over the Rocky Mountains, based on results from their harmonic analysis of hourly precipitation. The evolution of the plains nocturnal precipitation frequency maximum, beginning with the Rocky Mountain afternoon maxima discussed above, is illustrated in Figs. 19 and 22. In the 3-h sequence of July frequency patterns for ≥0.10 in. per hour (Figs. 22a–d), the nocturnal maximum reaches maturity in the area of the Nebraska–Kansas border to southwest Iowa during 0500–0900 UTC (Figs. 22c and 22d). For the heavier precipitation category of ≥0.50 in. during 0600–0900 UTC, the maximum exhibits better geographical organization (as noted previously by Winkler et al. 1988) and is labeled“G” in Fig. 22e. An attempt to trace this nocturnal central plains maximum to the afternoon frequency peaks in Colorado and New Mexico proved difficult, because most of the latter maxima did not remain intact as they migrated eastward to the high plains (Figs. 19, 22a, and 22b). In fact, new frequency maxima in eastern Colorado and extreme western Nebraska, each labeled“C” in Figs. 22a and 22b, developed east of the mountains, which supports the redevelopment hypothesis of Riley et al. (1987) and Winkler et al. (1988). It should be noted that the local frequency time series for selected points from central Colorado to southwest Iowa in Fig. 23a could be interpreted as a smooth eastward migration of the frequency peaks from the mountains to the plains. These results underscore the importance of the hourly spatial frequency analysis performed in this study to clarify the subtleties of the evolution of even a major climatic feature such as the Great Plains nocturnal maximum.
Careful inspection of the summertime hourly frequency patterns of ≥0.10 in. resulted in the finding of two additional frequency maxima over the plains area. The first maximum originated from a smooth eastward progression of the afternoon frequency peak labeled“B” in northern New Mexico in Fig. 19. The 3-h sequence of later frequency patterns in Fig. 22 shows that this maximum (also labeled “B” in these figures) retained its identity as it moved southeastward. This maximum appeared over the Texas panhandle during 0500–0600 UTC (Fig. 22c), where it is also easily recognizable in the heavier precipitation category of ≥0.50 in. during 0600–0900 UTC (Fig. 22e). This nocturnal maximum began to lose its identity after 0600 UTC (midnight), as suggested by Fig. 22d, and by 1000 UTC it was no longer evident (not shown). This feature appears distinct from the nocturnal maximum of the central plains in that it is more clearly rooted in the afternoon maximum over the mountains, and it disappeared much sooner; the central plains maximum remained evident until about 1600 UTC (not shown), about 6 h longer than the Texas panhandle maximum. Fosdick and Watson (1995) also observed this frequency maximum in their frequency analysis with lightning data. Its origin to the eastern slopes of the Rocky Mountains in northern New Mexico and its smooth subsequent eastward propagation suggest the leeside genesis and propagation mechanism described by Banta (1984, 1986) and Banta and Schaaf (1987). Although its continued eastward movement during the night into the southern plains qualifies it as a nocturnal maximum, its smaller size and earlier disappearance than the corresponding maximum over the central plains indicate that the governing precipitation mechanisms for the two locations are not identical.
Another feature evident in the sequence of frequency fields in Fig. 22 is a persistent frequency maximum just southwest of Lake Superior. This feature, labeled M in Figs. 22a–d, was evident only for the light precipitation categories, as it is barely identifiable for the heavier category of ≥0.50 in. (3 h)−1 (Fig. 22e). An examination of the full 24-h set of hourly frequency fields of ≥0.10 in. (not shown) revealed that this feature was quasi-stationary in its geographical location, and the diurnal variation in the frequencies was very small. To illustrate the latter, Fig. 23b shows the diurnal time series for point M together with that for point C, the latter being within the central plains nocturnal maximum (see Fig. 22 for the locations of both points). Note that while the daily average frequencies for these two nearby points are about the same, the southwest Iowa point shows a marked diurnal oscillation, while the point on the Minnesota–Wisconsin border shows almost no temporal variation. Obviously, the mechanisms that control summertime precipitation over the latter location must have a uniqueness from those that govern the central plains nocturnal maximum. [See Pitchford and London (1962), Wallace (1975), Easterling and Robinson (1985), and others for discussions of possible controls for the nocturnal maximum.] The Minnesota–Wisconsin maximum is essentially a newly discovered feature, as only very weak evidence of its existence appeared in the spatially smoothed frequency maps of Jensenius and Erickson (1987), the atlas maps of Miller and Frederick (1966), and the ESSA Climatic Atlas (ESSA 1968). It appears to be a significant climatic feature that should be examined further in future studies.
Winkler (1985) showed that the summertime climatology of the diurnal variation of heavy precipitation changes strongly from the central plains to the southern United States. She found that peak frequencies occur around 0600 UTC in the central plains and around midafternoon in the southeastern United States. Between these regions there is a narrow southwest–northeast transition zone extending from north-central Texas to Indiana, where frequencies have roughly a uniform distribution over the course of the day. Diurnal frequency profiles for 3-h precipitation of ≥0.50 in. in July are shown in Fig. 23c for point G within the central plains maximum, point H in the transition zone, and point I in the southern United States. (See Fig. 22e for the locations of these points.) Note that the central plains location exhibits a strong maximum during 0600–0900 UTC (midnight to early morning), the southern states location has a strong maximum during 2100–0000 UTC (mid to late afternoon), and the “transition-zone” location has a uniform diurnal distribution. While these results closely match the findings in the Winkler study, two points seem noteworthy; they reaffirm the finding of climatic features based on quite different analysis approaches, and they further dramatize the major climatic differences in the diurnal distribution of precipitation for locations with modest separation distances.
d. Summertime coastal effects
The distribution of precipitation during summer near ocean coasts of the United States has long been known to be influenced by land- and sea-breeze circulations (Frank et al. 1967; Cooper et al. 1982; Mass 1982). To illustrate the impact of these coastal circulations on the precipitation frequency distributions in our database, Figs. 24 and 25 show aspects of the summer season spatial and temporal patterns near the Florida panhandle coast. For the category–duration combination of ≥0.10 in. h−1, Figs. 24 and 25a show that a strong frequency peak appears along the immediate coast (point A in Fig. 24) during 1800–1900 UTC, which is consistent with the findings of Schwartz and Bosart (1979) based on detailed analysis of the diurnal distribution of precipitation over the Florida peninsula. For an inland location that is 150 km to the north (point B in Fig. 24), Fig. 25a shows that the corresponding peak occurs about 2 h later. Note further from Fig. 25a that maximum frequencies remain at the inland location from 2100 until 0400 UTC (the late afternoon to early evening). Also, Fig. 25b shows that a similar pattern for the two points appears for very heavy precipitation of ≥1.00 in. per h. Thereafter, maximum frequencies return to the coastal location and remain there until the cycle repeats itself the following day. A similar examination of the frequencies for coastal North Carolina (not shown) revealed a similar sequence of diurnal variations.
The results presented above are consistent with the rational that land- and sea-breeze circulations exert a strong control on the July distribution and intensity of precipitation along the gulf and Atlantic coasts. For instance, the finding that the frequencies are higher at the coast than inland during the period from about midnight to the early afternoon suggests that both the nighttime land breeze and daytime sea breeze contribute to the increased frequencies. These results are consistent with previous findings by Frank et al. (1967), López and Holle (1986), and Reap (1994).
A novel feature in the frequency profiles in Figs. 25a and 25b is that the frequencies are higher at the first inland location (point B) than for a second inland point 150 km farther north (point C in Fig. 24). In particular, note that while the phase of the afternoon frequency peak is almost identical at the two points, its amplitude is substantially higher at point B. (The increased frequencies at point B were not due to spatial smoothing of the raw frequencies, i.e., to northward diffusion of higher values from the coast.) In light of previous studies that show that sea-breeze fronts rarely propagate more than about 100 km inland (e.g., Simpson et al. 1977), the elevated frequencies at point B apparently result from a mechanism not directly related to the sea-breeze circulation. One possibility is low-level convergence along northward bound outflow boundaries that emanate from upstream sea-breeze-instigated thunderstorms (Purdom 1979; Cooper et al. 1982).
Another novel feature that appears in Fig. 25 is that each of the July frequency peaks for ≥1.00 in. lags the corresponding peak for ≥0.10 in. by at least 1 h. One interpretation of this result is that intense afternoon rainstorms along the gulf coast tend to evolve from more moderate storms. This finding contrasts with an analogous comparison of light and heavy precipitation amounts associated with the nocturnal precipitation maximum in the central plains. In the latter case, July peak frequencies for hourly amounts of ≥0.50 in. preceded those for ≥0.10 in. h−1 by about 4 h (not shown). The latter result is consistent with findings from previous studies of the morphology of summertime nocturnal rainstorms in the plains, where the most intense rains were observed early in the life cycle of a rainstorm (Wallace 1975; Kane et al. 1987; Riley et al. 1987; McAnelly and Cotton 1989).
A final possible climatic feature evident in Fig. 25b is the secondary frequency peak for ≥1.00 in. (intense precipitation) at 1000–1100 UTC (dawn) for the Florida panhandle coastal location. It was pointed out to the lead author (W. Junker 1997, personal communication) that such a secondary peak for intense rain has been frequently noted along the Florida east coast over the years by operational HPC forecasters. An examination of our data revealed only weak evidence of the secondary peak for that location. Instead, we found that the secondary peak appeared along the coast from the Florida panhandle to southeast Louisiana and along the coast of North Carolina (not shown). This possible climatic feature should be investigated further in future climatic studies based on longer data samples.
e. Lake effects
Previous studies have shown that the major lakes within the United States have a significant impact on the distribution of precipitation over nearby land areas. For example, Frank et al. (1967) and Michaels et al. (1987) noted a summer afternoon minimum in radar echoes over Lake Okeechobee in Florida due to its stabilizing effects, a small precipitation frequency maximum was analyzed downwind of the Great Salt Lake in winter in the ESSA Climatic Atlas (ESSA 1968), and Eichenlaub (1970), Passarelli and Braham (1981), Braham and Dungey (1984), Hjelmfelt (1990), Reinking et al. (1993), Blechman (1996), and others discussed the enhanced snowfall downwind of the Great Lakes. Here, aspects of the climatic impact of the Great Lakes on precipitation are examined.
The January frequency pattern for ≥0.10 in. during 1200–1800 UTC in the area of the Great Lakes is shown in Fig. 26. Note that frequency maxima appear along the southern shore of Lake Superior1 and along the eastern shores of Lakes Michigan, Erie, and Ontario. The positioning of each of these midwinter peaks is on the downwind side of the adjoining lake with respect to cold westerly or northwesterly flow. Note that peak frequencies for each of these maxima are about twice as large as adjacent background values. These results are consistent with previous observational studies (e.g., Eichenlaub 1970; Wilson 1977; Reinking et al. 1993; Blechman 1996) and with numerical simulation experiments with mesoscale models (Passarelli and Braham 1981; Hjelmfelt 1990; Bates et al. 1993; Reinking et al. 1993). These studies have shown that the lake-effect precipitation enhancement is due largely to the injection of heat and moisture from the relatively warm lake waters during the cool season.
The impact of these lakes as a function of the time of the year is illustrated for Lake Michigan (Fig. 27a) and for Lake Ontario (Fig. 27b) for the 1200–1800 UTC time period. In these figures, the impact is indicated by the difference in the monthly frequencies between the downwind peak and a nearby point upwind of the lake. In Fig. 26, the upwind and downwind locations are points A and B, respectively, for Lake Michigan, and the corresponding points for Lake Ontario are C and D. [Point C is obviously not an upwind location for northerly flow for Lake Ontario, but it was chosen because the observational studies of Reinking et al. (1993) and Blechman (1996) showed a minimum in the seasonal snowfall accumulation at this location, and because a precipitation data void (see Fig. 1) makes the frequency analysis suspect on the western and northern sides of this lake.] The frequency profiles (Fig. 27) show the downwind frequencies during the December–February period are about twice those for the upwind points, reflecting a strong lake enhancement of precipitation during winter. Note also, that for this 6-h morning period an apparent lake enhancement is evident throughout the year, although it is small during midsummer.
It is important to note that the lake effect is not the same in a diurnal sense during the cool and warm seasons. During cool season months, the downwind precipitation enhancement does not vary appreciably as a function of the time of the day (not shown). During the warm season months, on the other hand, the downwind lake impact was found to be reversed between the morning and the afternoon periods. The reversal is illustrated in Fig. 28, which shows July frequency patterns for ≥0.10 in. in the area of the Great Lakes during 1200–1500 UTC (morning) and 2100–0000 UTC (late afternoon). In these figures, the summertime lake effect relative to the prevailing southwesterly low-level flow is unambiguously defined from the network of precipitation data only for Lake Michigan (see Fig. 1). Note that for the morning period (Fig. 28a) the frequency pattern shows distinct maxima along the eastern shore of Lake Michigan. This climatic feature confirms the finding noted earlier from examination of month-to-month frequency profiles for the morning period between upwind and downwind points in the northern part of this lake (Fig. 27a). For the late afternoon period, the frequency pattern exhibits a minimum in the same location (Fig. 28b). The latter finding suggests suppression of summertime convective precipitation during the afternoon that could stem from the absence of boundary layer heating over the lake, a result that corroborates the findings of Wilson (1977), Purdom (1976, 1979), and others based on examination of radar and satellite images. These findings represent the first known quantification of the influence of Lake Michigan on the diurnal distribution of summertime precipitation.
5. Summary and remarks
Monthly relative frequencies for various precipitation categories for 1-, 3-, and 6-h periods were developed on a 20-km grid for the conterminous United States. The frequency fields were initially defined for about 2500 grid boxes (20 km on a side) from precipitation stations composing the U.S. Climatic Hourly Precipitation Network. To produce the monthly frequency data on a 20-km grid with spatial and temporal coherence, objective analysis and smoothing was required. The smoothing was performed spatially over the grid and temporally over consecutive months and consecutive time periods of the day. A major feature of the analysis approach was that the smoothing for each precipitation category and duration was flexible. The flexibility allowed us to minimize the smoothing for each category–duration combination so that the smoothed frequency fields contain the maximum detail the underlying 33-yr precipitation sample would support. The frequency fields contain the highest spatial and temporal detail currently available for a nationwide analysis of this type.
Selected features in the frequency fields were discussed on the basis of suspected precipitation controlling mechanisms and local physiographic features. The forcing functions discussed were orographic effects of mountains during winter, thermodynamic effects resulting from solar heating and cooling of mountains during summer, coastal effects during summer, and year-round lake effects. Also, because of the unique properties of the summertime nocturnal precipitation maximum of the central United States various aspects of its climatic features were discussed.
While the precipitation frequency analysis confirmed many of the larger spatial and temporal climatic features that were known from previous climatological studies, new features or features with improved definition were found at small scales. Examples of the latter include the spatial and temporal evolution of small-scale precipitation frequency maxima over the southern Rocky and Appalachian Mountains during summer afternoons, space–time changes in the summer afternoon Rocky Mountain frequency maxima that accompany their eastward migration to the high plains, the evolution of the summertime nocturnal maximum over the central plains, evidence of a secondary nocturnal maximum over the Texas and Oklahoma panhandles area, evidence of a stationary summertime frequency maximum for light precipitation just southwest of Lake Superior, and a small-scale frequency maximum during the morning and a minimum during the late afternoon downshore of Lake Michigan during summer. Many other interesting small-scale climatic features (some not previously documented) appear in the frequency data over various parts of the United States over the course of the year, but space limitations preclude their discussion in this article.
The climatic frequency dataset was developed for inclusion in a statistically based model that produces high-resolution quantitative precipitation forecasts. However, it is anticipated that the database will be useful for other research and operational forecast applications. The lead author plans to maintain the database and update it as additional data become available. Those with an interest in the database should contact the corresponding author.
Acknowledgments
The authors wish to thank Prof. Julie A. Winkler, Mr. Wes Junker, Dr. Robert A. Maddox, and Robert Kuligowski for their careful reviews of an earlier version of the manuscript, which led to significant improvements to the clarity and organization of the article. Also, the comments of the anonymous reviewers were quite constructive, and they too led to improvements in the clarity of the presentation, strength of the scientific arguments, expansion of the literature citations, and adherence to journal style standards.
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APPENDIX A
Error Checking
To alleviate the likelihood of erroneous data entering into the frequency analysis, various error checks were applied. First, any hourly precipitation report greater than 3.75 in. was rejected outright. It should be noted that if such hourly amounts were in fact true, they would have greater than a 100-yr return period over much of the United States (Frederick et al. 1977). Second, when 3- and 6-h precipitation accumulations exceeded 5.0 and 7.0 in., respectively, and the fractional inch amount for each hour accumulated was zero, the accumulated amount was rejected. This check was intended to eliminate a rare error made during data entry at NCDC as the tenths digit was mistakenly placed in the inch column. Finally, when the 3- and 6-h accumulations passed the second check and the respective accumulated amounts were greater than 6.50 and 9.00 in., the accumulations were rejected. These error criteria were determined empirically; although they might seem stringent to some, they resulted in the removal of about 10 or fewer precipitation measurements per year.
Another step in the removal of erroneous precipitation measurements was the application of bounds on seasonal station precipitation statistics. In particular, over the course of a 6-month warm or cool season the station total accumulated precipitation and the station mean 3- and 6-h relative frequencies of ≥0.10 and ≥0.25 in., respectively, were checked against geographically regionalized bounds. For determination of the error bounds, the 48 states were divided into 32 “climatologically homogeneous” regions, and the error bounds for each were determined from means and standard deviations of the precipitation relative frequencies and accumulations over all stations in a region. When the seasonal precipitation accumulation or relative frequency for a station within the region fell outside the bounds, the station was flagged as possibly having erroneous measurements. The final decision regarding validity of the accumulation or frequency value was based on a subjective judgement. If either statistic was judged invalid, the precipitation data for the station were rejected for the entire season. But, these checks also resulted in very few station rejections—not more than one or two per season.
A third step in the removal of erroneous precipitation measurements from the frequency analysis was a spatial consistency check on the raw station relative frequencies. In particular, the objective analysis scheme for the raw frequencies included an error checking procedure that acted to prevent possibly erroneous frequency values from influencing the analysis. The error checking routine, which is identical to that described by Glahn et al. (1985), is basically composed of two tests. The first test compared the current estimate of the analysis against the raw frequency value at the position of the latter. When the difference exceeded a prespecified value, the raw frequency value was flagged as possibly erroneous. The second test performed a similar comparison at the locations of the two nearest neighboring data points, but with a relaxed allowable difference between the current analysis and the frequency value. When the relaxed difference, which was 50% larger than that for the first check, was not exceeded at either of the neighboring locations, the flagged frequency value was rejected.
The above error checking scheme was applied only once following the first analysis correction pass and was intended to remove “obvious” relative frequency errors. Our experience with this error check was that obvious errors in the raw frequency values were quite scarce, and, in fact, this error detection procedure was unable to isolate any erroneous values for the ≥0.10, ≥0.25, and ≥0.50 in. precipitation categories. The reason is that for these lower precipitation amounts, the relatively rare instances of error in the underlying precipitation data are masked by the vast majority of correct observations. It is only for the rare heavy amounts, that is, ≥1.00, and ≥2.00 in., that a few erroneous precipitation measurements could result in a sufficiently anomalous frequency value that it could be isolated with confidence. Still, the number of rejected frequency values for these upper precipitation categories was rather small. For instance, Table A1, which contains the error criteria for the first check in the scheme together with number of rejected reports for each valid period and precipitation category, shows that only four erroneous monthly relative frequency values were detected for ≥1.00 in., and 20 for ≥2.00 in. In fact, among the total of 24 rejected frequency values, 16 were for the same station, involving the different precipitation categories, durations, or different months. This small set of rejected frequency values is dwarfed in comparison to the million plus frequency values checked for each of these two precipitation categories.
To summarize, the three types of error checks resulted in a rather small number of rejected station precipitation measurements and frequency values. Thus, the error checking effort indicated the precipitation data and the raw frequency values are rather devoid of significant error.
APPENDIX B
Adjustment to the Cressman Analysis Scheme
Charba et al. (1992) found that the adjustment resulted in a significant reduction in analysis error where the data distributions were highly asymmetric. Where the data are randomly distributed, the scheme reverts to the standard Cressman correction scheme. Thus, for the climatic frequency data, the modification contributed an improvement in the analysis where such asymmetry exists, that is, all along the continental borders of the 48 states and around many of the mountain ranges in the western United States.
Network of climatic hourly precipitation stations in existence in 1975. Stations are represented by dots.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Analysis grid indicated by plotted coordinate labels every fourth grid point along the left and bottom edges. The subset of the full 175 × 220 grid composed of 19636 points over the conterminous United States grid is shown. The grid points coincide with centerpoints of square boxes 20 km on a side within which occurrence/nonoccurrence values for the various precipitation categories were specified (see Fig. 3).
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Centerpoints (dots) of square boxes 20 km on a side with one or more precipitation stations during all or part of the period 1963–89. Centerpoints coincide with grid points in Fig. 2.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July mean relative frequency (%) of ≥0.10 in. during 1800–0000 UTC. The line labeled ACB denotes the cross section in Fig. 9a. The values are valid for the centers of 20-km boxes that contained one or more precipitation stations.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
As in Fig. 4 for ≥2.00 in. during 1800–1900 UTC. The line labeled ACB denotes the cross section in Fig. 12a.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Contour map of (a) raw and (b) smoothed gridded relative frequencies (%) of ≥0.10 in. during 1800–0000 UTC for July. Contour interval is 2.5%. The line ACB denotes the cross section in Fig. 9a.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
As in Fig. 6 except for relative frequencies (%) of ≥2.00 in. during 1800–1900 UTC. Contour interval is 0.02% in (a) and 0.01% in (b). The line labeled ACB denotes the cross section in Fig. 12a.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Gridpoint notation of the scalar variable ϕ as a function of the coordinate dimensions s and t.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Relative frequency profiles corresponding to the raw and smoothed frequencies in Fig. 6. The cross section (a) is along ACB in Fig. 6, with the tick marks along the abscissa denoting grid points. The month-to-month (b) and period-to-period (c) profiles apply to point C in Fig. 6. In (c), the period denoted, say, 1218 means 1200–1800 UTC.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July (a) raw and (b) smoothed mean relative frequency (%) for ≥0.10 in. during 1800–1900 UTC. Contour interval is 0.5%. The line ACB corresponds to the cross section in Fig. 11a.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Relative frequency profiles corresponding to the raw and smoothed frequency fields in Fig. 10. The cross section (a) is along ACB in Fig. 10, with the tick marks along the abscissa denoting grid points. The month-to-month (b) and period-to-period (c) profiles apply to point C in Fig. 10. In (c), the period denoted, say, 1213 means 1200–1300 UTC.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Relative frequency profiles corresponding to the raw and smoothed frequency fields in Fig. 7. The cross section (a) is along ACB in Fig. 7, with the tick marks along the abscissa denoting grid points. The month-to-month (b) and period-to-period (c) profiles apply to point C in Fig. 7. In (c), the period denoted, say, 1213 means 1200–1300 UTC.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
January relative frequency (%) for (a) ≥0.10 in. and (b) ≥0.25 in. during 1800–2100 UTC. Contour interval is 2.0% in (a) and 0.5% in (b). Point A specifies the location for the frequency profiles in Fig. 15.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Smoothed terrain height in units of 103 ft (equivalent to 328 m). Contour interval is 1.0 × 103 ft. Point A is the same as in Fig. 13a. The abbreviation CS denotes the Coastal Range, SN the Sierra Nevada, CA the Cascade Mountains, BL the Blue Mountains, WA the Wasatch Range, WI the Windward Range, RM the Rocky Mountains, and SL the Great Salt Lake.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Relative frequency profiles for ≥0.10 in. over consecutive months during 1800–2100 UTC (a) and over consecutive 3-h periods in January (b) for point A in Figs. 13a and 14. In (b), the notation, say, 0912 means 0900–1200 UTC, and the ordinate scale has been magnified over that in (a).
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
January relative frequency (%) of ≥0.25 in. during 1800–2100 UTC. Contour interval is 0.3%. The points A and B denote the locations for the frequency profiles in Fig. 18.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Smoothed terrain height in units of 103 ft (equivalent to 328 m). Contour interval is 1.0 × 103 ft. The points A and B are identical to those in Fig. 16.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Month-to-month relative frequency profiles for ≥0.25 in. during 1800–2100 UTC corresponding to points A (Triple Point) and B (central Tennessee) in Figs. 16 and 17.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July relative frequency (%) of ≥0.10 in. during 2000–2100 UTC. Contour interval is 0.5%. The points A, B, C, and D denote the locations for the frequency profiles in Fig. 21, and point E denotes the location of the Black Hills in western South Dakota.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Smoothed terrain height in units of 103 ft (equivalent to 328 m). Contour interval is 1.0 × 103 ft. The labeled points are identical to those in Fig. 19.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
(a) July relative frequency profiles for ≥0.10 in. over the 1-h periods indicated along the abscissa (e.g., 1213 means 1200–1300 UTC). The labels A, B, C, and D in parentheses in the legend are the same as for the corresponding points in Figs. 19 and 20. (b) As in (a) for month-to-month frequencies for points B and D during 2100–2200 UTC. In the legends of (a) and (b), the state abbreviations are CO, Colorado; NM, New Mexico; and TX, Texas.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July relative frequency (%) for ≥0.10 in. during (a) 2300–0000, (b) 0200–0300, (c) 0500–0600, and (d) 0800–0900 UTC. (e) As in (a)–(d) except for ≥0.50 in. during 0600–0900 UTC. Contour interval is 0.4% in (a)–(d) and 0.2% in (e). The points B, C, and M are referenced in the text and in the frequency profiles in Figs. 23a and 23b. Points G, H, and I in (e) refer to the frequency profiles in Fig. 23c.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
(Continued)
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
(a) July relative frequency profiles for ≥0.10 in. over the 1-h periods indicated along the abscissa (e.g., 1213 means 1200–1300 UTC). The “C” labels in parentheses in the legend refer to corresponding points in Figs. 22a–d. (b) As in (a) for the points C and M in Figs. 22a–d. (c) As in (a) for ≥0.50 in. for the 3-h periods indicated along the abscissa (e.g., 0912 means 0900–1200 UTC). The labels G, H, and I in parentheses in the legend are the same as for the corresponding points in Fig. 22e. In the legends of (a), (b), and (c), the state abbreviations are CO, Colorado; NE, Nebraska; IA, Iowa; KS, Kansas; TX, Texas; OK, Oklahoma; LA, Louisiana; WI, Wisconsin; and MN, Minnesota.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July relative frequency (%) of ≥0.10 in. during 1800–1900 UTC. Contour interval is 0.5%. The points A, B, and C denote the locations for the frequency profiles in Fig. 25.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July relative frequency profiles for (a) ≥0.10 in. and (b) ≥1.00 in. over the 1-h periods indicated along the abscissa (e.g., 1213 means 1200–1300 UTC). The labels A, B, and C in parentheses in the legend are the same as for the corresponding points in Fig. 24. In the legends, the state abbreviations are FL, Florida; AL, Alabama; and GA, Georgia.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
January relative frequency (%) of ≥0.10 in. during 1200–1800 UTC. Contour interval is 2.0%. The points A, B, C, and D denote locations for the frequency profiles in Fig. 27.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Month-to-month relative frequency profiles for ≥0.10 in. during 1200–1800 UTC near (a) Lake Michigan and (b) Lake Ontario. The labels A, B, C, and D in parentheses in the legends are the same as for the corresponding points in Fig. 26.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
July relative frequency (%) for ≥0.10 in. during (a) 1200–1500 UTC and (b) 2100–0000 UTC. The contour interval is 1.0%.
Citation: Weather and Forecasting 13, 1; 10.1175/1520-0434(1998)013<0025:GCMFOP>2.0.CO;2
Equivalent precipitation amounts in units of in. and mm.
Smoothing parameters. The smoothing parameters μ and b are defined in the text, and WPP, WMM, and WSS are centerpoint weights for the period-to-period, month-to-month, and spatial smoothing types, respectively.
Table A1. Raw relative frequency error bounds and number of rejected monthly relative frequency values.