1. Introduction
The windward sides of mountainous islands in the trade wind regime are among the rainiest places on earth, where rains exceed the regional oceanic precipitation by severalfold. Over Hawaii, where nearby oceanic rains are of order 50 cm per annum, favored island locations receive rainfall in excess 500 cm yr−1 (Giambelluca et al. 1986). Quantitative forecasts of this rainfall have proved elusive, despite good knowledge of trade wind layer properties and some of the orographic effects. This study examines the morphology of trade wind rainfall near the island of Hawaii as observed over the ocean and land during a 45-day field program called the Hawaiian Rainband Project (HaRP). A principal objective of our study is to test the island blocking hypothesis of Smolarkeiwicz et al. (1988) with respect to rainfall production and to compare this to the diurnally induced effects. To accomplish this, we have estimated the distribution of rainfall under controlled conditions, where wind speed (U, m s−1) and Brunt–Väisälä frequency (N, s−1) are unconstrained while all other factors associated with the environment are kept as invariant as is practically possible. In so doing, we have evaluated the statistical association of rainfall amount and distribution with the dimensionless island Froude number (Fr = U/Nh), where h is a characteristic mountain height (3300 m) determined by Fourier analysis of the island topography.
HaRP was conducted in the vicinity of Hilo (Fig. 1) during the summer of 1990, a period during which cumulative rainfall was close to the climatological average for July and August. The availability of more than 300 h of CP-4 Doppler radar data, more than 100 h of Electra research aircraft data, and the National Center for Atmospheric Research’s (NCAR) portable automated mesonet (PAM) allowed relatively complete documentation of rainfall patterns and related circulations at the mesoscale (Smith and Grubišić 1993; Chen and Nash 1994; Chen and Wang 1994; Carbone et al. 1995; Chen and Wang 1995; Wang and Chen 1995; Raymond and Lewis 1995; Austin et al. 1996).
Hawaiian rainfall has been studied for decades, including some landmark investigations by Leopold (1949), Leopold et al. (1951), Blanchard (1953), Lavoie (1967), Garrett (1980), Takahashi (1977), and Takahashi et al. (1989). These investigators and others have documented diurnal variations on the island including sea or land breezes, orographic rainfall, windward ocean rainbands, mountain-valley effects, the evolution of warm raindrop size distributions, and instances of convection much deeper than the trade wind layer. The principal emphasis of these studies was on the thermal forcing effects of the island, consistent with the pronounced diurnal cycle that is observed in rainfall, wind direction, and temperature near Hilo.
Rainfall over the island during HaRP was first examined by Chen and Nash (1994, hereafter referred to as CN). Their analyses revealed the variation in rainfall with respect to topography, phase of the diurnal cycle, wind speed, static stability, and other factors. Among other findings, CN (their Fig. 13) showed a steady eastward progression of rainfall from afternoon over the slopes west of Hilo to the windward coast later at night. They also showed that this progression of rainfall is statistically associated with a reversed (westerly) flow that propagates downslope and offshore. Carbone et al. (1995, hereafter referred to as CCL) examined the forcing of this flow reversal and found evidence of both evaporative and radiative cooling as operative mechanisms in the evolving westerly flow. They concluded that modest amounts of rainfall evaporation were most commonly associated with the initiation of westerly flow, and that radiative cooling maintained and strengthened the flow from evening until sunrise. Case studies analyzed by Wang and Chen (1995, hereafter referred to as WC) were consistent with CCL’s interpretations.
A series of numerical simulations by Smolarkiewicz et al. (1988, hereafter referred to as SRC) and related observations by Rasmussen et al. (1989) supported the argument that island blocking of the mean trade wind flow is principally responsible for the forcing of rainbands. They argued that this dynamical effect, in a low Fr regime, is dominant over thermally driven circulations—such as land breeze–trade wind interactions—that had been identified previously by Leopold, Lavoie, and others. The results of the Clark model simulations led to a fundamental shift in thinking about rainfall production over windward Hawaii, given that previous investigators had incorporated only vague notions of blocked flow in their conceptual models.
Since the trade wind inversion is usually near 2-km altitude, the island is typically immersed in a two-layer fluid, where the upper layer is potentially warm, dry, and hydrostatically stable. The lower (trade wind) layer is below the characteristic height of the island and it possesses small conditional instability (1–100 J kg−1). During HaRP, U and N each varied by about a factor of 2, from 5 to 11 m s−1 and from 0.006 to 0.012 s−1, respectively. Here Fr varied from 0.17 to 0.41 with a mean of 0.25. These low values suggest that the kinetic energy of the mean flow, in the absence of island thermal effects, is insufficient for flow over the mountain (Smolarkiewicz and Rotunno 1990). Table 1 provides estimates of Fr for the considered subset of HaRP days, as calculated by means of mass-weighted layer averages, from upstream soundings between the surface and the trade wind inversion base.
To determine the distribution of rainfall during trade wind conditions, and to quantify any dependence of its amount and distribution on the environment, requires rainfall estimation procedures that are similarly applicable over land and sea as well as a standard definition of “environment” that is not heavily influenced by the island itself. To satisfy the first of these requirements we rely on relative rainfall estimates that are derived from radar reflectivity data. These relative rainfall amounts are crudely “calibrated” by other data, such as rain gauge measurements and analyses thereof, and climatologies that are applicable to the island and the eastern North Pacific. The second requirement is satisfied by research aircraft soundings that were obtained approximately 100 km upstream east-northeast (ENE) of Hawaii, a distance presumed to be beyond the major blocking effects of the island. Our approach is a statistical/dynamical one, documenting the distribution of precipitation for those 19 days over a 35-day period when both radar data and upstream soundings are available, and the criteria that permit a test of the island-blocking hypothesis are satisfied.
Under trade wind conditions, rainfall production may exhibit sensitivity to many factors, most of which are not directly related to Fr. Among these are the trade wind layer depth, vertical distribution of humidity, convective available potential energy (CAPE), horizontal vorticity, capacity for negative buoyancy production, intrinsic spatial and temporal variability of thermodynamic properties, cloud condensation nucleii distribution, and others. On occasion, anomalously deep layers may become conditionally unstable near Hawaii, resulting in much deeper convection and even thunderstorms. Easterly waves, tropical cyclones, and precipitation associated with baroclinic waves in winter also account for part of the Hawaiian rainfall variance. It follows that only a fraction of the daily rainfall variance observed near windward Hawaii might be explained by dynamical blocking criteria as embodied in Fr.
Section 2 provides a brief description of data, data selection criteria, and analysis procedures. Since flow reversal and the position of a flow separation convergence line are prominent features in the composite rainfall patterns herein, we discuss the morphology of this circulation in section 3. The 19-day “climatology” of rainfall together with a dynamically based stratification of rainfall amount and distribution are discussed in section 4. These data are spatially and temporally integrated in section 5 to provide cumulative precipitation distribution results. A discussion of these findings is given in section 6 together with concluding remarks.
2. Data selection and data analysis procedures
a. Research aircraft data
Soundings of temperature, humidity, and winds were routinely acquired approximately 100 km upstream from Hilo by the NCAR Electra aircraft at the beginning of each flight. A total of 29 flights were made during HaRP in support of studies on both the windward and leeward sides of the island. Aircraft data were also used to detect mesoscale offshore reversals of flow from easterly to westerly winds. These detections were automated and then objectively and subjectively tested to satisfy basic spatial continuity criteria to reduce confusion with smaller-scale reversals caused by the proximity of active convection. Flow reversal tests were applied to all flight legs in the windward domain at or below 150-m altitude.
b. Selection of days for the rainfall time series
Twenty-two upstream soundings were used on 19 days when the CP-4 radar at Hilo airport was operational for at least 6 h and several qualifying criteria were simultaneously satisfied as follows.
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Mean wind direction was consistently between 050° and 100°.
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Trade wind inversion base was between 1.4 and 2.8 km mean sea level (MSL).
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There existed a level of free convection with small CAPE in the trade wind layer [1 < CAPE < 100 J kg−1].
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Cloud depth was 1 km or greater.
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Some morning rainband(s) exhibited some degree of island symmetry.
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Some orographic showers occurred over the windward slope in the afternoon.
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The principal organization of precipitation echoes was not suggestive of “disturbed” or highly unsteady conditions.
A total of 19 out of 23 possible days qualify for our time series. All eight days that have 24-h radar observations fully satisfy our criteria and these days are the basis for the major conclusions herein related to the variance of rainfall associated with Fr. Four of 15 partial (radar coverage) days failed to satisfy one or more of the criteria. The nonqualifying days are 19 July (criterion 2), 20 July (criteria 1, 2, 5, 7), and 24 July and 16 August (criterion 3). All but one of the days with partial radar coverage observe the morning rainband period 0430–1030 (1430–2030 UTC), thereby limiting the application of these data to improvement of the statistics during this phase of the diurnal cycle.
c. Radar data and the rainfall estimation technique
Reflectivity data, Z (mm6 m−3), are used to calculate the relative distribution of rainfall. Radial velocity data (m s−1) are a primary source of information to detect westerly flow reversals. Figure 1 illustrates a rainband echo just east of the island. Rainbands are typically quite cellular and often the cells are small, from 0.5 to 3 km in diameter. Tiny cores (<0.5 km) often exceed 50 dBZe (Szumowski et al. 1997, 1998) and instantaneous rainfall rates occasionally reach 100 mm h−1. Cells are usually short lived (about one overturning cycle) although some may exhibit greater longevity when located on the quasi-stationary flow separation line. Rainband motion toward the island is usually indistinguishable from the trade wind speed but quasi-stationary rainbands can maintain position at the flow separation line, through regeneration of successive cells, for up to 2–3-h duration.
The rectilinear pattern superimposed on Fig. 1 shows the computational domain that was used for quantitative application of radar data in this study. The domain is 100 km in length along the nominal trade wind direction of 70° and 40 km across. It extends roughly 70 km ENE offshore (+70) and 30 km WSW onshore (−30) with Hilo airport and the NCAR CP-4 radar located at (0, 0). The domain is divided into 20 slabs of 5-km width, each comprising a 200 km2 area. We have processed approximately 300 h of radar data in this fashion to depict the life cycle of coherent precipitation structures as a function of distance from Hawaii’s windward shore. Instantaneous rainfall rate is linearly averaged over each 200 km2 slab (Fig. 1). Typically, radar volume scans are performed on a 15-min cycle, or about 90–100 samples per day. The terrain 15–30 km west of Hilo requires sampling at 4.5° elevation over the 2.5° mountain incline. Over the ocean, data at 2.5° elevation are used out to 40-km range, and data at 0.5° elevation are used beyond 40 km. A consequence of this approach is that most of the domain is sampled within a few hundred meters of 1 km MSL. The entire dataset has been composited to formulate a two-dimensional “climatology” of precipitation as a function of distance from the windward shore and phase of the diurnal cycle. This is accomplished through arithmetic averaging of all samples in 1-h time bins and in the 20 slabs composing the computational domain.
The compilation of rainfall statistics is based on averages of relative rainfall calculated in each slab assuming the power-law dependence Z ∝ R1.5. Battan (1973) reviews relationships between Z and rainfall rate, R (mm h−1), for warm rain showers. From the numerous relations cited therein and elsewhere, the power-law dependence is commonly observed to range between 1.4 and 1.7, with many values close to 1.5. Our assumption of 1.5 is not critical to the success of this study, but it provides a transformation which, to a first approximation, linearizes the output with respect to rainfall. To achieve the major objectives of this study, it is unnecessary to independently derive a multiplicative constant between Z and R.
The spatially and temporally integrated relative radar rainfall distributions were normalized to the available climatological rainfall data and HaRP rain gauge data, so that we could report these results in physical units of rainfall as opposed to a nondimensional presentation. The normalization procedure made use of regional oceanic climatology as well as data from selected rain gauges (Fig. 1) on the windward side of Hawaii. Five estimates of rainfall, expressed below as annual rates, were obtained or calculated:
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Oceanic climatologies (Trewartha 1954; Riehl 1954; Pettersen 1958) 30–60 cm yr−1
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Hilo July–August climatology (NOAA 1988) 285 cm yr−1
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The CN analysis of the 45-day PAM dataset in slab 0 292 cm yr−1
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Rainfall at four coastal PAM stations for this 19-day time series 212 cm yr−1.
d. Relative radar-rainfall estimate biases
While it is reassuring that we can infer plausible amounts of rain both over the ocean and over the coastal plain with one transformation, the reader should be mindful of possible biases in our relative results. Potential sources of bias include partial or complete radar beam blockage by structures or vegetation, reflectivity underestimates that can increase with range due to beam broadening and increased beam axis altitude, and spatial and temporal variability of the drop-size distribution. Trial rainfall integrations indicated significant beam blockage in the 5–35-km slabs over the ocean at 0.5° elevation and over most inland areas at 0.5° and 2.5°. The blockage at 0.5° would have resulted in a significant underestimation of rainfall (50% or more). In our production processing of radar data, we were able to minimize blockage effects by selecting the lowest unblocked elevation angle for each slab (as noted earlier). Furthermore, the angles and ranges at which we are able to minimize beam blockage, with small exceptions, retain the property of sampling well below the tops of typical trade wind showers (2.0 km).
The transition between 2.5° and 0.5° elevation at 40-km range was objectively determined based on the maximum average echo strength at this range. The rainfall estimates from both angles near 40-km range are similar and data from both elevation angles indicate a substantially similar horizontal gradient zone of rainfall in this region.
The effect of beam broadening is akin to applying a low-pass Gaussian filter to the reflectivity data (and hence rainfall rates). The filter size increases linearly with range (a 1° beam has diameters of 0.175 and 1.22 km at ranges of 10 and 70 km, respectively). To estimate the magnitude of this effect, we simulated the beam filtering process by resampling rainband data, originally from 7 to 10 km offshore, as if these were located up to 70 km offshore with a 1° Gaussian beam. While individual pixels of rainfall decreased by as much as 30% or more at the most distant range, the decrease in integrated rainfall was only 5%. This apparent bias is insignificant when compared to the shore-relative rainfall differences shown in Fig. 2.
The drop-size distribution is expected to exhibit large spatial and temporal variability. Given that we have restricted the dataset to shallow, warm cumulus between 1.5- and 2.7-km depth, this variability should average out because of the extensive spatial and temporal integration process employed herein. However, over the higher terrain, beginning about 10–15 km west of CP-4, the drop-size distribution may be systematically different since the altitude of cloud base often increases with terrain height. The effect could be such that we underestimate the integrated rainfall relative to the lowland and oceanic areas, since reduced cloud depth can result in a narrower drop-size distribution (hence lowering the coefficient in a Z–R relation). A comparison of the cumulative 19-day rainfall at PAM station 10 (located at −13 km) with our oceanic-based normalization revealed only a 6% underestimate. Given that we have approximately 30% uncertainty inherent to absolute rainfall amounts over the domain as a whole, it is not possible to detect a statistically significant relative bias at −13 km.
e. Presentation of data
The principal format for display and analysis of data is a Hovmöller-type diagram (e.g., Fig. 4), which is commonly used in climate diagnostics. This type of presentation collapses one spatial dimension of structure in favor of a time/direction-of-propagation depiction of phenomena. Our distance coordinate is distance upstream (ENE) from shore, where “shore” is defined as the slab containing the CP-4 radar (Fig. 1). In Hovmöller format, it is especially easy to detect coherent structures, such as rainbands propagating shoreward from the ocean, and to determine where these amplify and decay most regularly. Since Hawaiian circulations are markedly diurnal in character, the diurnal cycle is readily depicted in this format. To minimize confusion pertaining to diurnal relationships, we will depart from the standard use of UTC time and employ Hawaiian Standard Time (HST), where HST = UTC-10. The dates provided on diagrams correspond to the date at sunrise HST, which is also the UTC date. This can be a source of confusion because our presentation of diurnal cycle begins at roughly 1400 HST of date (n − 1)—that is, 0000 UTC of date n.
3. Flow reversal and the evening transition
The prevailing surface wind at Hilo is westerly 12 months of the year (NOAA 1988). CCL, CN, WC, SRC, and others have shown that a shallow westerly flow develops over the windward island during the afternoon or early evening and it persists until sunrise or afterward. When an island-induced westerly flow exists, there will be a line along which the flow is strongly confluent with the prevailing easterly trade wind. Both the position and structure of this flow separation line (FSL) are intrinsic to the forcing of windward island rainfall. First we examine this statistically, and then we present the 3 August example of flow reversal and convection to illustrate some physical mechanisms at work.
a. FSL statistics and comparison with theory
Figure 3 illustrates the position of the FSL for all 19 days in this dataset. These observations are made by PAM stations over land (left of the dashed line) and by the CP-4 Doppler velocity and/or the Electra aircraft over water. The criteria for the occurrence of flow reversal are sustained changes (∼10 h) in the sign of u (zonal wind) that lead to mesoscale (>30 km) regions of reversed flow. With aircraft measurements alone, it was not always possible to confirm the dimensions of offshore reversals nor was it possible in some instances to fully confirm longevity; however, it was rare for reversals to be detected by aircraft without spatial and temporal confirmation from the CP-4 radar. Figure 3 reveals a strongly diurnal pattern of flow reversals, where flow is usually easterly everywhere between 1000 and 1600, and where the FSL is quasi-stationary, 5–20 km offshore, between 0400 and 0900 the next morning. These two periods are presumed to represent the radiative/dynamical daytime and nocturnal equilibria.
It is evident from Fig. 3 that there exists a strong asymmetry between the morning and evening transition periods. The morning transition is swift. It typically transpires within an hour or two between 0700 and 1000 with the earliest reversals often occurring over higher terrain (CN). Based upon PAM station virtual temperature fields (CN, CCL, WC) and idealized simulations of thermally forced low Fr conditions (Reisner and Smolarkiewicz 1994), the rapidity of this transition may be attributed to solar heating of the island. Evening flow reversal over the windward lowlands may occur early (1400) or late (2100). In contrast to the morning transition, the evening transition is protracted, often spanning a period of 6–12 h. The slowness of this transition may be attributed, in part, to cloudiness (a nonoptimal infrared radiative condition) below 2-km altitude (CN, CCL). In each instance of observed island flow reversal, there exists a buoyancy deficit (virtual temperature depression) near the time and place of its occurrence, even when the origin of reversal is before sunset (CCL, WC). Propagation of the FSL is usually slow (0.5–1.0 m s−1, from Fig. 3) when averaged over the event lifetime, but flow reversals can occur quickly and at diverse locations over the island in the afternoon or evening. Recent numerical simulations by some of the authors herein are able to reproduce the observed flow reversal with considerable accuracy, especially in those instances where thermal forcing is purely radiative (e.g., 14 August).
CCL concluded that reversed flow is essentially thermally driven over the windward lowlands, and they speculated that there is an increasing dynamical influence offshore where the pressure gradient is presumed strong and buoyancy forces tend to decrease. It is possible to estimate, by aircraft and Doppler radar, the slowing (Δu/Δx) of the easterlies in late afternoon when island thermal forcing is weak. If the pressure gradient is quasi-steady, this deceleration should be opposite in sign and similar in magnitude to positive forcing of the westerlies, just a few hours later, when the island is also acting as a heat sink. Data to support this evaluation are sparse because late afternoon is a period of minimum aircraft flight activity, and there are few radar echoes offshore. On 7, 8, and 9 August, the available data consistently show Δu/Δx ≈ 2 × 10−4 s−1, which accounts for a 4 m s−1 slowing of the easterlies in the 20 km nearest shore. These data suggest that pressure gradient forcing of the offshore westerlies may be similar in magnitude to the buoyancy forcing in that region. Further study of the three-dimensional flow in this offshore region is required to assess the balance of buoyancy versus pressure forces.
Figure 3 illustrates the systematic difference in position of the FSL near sunrise under ordinary and elevated (>0.3) Fr number conditions. The FSL is 5–10 km closer to shore when Fr is elevated. This difference may be attributed, all or in part, to the blocking interpretations given by SRC and Smolarkiewicz and Rotunno (1990), and to the retardation of gravity currents in opposing mean flow. An additional factor in this balance of forces is the role of banded convection, which can regulate gravity current properties by means of convectively generated heat sources and sinks.
b. Case of 3 August
The rainfall pattern for 3 August is shown in Hovmöller format (Fig. 4) depicting the distribution as a function of time and distance from the island’s windward shore. The FSL position is also indicated as in Fig. 3. Rainfall contours represent approximate rates averaged over 200 km2 where the maxima are approximately 3 mm h−1. Areally averaged rates <0.1 mm h−1 are not shown. Flow reversal occurs west of Hilo at 1720 and expands upslope and downslope in the usual manner (CN, CCL), reaching the coastline shortly before midnight. Significant evening rainfall appears near the FSL shortly after the occurrence of first flow reversal (Fig. 4). Moderate rainfall persists over land until after midnight as the FSL progresses 10 km offshore. Shortly before midnight oceanic rainfall, as described by Austin et al. (1996), begins to enter the island domain and initially dissipates before reaching the island. Subsequent episodes of oceanic rainfall amplify in the upstream domain and these are coincident with an uncharacteristically chaotic behavior of the FSL between 12 and 27 km offshore. Amidst the succession of vigorous offshore rainbands, we speculate that FSL position is intermittently thrust eastward by convective-scale cold pool production. The morning return of easterly winds first occurs over high terrain at 0800 and soon thereafter over the ocean. Offshore rainfall activity rapidly dissipates after termination of the FSL and late morning orographic showers develop over the windward mountainside.
The plan view of radar echoes during early rainband evolution on 3 August (Fig. 5) reveals a well-defined sequence of events beginning with weak orographic showers over 400-m terrain west of Hilo (Fig. 5a). The origin of sustained flow reversal (1720) is first detected at PAM station 15, soon after a buoyancy reversal (CCL), under the band of afternoon orographic showers. Decreased solar heating in late afternoon permits subcloud evaporative cooling to reverse the buoyancy field, thereby reversing the flow to the downslope direction (CCL). In the sequence of panels (Fig. 5), one sees the serial dissipation of rainbands and subsequent regeneration of new rainbands slightly eastward as the reversed flow propagates down slope. While this slow eastward propagation occurs, cloud and radar echo motion is westward, owing to the easterly steering winds just above the surface. Animation of this sequence with radar scans at 15-min intervals reveals several generations of rainbands over land during the long and slow evening transition. By 2146 (Fig. 5c), evening convection has strongly intensified in association with the propagation of a more mature gravity current. By 0200 (Fig. 5d), the FSL is significantly offshore, and develops a bowlike structure east of Hilo. The event depicted in Fig. 5 exemplifies the Hilo precipitation climatology as characterized by CN and the longer-term climate record at Hilo.
Figures 6a and 6b are vertical cross sections of radar reflectivity and Doppler velocity, respectively, looking west from CP-4 at the time of Fig. 5c. The reflectivity pattern suggests that a dynamically active rainband is positioned over the head of a gravity current and a developing cell (aloft) is over the nose. A dissipating rainband is centered 6 km farther to the west. The gravity current kinematic structure, as revealed by the Doppler velocity field, is outlined by the “green” (westerly) flow hugging the mountainside. It possesses the characteristic head, nose, and body structure universal to atmospheric gravity currents as often reported in the literature over the past 30 yr. A surge (deepening) feature is observed rearward of the head, owing to the increased source of cooled air from the dissipating rainband. Such surges of cooler air were often observed at PAM stations in time series analyzed by CCL and WC. Some four hours later, we observe the evolution of this gravity current (Figs. 6c and 6d) coincident in time with Fig. 5d. The body and head of this gravity current are now fully developed and have progressed more than 5 km over the windward ocean (10 km east of CP-4). The head is 700 m deep and the body depth varies between 200 and 600 m. The buoyancy deficit (from PAM stations and the Hilo sounding) is estimated to exceed 1% (CCL) thereby easily overtaking the relatively weak easterly winds just offshore (Fig. 6d). The sequence (right to left) of developing, mature, and dissipating showers in relation to the nose, head, and body of the gravity current, respectively, is apparent and qualitatively similar to the earlier mountainside process. On 3 August, the positive feedback loop between gravity current propagation, convection initiation, the sedimentation and evaporation of raindrops behind the FSL, as well as the background eastward-directed pressure gradient, permits this circulation to propagate as far offshore as any westerly winds that were observed during HaRP.
4. Composited and stratified data
a. 19-day composite rainfall
The 19-day composite rainfall (Fig. 7) reveals characteristics similar to those exhibited on 3 August. Light rain is evident over the island from late morning through midafternoon. Flow reversal occurs over the island sometime between 1500 and 2000. Over the windward slopes, increased raininess begins at 1800, 1 h before local sunset, and the forcing envelope associated with the FSL progresses toward the coastal plain at a rate of about 1 m s−1. The FSL propagates offshore by midnight with the heaviest average rains (>1 mm h−1) occurring shortly thereafter (0100–0400). According to these data, Hilo should experience more rain between 2200 and midnight than any other period. This is in agreement with long-term climatology and the findings of CN for the 45-day HaRP rainfall analysis. The FSL reaches a quasi-stationary position nominally 15 km offshore just before sunrise and usually maintains that position from 0500 to 0900. There is a rainfall maximum 10–15-km offshore during this period, but average rainfall rate is markedly reduced from the preceding period.
Rainfall from the open ocean enters the domain after midnight and it exhibits space–time coherence with some of the heaviest rain on the island about 3 h later. This slope corresponds to a 7 m s−1 advection speed, which is slightly slower than the average upstream trade wind speed of 7.9 m s−1. These upstream rainfall data seem to confirm some of the conclusions of Austin et al. (1996) concerning a diurnal rainfall cycle over the open ocean and the modulation of island rainfall. Little rainfall entered our domain from the open ocean except at night. Austin et al. speculate that this may be due to nocturnal radiative destabilization of trade wind stratocumulus. Our examination of the literature finds longstanding support for this hypothesis (e.g., Kraus 1963) and more recent supporting data with respect to marine stratocumulus (Betts et al. 1995).
Somewhat more difficult to discern in Fig. 7 is a secondary maximum of rainfall amplification which occurs approximately 30 km upstream (25–45 km) of the FSL between 2000 and 0500. From examination of several individual cases, we are confident that this feature is not a statistical artifice, but rather a systematic upstream divergence feature. Figure 8 (9 August) is one of several examples of this phenomenon.
b. Ordinary versus elevated Fr days
The 19-day dataset is naturally stratified into four“elevated” Fr days and 15 “ordinary” Fr days. These populations are statistically different, with ordinary days averaging Fr = 0.23 ± 0.03 (extrema of 0.17 and 0.27) and elevated Fr days averaging 0.35 (extrema from 0.31 to 0.41). Figure 9, representing the large majority of days, exhibits nearly all the characteristics previously described for the 19-day composite. One major difference is markedly reduced rainfall in the coastal zone from 0800 to 1300 where areally averaged rates are generally <0.4 mm h−1. Another difference is that offshore rainbands around sunrise nearly always dissipate before reaching shore, while retaining a well-defined maximum 10–15 km offshore.
Elevated Fr days exhibit much more rainfall over the island (Fig. 10) where areally averaged rates peak over 2.5 mm h−1. As with ordinary Fr days, a similar diurnal cycle prevails. Flow reversal occurs over the windward slopes between 1500 and 2200 and the FSL propagates offshore by midnight. As previously shown in Fig. 3, the FSL establishes a quasi-stationary position before sunrise 5–10 km closer to shore, qualitatively as predicted by SRC and Smolarkeiwicz and Rotunno (1990). This is a significant factor with respect to rainfall experienced in the coastal zone, since offshore rainbands are not in such an advanced stage of dissipation upon landfall. Furthermore, the FSL (and heavy rainfall) usually returns to shore around sunrise as opposed to the 2–4-h lag that is observed when Fr is ordinary. The secondary zone of upstream forcing between 25 and 45 km is also evident in Fig. 10, as is the nocturnal arrival of oceanic rainfall from beyond the domain.
5. Domain rainfall integrations
It is evident from the diagrams in sections 3 and 4 that there are systematic variations in rainfall as functions of distance from the windward shore, phase in the diurnal cycle, and island Fr. In this section we will present temporal integrations to examine mean rainfall rate as a function of distance from the island; distance integrations to examine total domain rainfall by phase of the diurnal cycle; and stratifications and integrations of data to examine sensitivity to Fr and its component variables, U and N.
a. Rainfall as function of distance upstream
1) Forcing zones and mechanisms
Rainfall equivalent, normalized to an annual rate (cm yr−1), and as a function of distance upstream is given in Fig. 2. We distinguish three forcing zones:
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“oceanic” background zone (>50 km),
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“upstream” divergence zone (20–45 km), and
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“reversal” zone (<20 km).
The upstream divergence zone, as its name connotes, is a region immediately upstream from the FSL and within which the effects of island blocking seem to be experienced. The net effect of upstream divergence is to more than double the estimated oceanic rainfall rate from 40 cm yr−1 to about 100 cm yr−1. We know from the Hovmöller diagrams that upstream rainfall amplification often maintains a relatively fixed distance of 20–30 km from the FSL, whereas both the FSL and this zone propagate eastward at night. Preliminary studies of airflow 40–50 km from shore (Lee and Johnson 1991;Johnson and Lee 1993) found strong deformation in the upstream region, but their examples do not reveal deformation to the extent that flow becomes shore-parallel (NNW). Based on outlier FSL data points from 22 July (Fig. 3, 1600–1800) and other analyses of NNW flow near the shore (CN), it is speculated that the upstream zone may sometimes be characterized by a very high rate of deformation that can lead to NNW flow south of the stagnation streamline (a reversal of sorts) and with it, an enhanced convergence zone.
Within about 20 km from shore, the island produces a reversed westerly flow by means of thermal and dynamical forcing. From the Doppler data, we know that the two-dimensional confluence magnitude across the FSL is of order 10−2 s−1 over a layer 100–500 m deep, thereby associated with ascent of roughly 1–3 m s−1. Such strong forcing leads to an average maximum rainfall rate in the reversal zone of nearly 300 cm yr−1 for the 19-day period. From the evidence presented in section 3, and that previously by CN, CCL, and WC, it would appear that gravity current dynamics are applicable during the 11–16-h period when reversed flow is present and precipitation rate is maximized. During this period, the dynamical and thermal forcing processes are fully cooperative. Blocking accelerates westerly flow, landward nocturnal radiation forces air downslope, and the FSL-initiated precipitation falls west of the FSL further cooling the reversed flow through evaporation (CCL). These factors can create a self-sustaining feedback loop until solar heating overcomes them about 2 h after sunrise. The reversal zone extends from the rain forest west of Hilo to approximately 20 km offshore, with a nocturnal eastward progression, the rate of which is governed by the delicate balance among these forcings.
2) Rainfall sensitivity to Fr, U, N
The apparent sensitivity of rainfall amount to Fr is quite strong, as illustrated in Fig. 11. Elevated Fr days average 540 cm yr−1 equivalent rainfall rate over the coastal lowlands (−5), whereas ordinary Fr days average less than 150 cm yr−1. Some increase is suggested in the oceanic background, but this pales in comparison to Fr sensitivity near the island. We note that a similar form of rainfall distribution appears in each stratification. The principal effect of elevated Fr is to increase rainfall.
We have examined the sensitivity of rainfall to increased U and 1/N (decreased static stability) to determine if increased rainfall is primarily associated with one component variable or another. This was accomplished through stratification of the five highest wind speed days (three of which have elevated Fr) and the four least stratified days (two of which have elevated Fr). The results (Fig. 12) suggest an association with both wind speed and static stability, but neither as strong individually as elevated Fr. The distribution of rainfall for days with decreased stability shows a shift westward in the island maximum, but no tendency toward increased rainfall over the background ocean. The distribution for high wind speed shows increased rainfall over the ocean (relative to the 19-day dataset) and a slight shift eastward in the island maximum. We speculate that increased rainfall over the open ocean is physically plausible given increased latent heat fluxes and the shorter time required to “recharge” the marine boundary layer with water vapor (Raymond 1995).
Owing to small sample populations in the aforementioned stratifications, and the uncertain statistical significance of differences among curves in Fig. 12, we have performed linear regressions on estimated rainfall amounts in four island zones for the eight days during which there were 24-h radar operations. This is a unique subset of data for which partial-day normalization procedures are not required, and to which 24-h cumulative rainfall regressions can be applied. The mean Fr for this group is 0.26 and the extrema are 0.19 and 0.41. Figure 13 shows total rainfall for each day, as ordered by Fr, U, and 1/N (from left to right), and by distance zone (from top to bottom). By inspection of Fig. 13, it can be seen that rainfall correlation with Fr over the island (−25 to 0) and near shore (0 to 20) is near unity, with island rainfall increasing 10-fold when Fr increases from 0.2 to 0.4. Beyond the reversal zone, correlation with Fr diminishes sharply from near unity to 0.6. Over the oceanic zone (>50 km) this apparent dependence may be a consequence of one rainy day, 8 August. A strong correlation exists between rainfall and U over land and near shore, but the strength of the dependency (slope of the regression) is diminished from that obtained with Fr. Correlation with U beyond the reversal zone is sharply reduced (0.5) but significantly positive. Correlation between rainfall and static stability is poor in all zones and, near the island, retains a positive sign because of one rainy day, 8 August.
Rainfall for the entire computational domain can be further examined for sensitivity to Fr from the composites of ordinary Fr and elevated Fr groups. The 19-day composite data are in substantial agreement, with rainfall increasing by a factor of 2.4 when Fr increases from 0.23 to 0.35. Because of the rather small sample size, we caution readers not to attach too much significance to the strength of these associations nor to their potential prognostic value, since many other factors can modulate convection.
3) Rainfall near sunrise
Cumulative rainfall for the 6-h period, from 0430 to 1030, constitutes only 18.7% of all rain in the coastal zone (Fig. 1 slab encompassing Hilo, distance = −5 km), or 75% of the average rate (Fig. 14). For the 15 ordinary Fr days the rainfall is 40% of average, an estimated 19 cm yr−1 rate, or 7.5% of all rain in Hilo for these 19 days. However, for the four elevated Fr days, the estimated rainfall rate is 115 cm yr−1, which is 180% of the average and accounts for 28.5 cm of rain or 11.2% of Hilo’s average precipitation. Note from Fig. 14 that rainfall is relatively heavy 10–25 km offshore on ordinary Fr days. This is the range of positions normally associated with the FSL and amplification of convection. The rainbands are nearly always dissipated by the time they reach shore, except when Fr is elevated. A number of factors contribute to the latter behavior. When Fr is elevated, the FSL is 5–10 km closer to shore; higher wind speed transports the bands onshore faster (while dissipation is in progress); a greater fraction of rainband residence time is over land; and the rainbands are stronger.
For reasons discussed in section 1, we did not anticipate that Fr could account for most of the day-to-day variance in island rainfall as suggested by Fig. 13. In an effort to expand the sample size to the maximum extent possible, we have also examined Fr correlation with rainfall from all days for the period 0430–1030 (Fig. 15). While a pattern similar to Fig. 13 is apparent, the regression yields a reduced correlation (0.80) and an increased estimate of uncertainty. The period around sunrise is one during which the thermal forcing of the island is at a diurnal maximum and thus might diminish the relative strength of dynamical influences. Farther from the island (not shown), the Fr correlation drops precipitously to 0.18, perhaps consistent with the dominance of thermal forcing at this phase of the diurnal cycle.
b. Diurnal variation
The HaRP premise was that the landfall of rainbands near sunrise is an important component of precipitation in Hilo. While this is less significant than originally thought, it is apparent from earlier diagrams that rainfall is strongly modulated by the diurnal cycle. Figure 16 quantifies the diurnal variation of rainfall, integrated over the entire domain, for days with 24-h observations, elevated Fr days, and ordinary Fr days. Qualitatively these are similar, with marked nocturnal maxima at 0400 (ordinary), 0300 (24-h observation days), and 0100 (elevated), and a daytime minimum near 1200. The amplitude of this diurnal variation greatly exceeds one order of magnitude (600:20) when Fr is elevated, and this remains large, roughly 180:30, when Fr is ordinary. There is a systematic phase displacement of this diurnal variation with Fr, as evidenced by the trend toward an earlier rainfall maximum with increased Fr in the ordinary, 24-h, and elevated groups. This trend suggests either a smaller rainfall phase lag when Fr is elevated or, alternatively, an increased phase lead. The diurnal variations seem to result, in part, from the island’s own forcings of flow reversal, the positive feedback loop among these, and from increased nocturnal rainfall over the open ocean as described by Austin et al. (1996). Each of the factors appears to be important, but these are not easily separable.
6. Discussion and conclusions
We have estimated the temporal and spatial variations of rainfall over the windward side of Hawaii and over the adjacent windward ocean. These estimates were accomplished through application of a transformation function (1.5 power) to the radar reflectivity data. Based on expected amounts of rainfall from climatologies and independent rainfall observations, we attributed absolute rainfall amounts to the relative rainfall estimates mostly to avoid a nondimensional presentation of the data. According to our estimate, actual rainfall could have deviated from the amounts shown herein by as much as 30%. An inference resulting from the latter procedure is that the drop-size distribution is generally poorly developed in shallow trade wind clouds, thereby lending a “heavy drizzle” character to the rain similar to that observed by Blanchard (1953). We draw this conclusion in full awareness of large drops near the top of updrafts in some Hawaiian clouds (e.g., Beard et al. 1986; Szumowski et al. 1998). These are not contradictory findings, since the former is the consequence of integration over all space and time, dominated by small average rainfall rates, whereas the latter is observed in small regions of stronger updrafts for relatively brief periods of time (Szumowski et al. 1998).
Estimated rainfall amounts appear to asymptotically approach oceanic background beyond 50 km from shore. Oceanic rainfall climatologies, derived from a limited database, vary between 1.0 and 1.6 mm day−1. Somewhat arbitrarily, but influenced by independent rain gauge measurements on the island, we have set our oceanic background at 1.1 mm day−1 or 40 cm yr−1. This may be an underestimate on an annual basis, but it fits our 19 days of observation in midsummer reasonably well.
These data reveal that a strong diurnal cycle of rainfall, although mostly driven by nocturnal cooperation between the thermal and dynamical forcings of the island, is also influenced by increased oceanic raininess at night. Factors in the diurnal cycle strongly influence both the amount and distribution of rain within the windward domain. Total domain-scale rainfall reaches a peak at roughly 0300 HST, whereas the maximum average rainfall rate at Hilo occurs during a period of several hours duration around midnight. Heavy rainfall is associated with showers, usually organized in bands, that are initiated or amplified by a confluent flow separation line that propagates eastward through the windward lowlands. The cumulative evidence presented herein and by Carbone et al. (1991), CCL, WC, and CN suggests that the mature westerly branch of flow is a 200–300-m-deep gravity current with about 1% buoyancy deficit that propagates slowly eastward into an easterly “headwind” of similar magnitude. Most of the rain in the windward coastal plain falls during this period of evening thermal transition. Once the flow separation line propagates offshore, the increased pressure gradient forcing of the westerlies appears to become comparable in magnitude to the buoyancy forcing, thus leading to a hybrid buoyancy/pressure-driven circulation. The flow separation line achieves a quasi-stationary condition near sunrise, maintaining a fixed position, typically 15 km offshore, for a period of four or more hours. During this period heavy rain may occur offshore, but the rainfall over land as well as that over the entire computational domain is diminished. Rainfall dips to a sharp diurnal minimum by late morning when solar heating eliminates the source of cool air and, not long thereafter, the convergence associated with the flow separation line. This morning transition is relatively swift and very dry compared to the agonizingly slow and wet evening transition. The diurnal asymmetry is likely to be a consequence of nonoptimal infrared radiative cooling conditions in the evening and faster shortwave heating in the morning, but additional research is required to quantify this aspect. The transition periods are separated by the afternoon orographic regime and the morning equilibrium previously described.
Statistically, the strongest result of this study concerns the association of rainfall amount with Fr as defined by SRC. Average total domain-scale rainfall increases by a factor of 2.4 when average Fr increases from 0.23 to 0.35. Furthermore, equivalent rainfall rate over the coastal lowlands increases even more sharply, from 150 cm yr−1 to 540 cm yr−1. Oceanic background rainfall is weakly associated with Fr, but rainfall seems to increase with trade wind speed, a component variable of Fr. There are relatively small but significant shifts in the location of rainfall event amplifications associated with Fr variation. Convection is usually amplified at the flow separation line, the position of which seems relatively insensitive to Fr for most of the diurnal cycle, except in the hours around sunrise when rain is predominantly offshore under ordinary Fr conditions. During this 4-h period only, the flow separation line is nearly 10 km closer to shore when Fr is elevated (Fig. 3), thus contributing to the occurrence of substantial coastal rains.
It was discovered that a secondary “upstream” divergence zone exists, often maintaining a position 20–30 km upstream from the flow separation line. This zone, which may be a consequence of blocking dynamics, is associated with a doubling of the oceanic rainfall between 20 and 45 km offshore. The detailed mechanisms underlying the secondary upstream divergence zone are not understood, but we take note of its coherent eastward propagation with the FSL during the evening/nocturnal transition. In some instances the flow in this region can be shore-parallel—that is, from the NNW (south of the stagnation streamline) when the trade wind is northeasterly. This direction of flow suggests that strong deformation has taken place in the upstream zone.
In conclusion, we have established a strong statistical association of Hawaiian rainfall with the island Froude number, an idea first advanced by SRC. This association is principally related to the amount of rainfall in the windward domain and not the location of the rainfall maximum. The relationship between total domain-scale rainfall and island Froude number is approximately linear. A much larger fraction of total rainfall is deposited on the windward lowlands when Fr is elevated, but the position of maximum rainfall is nearly invariant for all Fr <0.4. The principal factors determining the location and timing of island-induced rainfall are thought to be thermal effects as part of the diurnal cycle, including infrared radiative cooling and evaporative cooling resulting from orographic rainfall. Domain-scale rainfall is maximized over the windward lowlands when a flow separation line propagates eastward during the sequence of evening cooling processes. The strong tendency for oceanic rainfall to be nocturnal also influences the temporal distribution in favor of increased nighttime rain as observed by Austin et al. (1996).
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Windward Hawaii and the computational domain. An example of an offshore rainband is shown for 3 August 1990. The CP-4 radar and selected PAM station locations are also shown. CP-4 is defined as distance = 0 km in the distance-offshore coordinate.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Distribution of cumulative rainfall as a function of distance offshore. The approximate shoreline is given by the thin dashed line. The forcing zones, delineated by the thick dashed lines, are described in section 5.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Positions, relative to shore, of flow reversals as a function of time and Fr. Reversal data over land are from PAM stations. Reversal data over water are from radar Doppler velocity data and low-level aircraft observations. Outlying points near (40, 17) are from 22 July when a zone of shore-parallel flow (NNW) prevailed well beyond the typical WSW offshore flow. The region inside the backward “C” contains westerly flow. With exceptions, between 1000 and 1600, flow is easterly everywhere.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Hovmöller-type depiction of rainfall and FSL data for 3 August 1990. Area-averaged rainfall rates are given in the legend. Chaotic behavior of the FSL around 0600 is very unusual.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Plan view of rainband radar echoes on 3 August over land and their subsequent propagation toward shore. Dots show locations of PAM stations used to identify flow reversals and buoyancy deficits in CCL. The origin of flow reversal on this day is at station 15, under the orographic showers at 1720 (a).
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Two RHI (vertical) radar scans: upper panels depict the region west of Hilo approximately at the time of Fig. 5c (2151). Reflectivity (a) shows showers at various locations with respect to the gravity current (b) delineated by approaching Doppler velocities (green) near the lower bound of data on the mountainside. Lower panels: (c,d) same as upper pair but looking eastward near the time of Fig. 5d (0152), 4 h later. Note the well-developed gravity current and the relationship of developing and dissipating showers to the gravity current kinematics.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Hovmöller presentation of the 19-day composite rainfall dataset and FSL data.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Example of diurnal variation on 9 August 1990. Note weak rainfall amplification in a line from (25, 1600) to (50, 0800). This parallels the FSL position, ∼30 km landward.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Same as Fig. 7 but for ordinary (<0.28) Fr days.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Same as Fig. 7 but for elevated (>0.3) Fr days.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Rainfall as function of distance from shore for elevated Fr (0.35), all days (Fr = 0.25), and ordinary Fr (0.23). Note strong dependence near the island.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Rainfall dependence for days with elevated Fr, high wind speed (U), and reduced static stability (1/N). All rainfall amounts over the island are markedly above average.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Linear regressions of rainfall vs Fr, U, and 1/N for four zones 1) Island, 2) Near Shore, 3) Upstream, and 4) Ocean. Zones 1 and 2 form the “reversal zone” described earlier. The numbers in upper-left corners of each panel are correlation coefficients. Note high correlations for Fr and U in the reversal zone and the strength of dependency for Fr rainfall over the island. Apparent dependency of rainfall on 1/N illustrated in Fig. 12 is shown to be of questionable significance.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Cumulative rainfall in the hours around sunrise (0430–1030). Note strong dependence on Fr for both location and amount of rainfall. Under ordinary Fr conditions, morning rainbands grow and die offshore.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Linear regression for rainfall over the island (0 to −25 km) vs Fr (as in Fig. 13) for the period around sunrise (1430–2030). Offshore, the correlation drops sharply to 0.18.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Cumulative domain-scale rainfall as a function of phase in the diurnal cycle. All maxima are nocturnal, but elevated Fr seems to peak earlier in the cycle, whereas ordinary Fr peaks later.
Citation: Monthly Weather Review 126, 11; 10.1175/1520-0493(1998)126<2847:TWRNTW>2.0.CO;2
Daily average Froude numbers calculated from upstream aircraft soundings during July and August 1990.