Investigating the Effects of Orography and Ambient Wind on Deep Convection over Tropical Islands

Frank Robinson Department of Chemistry and Physics, Sacred Heart University, Fairfield, Connecticut

Search for other papers by Frank Robinson in
Current site
Google Scholar
PubMed
Close
,
Daniel J. Kirshbaum Atmospheric and Oceanic Sciences, McGill University, Montreal, Quebec, Canada

Search for other papers by Daniel J. Kirshbaum in
Current site
Google Scholar
PubMed
Close
,
Steven C. Sherwood Climate Change Research Center, University of New South Wales, Sydney, New South Wales, Australia

Search for other papers by Steven C. Sherwood in
Current site
Google Scholar
PubMed
Close
,
Lucinda Cahill The Fu Foundation School of Engineering and Applied Science, Columbia University, New York, New York

Search for other papers by Lucinda Cahill in
Current site
Google Scholar
PubMed
Close
,
Erica Juliano Department of Mathematics, Sacred Heart University, Fairfield, Connecticut

Search for other papers by Erica Juliano in
Current site
Google Scholar
PubMed
Close
, and
Chuntao Liu Department of Physical and Environmental Sciences, Texas A&M University at Corpus Christi, Corpus Christi, Texas

Search for other papers by Chuntao Liu in
Current site
Google Scholar
PubMed
Close
Open access

Abstract

Using an observation–model synthesis, we investigate variations of cumulus convection over islands with varying characteristics and under varying environmental conditions to clarify controls on convective vigor. In this paper, we define the intensity of deep convection as the average 40-dBZ-radar echo-top height or 85-GHz brightness temperature among raining precipitation features having 40-dBZ echoes (RPF40s) and the frequency of deep convection as the fraction of RPF40s to the total number of precipitation features. Examination of the Tropical Rainfall Measuring Mission (TRMM) satellite database (1994–2015) of 272 tropical and subtropical islands reveals a modest weakening of convective intensity with increased terrain height h or ambient wind U (for a given island area A) and a strengthening with increasing A. Quasi-idealized, convection-permitting simulations broadly reproduce these sensitivities to h and A, but not that to U. In both observations and simulations, intensity increases with the island-averaged convective available potential energy (CAPE). Because CAPE generally decreases over taller islands that protrude deeper into the free troposphere, convective intensity varies inversely with h. The frequency increases with the total island area over which both large CAPE and strong near-surface horizontal convergence coincide. This trend favors higher frequencies over larger islands with complex (but shallow) terrain. The model’s inability to reproduce the observed decrease of convective intensity with U stems from a negative observed correlation between CAPE and U that was neglected in the simulations. Thus, as with h, the negative observed trend between intensity and U ultimately stems from the impacts of CAPE on convective intensity.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Frank Robinson, robinsonf3@sacredheart.edu

Abstract

Using an observation–model synthesis, we investigate variations of cumulus convection over islands with varying characteristics and under varying environmental conditions to clarify controls on convective vigor. In this paper, we define the intensity of deep convection as the average 40-dBZ-radar echo-top height or 85-GHz brightness temperature among raining precipitation features having 40-dBZ echoes (RPF40s) and the frequency of deep convection as the fraction of RPF40s to the total number of precipitation features. Examination of the Tropical Rainfall Measuring Mission (TRMM) satellite database (1994–2015) of 272 tropical and subtropical islands reveals a modest weakening of convective intensity with increased terrain height h or ambient wind U (for a given island area A) and a strengthening with increasing A. Quasi-idealized, convection-permitting simulations broadly reproduce these sensitivities to h and A, but not that to U. In both observations and simulations, intensity increases with the island-averaged convective available potential energy (CAPE). Because CAPE generally decreases over taller islands that protrude deeper into the free troposphere, convective intensity varies inversely with h. The frequency increases with the total island area over which both large CAPE and strong near-surface horizontal convergence coincide. This trend favors higher frequencies over larger islands with complex (but shallow) terrain. The model’s inability to reproduce the observed decrease of convective intensity with U stems from a negative observed correlation between CAPE and U that was neglected in the simulations. Thus, as with h, the negative observed trend between intensity and U ultimately stems from the impacts of CAPE on convective intensity.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Frank Robinson, robinsonf3@sacredheart.edu

1. Introduction

The understanding and prediction of atmospheric deep convection remains incomplete due to the inherent complexity of related processes and difficulties in fully observing it. In a very basic sense, the formation of a cumulonimbus cloud requires a conditionally or potentially unstable atmosphere and sufficient low-level moisture and lifting to bring air parcels to their level of free convection. Upon cloud formation, the complications multiply, as numerous factors like environmental wind shear, entrainment and detrainment, and cloud microphysics (viz., precipitation and ice formation) determine the depth, intensity, and organization of the resulting cumuli (Markowski and Richardson 2011). As an additional complication, the prediction of moist convection is challenged by the highly nonlinear and chaotic nature of convection itself. The strong sensitivity of cloud development to small changes in environmental conditions and/or low-level circulations, which themselves are generally uncertain, render the life cycles of individual storm cells extremely difficult to predict (e.g., Surcel et al. 2015).

Among the variety of approaches that have been followed to improve the understanding and prediction of deep convection, one involves focusing on observational and/or numerical analyses of convective hotspots—places where cumulonimbi frequently develop. Such hotspots are found where conditionally unstable air masses and robust mechanisms of low-level lifting coincide. These include subtropical and tropical islands (e.g., Qian 2008; Smith et al. 2009; Sobel et al. 2011; Zhu et al. 2021), which are regularly exposed to moist, conditionally unstable air masses and provide robust ascent from diurnal thermal circulations and/or forced orographic lifting. These islands serve as excellent natural laboratories for convection, and studies have targeted them for observational case study analysis (e.g., Wang and Kirshbaum 2015; Barthlott et al. 2016) and intensive field campaigns (e.g., Smith et al. 2012).

Statistical analysis of many deep convection events over diverse subtropical and/or tropical islands can yield newfound insights into the sensitivity of these clouds to environmental and topographic factors. For example, such analyses have successfully shown that larger islands tend to exhibit more intense thunderstorms than smaller islands (Robinson et al. 2011), a trend that has been explored through detailed theoretical and modeling studies (Robinson et al. 2008; Cronin et al. 2015; Wang and Sobel 2017). The ability of a relatively simple numerical modeling framework to capture an observed trend can help narrow down the possible explanations for the trend. Thus, climatological analysis over many storm hotspots, in conjunction with reduced-complexity modeling frameworks, helps continue building and refining the conceptual understanding of cumulus convection in general.

Along with conditional instability and island area, two other prominent factors affecting island convective intensity are terrain height and ambient wind speed. Over unheated mountains where the island forcing is purely mechanical, wind speed partially controls the orographic flow “regime,” which, at least according to dry dynamical solutions, may be roughly assessed by the nondimensional mountain height (M = Nh/U, where h is the mountain height, N is the buoyancy frequency, and U is the wind speed) (Smith 1989). For M ≪ 1, the dynamics resemble linear mountain-wave solutions (e.g., Durran 1990), where the low-level air ascends the barrier and vertically propagating mountain waves form above it. In such cases, the forced lifting, and hence the resulting moist convection, tends to strengthen with both h and U (Nicolas and Boos 2022). In contrast, for M1, the low-level flow tends to split and detour around the island, and the mountain wave breaks over the crest or lee slope, sometimes forming a hydraulic jump. In these cases, convection may form in converging regions well upstream or downstream of the mountaintop or not at all, and the sensitivities to h and U may greatly differ from linear predictions.

Thermal forcing, in the form of diurnal surface heating and cooling, also determines orographic flow dynamics (e.g., Nugent et al. 2014). Under weak winds and/or large island sizes and surface heating rates, thermal forcing is maximized and drives up-mountain flow (e.g., Kirshbaum 2013). Upslope flows from different sides of the mountain converge near, or just downstream of, the crest to force strong ascent and moisture convergence, as moist low-level air sourced from nearby valleys is transported upward. In conditionally unstable flow, this combination is highly favorable for thunderstorm development. In contrast, stronger background winds over narrower islands may ventilate the anomalous island warmth downwind to weaken the impact of island heating on the flow dynamics. Kirshbaum (2017) developed two nondimensional parameters, one similar to M for the mechanical flow regime and the other related to the thermal flow regime, to form a 2D regime diagram for diurnally heated orographic flows.

Linear theory suggests that thermally forced boundary layer circulations should intensify as h increases and U decreases, a combination that produces the largest local baroclinicity (e.g., Kirshbaum 2013). Given that ambient winds also tend to limit the buildup of locally enhanced moist instability over the island, taller islands with weaker winds may thus be expected to exhibit the most intense moist convection. However, as with its mechanically forced counterpart, thermally forced convection does not always conform to linear theory (e.g., Kirshbaum and Wang 2014). Specifically, convective intensity over taller islands may be limited by a lack of background midtropospheric moisture supply. Although up-mountain flows may transport moist air up to the high terrain, this effect may be partially to fully balanced by the drying effects of vertical mixing with the overlying free troposphere. Thus, the effects of h on thermally forced island convection remain unclear.

No physical theory currently accounts for the many complexities inherent to island flows on the dry flow dynamics, let alone the response of moist convection to these processes. Such complexities include, to name a few, the effects of flow blocking at large h and U, nonlinear interactions between mechanical and thermal flow responses, and the feedbacks of spatiotemporally intermittent latent heat release (like that associated with moist convection) on the flow dynamics. Thus, conceptual understanding of the dynamic factors regulating island convection remains limited.

To address these limitations and better constrain local environmental controls on convective activity, we build on the framework of Robinson et al. (2011) to study the impacts of h and U on island convection. We carry out this inquiry through a synthesis of satellite observations and convection-permitting numerical simulations. We also distinguish between circumstances that promote the occurrence of relatively strong convection (e.g., cumulus congestus or stronger) from those that regulate its intensity, using an intensity threshold to distinguish between stronger and weaker convection. Section 2 describes the observational data and numerical model, and section 3 describes the analysis of the observations and corresponding simulations. Section 4 explains the physical origins of the main trends, section 5 discusses the importance of terrain complexity in the simulated trends, and section 6 presents the conclusions.

2. Data and models

a. Observations (TRMM)

To observationally characterize storm properties, we use data from the Tropical Rainfall Measuring Mission (TRMM) satellite. TRMM is a nongeosynchronous weather satellite with orbit inclination of 35° that launched in November 1997 with the purpose of measuring rainfall and energy exchange in tropical and subtropical regions (Kummerow et al. 1998). It is equipped with the TRMM Microwave Imager (TMI; for total precipitation rates), [TRMM] precipitation radar (PR; for vertical distribution of precipitation-sized particles), Visible and Infrared Scanner (VIRS; for temperature and peak altitude of clouds), and Lightning Imaging Sensor (LIS; Kummerow et al. 1998).

In this study, we specifically make use of the University of Utah precipitation feature database (Liu et al. 2008). This database contains so-called raining precipitation features (RPFs) defined by grouping contiguous areas with TRMM PR–derived nonzero rainfall (Iguchi et al. 2000). These RPFs contain a maximum radar reflectivity of 20 dBZ or greater. Any objects that exceed 40 dBZ are denoted as RPF40s. Due to the precession of the TRMM orbit, it does not generally return to the location of a precipitation feature for at least another 24 h, so the RPFs reported mostly correspond to unique storms.

Here, we focus on the maximum RPF40 height (Z40max) and the minimum 85-GHz polarization-corrected temperature (PCT85min) (Spencer et al. 1989) seen by the TMI. Previous studies have found these quantities to be useful proxies for convective intensity (e.g., Zipser et al. 2006). The 40-dBZ echo is an indicator of very strong updrafts (Liu and Zipser 2015) and often does not occur at all in a precipitation feature. The brightness temperature PCT85min indicates the altitude at which large precipitation-sized water masses were encountered [e.g., hail diameters above 20 mm (Cecil 2009)]. Lower cloud tops have higher PCT85min and are associated with weaker storms (Mohr and Zipser 1996).

This TRMM-based database also provides a thermodynamic sounding, 1–3-km layer-averaged wind speed, convective inhibition (CIN), and CAPE for each RPF, taken from the nearest grid point in the 6-hourly, 0.75° × 0.75° resolution ERA-Interim reanalysis data. These soundings will be used to characterize convective environments and provide inputs for numerical modeling.

The islands selected for this study all have a horizontal aspect ratio smaller than three (to focus on more axisymmetric shapes) and are distant from the nearest continent by at least 5 times their effective radius (the latter is defined as A/π, where A is the island area). Based on these criteria, we retained 272 islands between 35°S and 35°N (Fig. 1). These islands include all those used by Williams and Stanfill (2002) and Robinson et al. (2011). They range in area from 1.5 km2 (Lisianski Island, Hawaii) to 743 330 km2 (Borneo, Indonesia).

Fig. 1.
Fig. 1.

Islands in TRMM dataset.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

To link RPFs to specific islands, a distance d was calculated between the RPF and the island center (IC), as
d=111km(θICθRPF)2+cosθIC(ϕICϕRPF)2,
where θICandϕIC and θRPF and ϕRPF are the latitude and longitude of the island center and RPF centroid, respectively. The 111-km coefficient is the conversion factor from degrees to kilometers (1° ≈ 111 km on Earth’s surface at the equator). An RPF was selected if d was less than twice the island effective radius. This approach is different from the more labor-intensive technique used in Robinson et al. (2011), where polygons were manually drawn around each individual island and the RPFs within the island polygon were associated with that island. We have confirmed that the different methods produce very similar results (not shown).

Note that the above analysis associates RPFs with islands even if the islands were not responsible for the RPFs. Depending on the regional climate of each island, some fractions of its RPFs are associated with mobile, larger-scale systems that happen to cross the island and may not be strongly affected by it. In contrast, this study seeks to understand how island geometry influences storm intensity. Thus, some of the relevant observed trends may be weakened by the contributions of larger-scale systems to climatology.

b. Numerical simulations

To complement the TRMM RPF analysis, we use the Weather Research and Forecasting (WRF) Model, version 4.2.2 (Skamarock et al. 2008). The simulations are idealized in that the initial state is horizontally homogeneous and the terrain and time-varying surface fluxes are all prescribed. However, as will be seen, these parameters are strongly constrained by observations where possible.

The computational domain is 400 km in each horizontal direction (x and y) and 25 km in the vertical (z), with periodic lateral and rigid vertical boundaries and Rayleigh damping over the uppermost 5 km. The horizontal grid spacing is 2 km (we do not parameterize shallow convection), and the vertical grid spacing varies from 60 m at the surface to 1.3 km at the model top (150 levels). The Coriolis parameter, f, is set to zero in all the simulations. To seed convective motions, random initial perturbations of maximum amplitude 1.5 K were added to the potential temperature field between 1 and 3 km above the surface. Parameterized physics include the Yonsei University (YSU) planetary boundary scheme (Hong et al. 2006), 3D turbulent mixing using a 1.5-order turbulent kinetic energy (TKE) scheme, land and ocean surface drag, and the most recent Thompson (double-moment ice) cloud microphysics scheme (Thompson et al. 2008).

Prescribed surface sensible and latent heat fluxes were applied only over land, both varying sinusoidally in time starting from zero to a maximum at 6 h and back to zero at 12 h (i.e., the model integration time is 12 h). Because surface energy balance observations are not available from the TRMM RPF database and are generally poorly constrained by observations, we conducted simulations with a range of surface heating amplitudes, with the sensible and latent heat fluxes ranging between 0 and 200 W m−2 in different suites. Since the Bowen ratio varies widely over the TRMM island domain, we set it to unity for simplicity. The possible consequences of this simplification have not been explored in this study.

Moreover, to examine the effects of environmental thermodynamic conditions on the island convection, we used three different composite soundings extracted over the largest TRMM island, Borneo (which had by far the largest number of precipitation features in the TRMM database). The soundings were computed by averaging over all the Borneo soundings that had surface-based convective available potential energies (CAPEs) from 0 to 220 J kg−1 (low CAPE or LCAPE), 100–400 J kg−1 (medium CAPE or MCAPE), and 750–1500 J kg−1 (high CAPE or HCAPE). The resultant soundings had CAPEs of 170 J kg−1 (LCAPE), 325 J kg−1 (MCAPE), and 1050 J kg−1 (HCAPE). To test the effect of an ocean versus a land-based sounding, we ran an additional suite of simulations for a sounding that was averaged over soundings from RPFs offshore of Borneo so that the coincident sounding was over water (MCAPE200W-OS).

The simulated terrain fields are based primarily on the big island of Hawaii (HI), the largest of the Hawaiian archipelago (Fig. 2). HI was chosen based on its relatively large size and axisymmetry, combined with the presence of smaller-scale ridges and valleys that provide realistically complex surface forcing. To avoid reaching any highly specific conclusions applying to HI alone, we also conduct simulations over a very differently shaped Hawaiian island—Oahu—with its area rescaled to match that of HI. In contrast to the more axisymmetric HI with very tall terrain, Oahu is more irregular with two smaller ridges on the western and eastern sides and a saddle in between. To modify the island peak height, we rescaled the actual height of Hawaii by a factor h/Hp, where Hp is the peak height of Hawaii and h is the simulation peak height. Although we use Hawaiian terrain for the majority of the simulations, this study in no way is meant to be specific to Hawaii. Rather, Hawaii was chosen simply as a real-world terrain, which avoids any unphysical symmetries that might be found on an arbitrary idealized island. Therefore, the results from these simulations should not be compared to real-world convection over Hawaii or interpreted as representative of Hawaii.

Fig. 2.
Fig. 2.

Maps of terrain height and areal coverage of HI and Oahu (inset) (m).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

Each suite of simulations is defined by a combination of initial sounding, surface forcing (Table 1), and island area (A). The latter was varied by scaling the reference area (that of HI) by a coefficient of 0.5 (half island) or unity (full island). Within each suite, the island terrain height and ambient wind speeds are systematically varied over realistic ranges. In the TRMM database, 98% of the islands had peak heights below 3 km and 90% of RPFs had associated 0–6-km average wind speeds below 9 m s−1. Consequently, the range of h and U explored within each suite is 0–3 km and 0–8 m s−1, respectively. For simplicity, the simulated winds are initially uniform in height and oriented purely westerly. To test the effect of wind direction, which can be important (e.g., Van Nguyen et al. 2010), we ran an additional suite of simulations with a uniform northeasterly wind over Hawaii (MCAPE200W-NE).

Table 1.

Combinations of initial CAPE and surface heat flux amplitudes for each suite of simulations. The surface Bowen ratio is unity, so these values correspond to both sensible and latent heat flux amplitudes.

Table 1.

As the emphasis of this study is the effect of height and wind speed on convection, we did not examine in detail how different island shapes affect convection (even though there are a large variety of shapes within the islands), instead holding this constant. Other than changing the area of Hawaii by a factor of 0.5 or modifying the wind direction in one simulation suite, neither did we look in detail at the variation with island area nor other aspects such as wind direction (which is only meaningful relative to a particular island geography) or vertical wind shear. To limit the paper length and computational requirements, this study is restricted to two control parameters (h and U). Variation of convection with island area has already been the subject of two previous studies, Robinson et al. (2011) and Cronin et al. (2015), both of which found a general increase in convective intensity with island area.

c. Comparing satellite and model data

To compare WRF and TRMM on equal footing, we use the Satellite Data Simulator Unit (SDSU), version 2 (Masunaga et al. 2010), as a forward model to compute the radar reflectivity and brightness temperatures from the WRF data [as in Robinson et al. (2011)]. The simulator computed Z40max and PCT85min every 5 min over each of the 12-h WRF simulations. Following the same procedure used for TRMM, any 12-h averages were computed only over RPFs with radar reflectivities reaching 40 dBZ or greater.

1) Averaging over TRMM islands

Of the 272 islands selected for the TRMM analysis, we found that 12 did not have any 40-dBZ echoes detected by the TRMM satellite. These were excluded from the subsequent analysis, leaving 260 islands in total. The remaining islands were sorted into four area bins with 60–71 islands in each bin. The area bins, 0–69 (TRMM1), 70–259 (TRMM2), 260–999 (TRMM3), and 1000+ (TRMM4) km2, were then subdivided into height (maximum surface elevation) bins with around 10–20 islands per area-height bin. Each island had a number of detected TRMM RPFs, with each RPF having a Z40max and a PCT85min.

Two ways of computing the TRMM averages in different island height (h) bins are (i) to organize all RPFs into h bins and then average over all RPFs in each bin or (ii) to find the average RPF value over each island (called the island average) and then find the average of the island averages in a given h range. The first approach gives much more weight to islands with more RPF40s, whereas the second weights all islands equally (i.e., one average per island) as long as they meet a sampling criterion. We compared results using the different approaches and found that the overall trends were largely unaffected by the choice of averaging method (not shown). As we wish to obtain general results not overly influenced by details of a few particular islands, we use the second method henceforth.

Similarly, to compute the TRMM averages (for each area bin) versus the 1–3-km layer-averaged U, we compared (i) averaging over all the RPFs in each U bin and (ii) averaging over all the U bins for each island and then averaging over all the islands. Once again, both methods produced similar results and will use the second method henceforth.

2) Convection metrics

The average Z40max and PCT85min over RPF40s represent two alternate measures of “strong” convective intensity for an island. In addition, we evaluate each island’s strong convective frequency as the fraction of RPF40s to RPFs. Thus, the frequency relates to the fraction of precipitating features that reach a strength threshold, and the intensity is the mean strength of all such features. Henceforth, the terms “intensity” or “frequency” always refer to strong convective events with reflectivities exceeding 40 dBZ (i.e., RPF40s).

3. Results

a. TRMM analysis

1) Variation with island dimensions

Figure 3 shows the variation of the two intensity metrics with island height and area in the TRMM data, averaged over 24 h (Figs. 3a and 3b) and between 1000 and 1800 local time [LT (Figs. 3d,e)]. The latter loosely represents the daytime period, which will be used for comparison against WRF results. The error bars were computed as σsz/N, where σsz is the standard deviation of all island averages of that area bin (across all heights) and N is the number of islands in the specific area-height bin. This was done to obtain a more accurate estimate of σsz, which did not exhibit strong dependence on island height. This method of computing the error bars assumes that the RPFs in each area bin are independent.

Fig. 3.
Fig. 3.

Variation with island area and terrain height of convective metrics averaged over (a)–(c) 24 h and (d)–(f) from 1000 to 1800 LT: intensity measured via (a),(d) Z40max; (b),(e) PCT85min; and (c),(f) frequency. The number of islands in each area-height bin is given in the top inset box; at least five islands were required for a point to be included in the plot. The error bar for each bin represents the standard error (1-σ uncertainty), taking the number of islands as the sample size. Note that the vertical axes in (b) and (e) have been flipped to show a decrease in intensity with height.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

A general reduction of intensity with h is found for both measures. For the two largest area bins, intensity starts to increase again with height for the last 1–3 height bins, but it remains lower than for h < 700 m. The intensity also generally increases with increasing A, consistent with Robinson et al. (2011). Since PCT85min and Z40max show similar intensity trends, we henceforth focus on the latter metric for brevity.

Frequency also generally decreases with h, but the trend is not as clear as that for intensity (Figs. 3c,f). The frequency is similar for the two largest area bins but is about 50% lower than the two smallest bins. Even though RPFs are observed over the whole 24-h diurnal cycle, both the intensity and frequency are higher in the afternoon (Figs. 3d–f) compared to the full-day average (Figs. 3a–c). This daytime convection is more likely to be associated with island heating than convection occurring at other times of day (such as mobile systems entering from outside the island’s domain). As will be seen, the only WRF simulations that generate strong convection (exceeding 40 dBZ) are those with diurnal surface heat fluxes. For this reason, the simulations will be compared to TRMM data from 1000 to 1800 LT. Nevertheless, the trends of interest herein are not strongly affected by this choice (e.g., compare Fig. 3a vs Fig. 3d).

Based on a separate analysis of TRMM data, Sobel et al. (2011) found that precipitation tended to increase with island height but intensity did not. The latter is consistent with the present TRMM analysis, which suggests that, in general, taller islands exhibit weaker convection than shorter ones of the same horizontal area. This finding sharply contrasts that of other studies suggesting increased convective precipitation over taller islands (e.g., Kirshbaum and Smith 2009; Nicolas and Boos 2022).

2) Diurnal variation

The diurnal cycle of RPF occurrence for all the islands exhibits a primary maximum in the midafternoon (1500 LT), a secondary maximum in the early morning (0400 LT), and two minima in the late morning (1000 LT) and evening (2100 LT) (Fig. 4). This trend applies to both RPFs (blue bars) and RPF40s (red bars). The frequency over all islands can be roughly estimated as the ratio of the red to the blue bars, which is about 0.3 at 0000 LT and reaches a peak of around 0.4 at 1500 LT.

Fig. 4.
Fig. 4.

Number of RPFs vs LT of day. The upper (blue) bars show RPFs, while the lower (red) bars show RPF40s.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

Although a diurnal cycle is evident, its variations are superimposed on even larger baseline values. For the RPFs, the diurnal peak-to-trough variation (≈3 × 104 entries) is only about 30% of the mean value (≈7.5 × 104 entries). This fraction increases to around 50% for the stronger RPF40 events. Thus, while diurnal heating is associated with increased storm occurrence during the afternoon, many storms occur at other times of the day. From this finding, we infer that many of the RPFs are associated with larger-scale maritime disturbances that are not driven by diurnal heating.

b. Model comparison

In the highly idealized setup of our WRF simulations (section 2b), mobile precipitation systems originating over the upstream ocean are absent. Hence, the only forcing for convection arises from the island itself: thermal circulations driven by surface heating and/or mechanical lifting over complex terrain. However, the analysis in the previous section suggests that a major fraction of the TRMM-observed storms originate offshore. Our methodology effectively assumes that any systematic trends in storm properties with island geometry or wind speed must arise from local forcing, i.e., that variations in the properties or number of arriving storms among the islands are uncorrelated with island properties or wind speed. The independence of island properties appears quite reasonable, but independence from wind speed is a stronger assumption.

With this caveat in mind, we evaluate whether the variation of intensity and frequency with h, U, and A obtained from the TRMM data can be, at least qualitatively, reproduced by our WRF experiments. As the full idealized Hawaii island (area of 10 000 km2) falls into area bin 4, we compare the set of full-area simulations over Hawaii with the results for TRMM area bin 4.

To illustrate the general evolution of the idealized simulations, Fig. 5 shows the time series of the maximum heights of the 20-dBZ (RPFs) and 40-dBZ echoes (RPF40s) for four simulations from the LCAPE60W suite with differing h and U. In these cases, precipitation starts almost immediately after model initialization due to the mechanical forcing of the background winds over the island terrain, but no RPF40s (signaling the onset of deep convection) develop until near the peak of diurnal heating at around 5–6 h. From these plots, the intensity may be diagnosed as the average height of the RPF40s (large circles) and the frequency from the number of RPF40s divided by the number of RPFs (small circles).

Fig. 5.
Fig. 5.

Simulated maximum height of RPFs and RPF40s vs time of day; (top) two with h = 1 km, U = 2 m s−1, or 8 m s−1 and (bottom) two with h = 2 km, U = 2 m s−1, or 8 m s−1. For each simulation, the intensity is given by the average height of a cluster of large filled circles and the frequency by the number of large circles divided by the number of small circles.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

For the lower terrain (h = 1 km), the average RPF40 height is about 3.5 km for both U = 2 m s−1 and U = 8 m s−1, while there are about 4 times as many large green circles (U = 2 m s−1) as large blue circles (U = 8 m s−1); hence, the frequency is about 4 times greater for the smaller U. For the higher-terrain cases with h = 2 km, the dependence of the RPF40 height on wind is similar to the h = 1 km case but with slightly less intensity and about one-third the frequency. The reduction in intensity and frequency with increasing h is generally consistent with the trends seen in the TRMM results, except that the magnitude of the frequency decline is much larger in WRF. On the other hand, the average height of the RPFs does not appear to show a consistent variation in wind speed or height between the two panels. For the h = 1 km case, the maximum RPF height is greater for the lower wind speed, while for h = 2 km, the opposite is true. This is probably just due to the chaotic nature of convection. The more rigorous deep convective proxy, RPF40, still shows a systematic variation with height and wind speed.

For the remainder of this study, the only cases that are shown and analyzed in detail are the ones with nonzero surface heat fluxes. This is because, regardless of the choice of h and U, convection is generally weak in the HCAPE0W suite. Although precipitation develops over the windward-facing slopes in the cases with larger U, this convection never produces 40-dBZ echoes. We speculate that the inability of strong convection to develop in this suite is owing to a combination of upstream flow blocking, which inhibits the ascent of near-surface, highly unstable air parcels, and the limited time for deep convection to develop over the windward slope before weakening rapidly under lee-side descent.

1) Intensity variation

To compare a given metric from a WRF suite with corresponding TRMM observations for a given h, we average the former uniformly over a set of simulations with U = 0, 2, 4, 6, and 8 m s−1. Similarly, for a given U, we average over a set of simulations with h = 0, 0.5, 1, 2, and 3 km. For the TRMM analysis, we average over the TRMM island averages within each h or U bin (section 2c).

Selected suites of WRF simulations show a general reduction in intensity with h for h > 0.5 km, particularly the more intense convection in suites MCAPE200W and LCAPE60W (Fig. 6). This response loosely matches the observed TRMM trends for the two largest area bins (3 and 4). The maximum intensity for each suite is about the same for Oahu and Hawaii, likely because the Oahu area has been rescaled to match that of Hawaii and it uses the same range of h values. Although the shapes and terrain distributions of Hawaii and Oahu greatly differ, the magnitude and variation of intensity with height are similar on the two islands though more pronounced for LCAPE60W over Hawaii.

Fig. 6.
Fig. 6.

Intensity of convection versus h and U for full- and half-sized HI and Oahu, compared to TRMM observations in the nearest respective size category (black). The number of islands in each height bin is given in brackets for islands in TRMM3 and TRMM4, with the error bars being defined in the same way as in Fig. 3. Data points are shown only for WRF simulations that had more than a total of 20 min of deep convection.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

The simulation suites shown in Fig. 6 comprise only a subset of the full array of simulations (see Table 1). These have been chosen to show the overall trends and to bracket the TRMM results. To briefly summarize the full suite of simulations, the intensity increases with either the surface heating rate or CAPE. On average, the variation of intensity with h is similar to TRMM and consistent with the results of Fig. 6. One consistent exception to this trend is for h < 500 m, where intensity increases with increasing h (e.g., Figs. 6a,c,e). Only a very slight corresponding increase is found in TRMM4, while TRMM3 exhibits the opposite trend. An explanation for this simulated trend is provided in section 5.

Although the WRF simulations reasonably represent the observed modest decrease in intensity with h, they do not reproduce the observed (and stronger) decrease in intensity with U (Figs. 6b,d,f). The simulated trends are generally weak and vary between different suites. This discrepancy is discussed further in section 4a.

The simulations also reasonably represent the observed sensitivity of intensity to island area A. The TRMM observations reveal a weak (hundreds of meters) reduction in intensity between full HI (area bin 4) and half HI (area bin 3) (Figs. 6a–c and Figs. 6b–d, respectively). As A is halved, the WRF simulations exhibit similar decreases in intensity for each simulation suite. While this sensitivity of intensity to A is robust, the impacts of the A variations considered here are less than for variations in h and U and much less than for variations in initial CAPE and surface heating.

2) Frequency variation

For TRMM and the WRF simulations, the frequency increases from h = 0 to 0.5 km and then weakly decreases for larger h (Figs. 7a,c,e). The simulated trend is similar to the TRMM-observed trend in area bin 4 over full HI and Oahu but stronger than the observed trend in area bin 3 for half HI, at least up to h = 2 km (there are no taller islands in this area bin). In both observations and simulations, the frequency generally decreases with U. The only exception is LCAPE60W which increases for small U but then drops again for larger U values. In all cases, the lowest frequency is found at the largest value of U.

Fig. 7.
Fig. 7.

As in Fig. 6, but for frequency of convection and without requiring the 20-min duration.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

When A is halved from full HI to half HI, the frequency in the LCAPE60W and HCAPE20W suites also roughly halves. In contrast, the frequencies of the MCAPE200W suite and TRMM (from area bin 4 to area bin 3) do not change appreciably. These results suggest that in cases with strong surface forcing and medium-to-high CAPE (e.g., MCAPE200W), most convective cells rapidly deepen and the frequency is less dependent on A. By contrast, in marginal cases with limited CAPE or surface heating, convective cells struggle to deepen and may require more residence time over the heated island to develop. When the island area is halved, the residence time decreases by an equivalent amount, which curtails the frequency. This effect is captured in TRMM but at a smaller magnitude, possibly because many of the RPFs are from non-island-generated storms. The similar simulated responses over full Hawaii and Oahu suggest that details of the island shape do not strongly affect the overall trend between frequency and h.

Finally, the results appear to be relatively robust to changes in wind direction (MCAPE200W-NE) or sounding (MCAPE200W-OS). The convective vigor is slightly weaker for the ocean sounding, with a lower intensity and frequency, but the overall trends with h and U are similar.

4. Explaining the sensitivities

a. Intensity

Environmental conditions other than wind, particularly metrics of moist instability (CAPE and CIN) and surface heating rates, clearly exert a strong influence on both convective intensity and vigor (e.g., Figs. 6 and 7). Geographic and temporal variations in these quantities could thus affect some of the TRMM-observed trends. For example, weaker climatological winds may coincide with a higher-CAPE geographic region (e.g., the west Pacific warm pool), thereby confounding the relationship between wind and convective properties.

To evaluate the correlation between reanalysis-derived CAPE and CIN from the TRMM RPF database and h and U, the former are averaged over each h or U bin in Fig. 8.

Fig. 8.
Fig. 8.

TRMM: Mean CAPE and CIN vs h and U for all TRMM area bins (compared to Fig. 3d and Fig. 6).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

The CAPE variations with h, U, and A resemble the corresponding variations in TRMM intensity (Figs. 3a and 6). CIN also decreases weakly with h and U (but not A); hence, the more intense storms tend to coincide with larger CIN, rather than smaller CIN as might be expected. This finding, along with the small mean CIN values and weak variations in mean CIN across the h bins (with a dynamic range of only about 6 J kg−1), suggests that CIN is generally not large enough to meaningfully control the observed intensity or frequency variations.

Accordingly focusing on CAPE, corresponding relationships for the WRF simulations are obtained by averaging CAPE (with a surface-based starting parcel) over the land area and 30-min period before the occurrence of the first 40-dBZ echo (Fig. 9). CAPE decreases monotonically with h at a rate stronger than in TRMM. Specifically, simulated CAPE decreases by a factor of 2–4 compared to a decrease of only around 25% in TRMM. This difference may stem from the fact that the ERA profiles are collocated to the geographic center of the RPF (rather than the island), which means the reanalysis CAPE is often drawn from an ocean location. In contrast, the simulated CAPE is calculated only over the land surface.

Fig. 9.
Fig. 9.

Island-averaged CAPE versus h and U in WRF simulations over full HI, half HI, and Oahu (resized to match the area of fullHI) (compared to Fig. 6).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

The WRF simulations and the TRMM observations exhibit different relationships between CAPE and U. Whereas the former exhibits no consistent variation in CAPE over the simulated range of U, the latter exhibits a modest CAPE decrease with an increase in U of around 10% for area bins 1, 3, and 4 (TRMM1, TRMM3, and TRMM4, respectively) and almost no variation for bin 2. The reduction in intensity with U for TRMM3 and TRMM4 (Fig. 6) is similar to the reduction in CAPE with U (both are 10%–15%). Also notable is that neither the observations nor the simulations indicate much sensitivity of CAPE to A. This is consistent with Robinson et al. (2011), who found only a small increase in CAPE with increasing A. For WRF, a very weak simulated sensitivity of CAPE to A is apparent, particularly for the MCAPE200W suite. Altogether, the WRF simulations qualitatively reproduce the observed trend of CAPE decreasing with h, but not the trend of CAPE decreasing with U. This suggests that the former effect is naturally included in our simplified modeling framework, while the latter is not. In the TRMM observations, the different wind speeds come from different environments, whereas in the simulations, CAPE and U are varied independently by design. The reduction of CAPE with wind speed for TRMM is consistent with our expectation that the highest CAPE in the tropics is found in doldrums regions (or intertropical convergence zone).

To more carefully investigate the effects of CAPE and CIN on intensity and frequency, we looked at the full set of simulations described earlier (Table 1), as well as some additional simulations based on soundings averaged over different ranges of initial CAPE or CIN (Table 2). All of these simulations used an intermediate h of 1 km. By far, the strongest and most consistent correlation in these cases is between intensity and CAPE, for which the TRMM and WRF trends are generally consistent (Fig. 10a). Thus, the fact that observed CAPE generally decreases with h and U (Fig. 8) appears to explain the weakening of the convection as these parameters increase in value (Fig. 6). The correlation is much weaker for CIN and exhibits minimal dynamic range (Fig. 10b), reinforcing the minimal impacts of CIN on convective intensity in this analysis.

Table 2.

Range of initial CAPE and CIN for additional simulations in Fig. 10.

Table 2.
Fig. 10.
Fig. 10.

WRF: Frequency and intensity versus CAPE and CIN for a range of conditions (all full HI with h = 1 km and U = 2 m s−1, unless otherwise stated). As with Fig. 9, CAPE and CIN have been averaged over land and over the 30-min period before the occurrence of the first RPF40. The black dots represent additional simulations designed to sample a range of CAPE and CIN values (see Table 2). The respective size of each color symbol represents the magnitude of the quantity (with values given in the inset box).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

b. Frequency

The frequency also generally increases with CAPE in both the WRF and TRMM data, but the former exhibits a much less coherent trend than for intensity (Fig. 10c). Thus, CAPE alone is likely insufficient to explain all of the frequency variations. Although one might expect that higher CIN would inhibit convection and thus decrease the frequency, the correlation between CIN and frequency differs between the WRF simulations (negative trend) and the observations (positive trend) (Fig. 10d). However, as noted previously, the narrow range of CIN values in both the observations and simulations makes CIN an unlikely control factor for either intensity or frequency.

The above results suggest that while intensity is largely explained by CAPE alone, frequency is at best partly explained by CAPE, with CIN having minimal effect due to its limited dynamic range. Considering that the ingredients necessary for deep convection include not just moist instability (as quantified by CAPE) but also sufficient low-level lifting to release the instability, we turn to an analysis of low-level vertical motion. As a proxy for this motion, we use the surface horizontal convergence, which by mass continuity indicates a positive gradient in vertical velocity above the surface. In principle, the combination of large CAPE (and small CIN) and strong surface convergence should favor large frequency, as parcels with large subcloud vertical momentum are more likely to reach saturation and generate positive buoyancy. To quantify this combination of factors in the WRF simulations, first, we define a deep convective index (DCI) as the product of the two:
DCI=CAPE×v,
where the divergence is measured 2 m above the surface. The DCI is only evaluated over island grid points.

Second, we define Nconv as the number of locations (i.e., grid points) and times where DCI exceeds 100 J kg−1 min−1 over the 30 min prior to the first 40-dBZ echo. In general, the frequency increases with Nconv, asymptotically approaching a value of around 0.8 for Nconv > 100 J kg−1 min−1 (Fig. 11a). However, a number of cases (indicated by blue filled circles) clearly do not follow this trend. These cases are all characterized by relatively small values of h (0–125 m), suggesting that h must be sufficiently large for Nconv to reliably characterize the frequency trend. For these low h cases, the frequency remains relatively small even at large Nconv. The blue filled circles all denote cases where h < ht, where ht is a threshold height at which terrain effects become important for determining the boundary layer dynamics. A simple theoretical analysis that is used to determine ht for all simulations is provided in section 5.

Fig. 11.
Fig. 11.

Frequency and intensity versus Nconv, the number of grid points where DCI > 100 J kg−1 min−1. The blue and black circles are for individual simulations with heights below and above the threshold, respectively (see text). The green triangles and red squares are averages over h and U, respectively. The golden filled circles are averages over all the simulations in the full HI or half HI bins. The respective size of each color symbol represents the magnitude of the quantity (with values given in the inset box). These simulations are from the MCAPE200W suite.

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

As the intensity depends on the average strength of convection, rather than the number of events (or area of CAPE), it does not noticeably depend on Nconv (Fig. 11b). The intensity is in general higher for h > ht (black filled circles) than for h < ht, where it drops by about 10% (blue filled circles). This drop in intensity with a reduction in h occurs despite the increase in CAPE (Figs. 8 and 9).

In summary, provided sufficient island terrain height (h > ht), the variation of frequency with h, U, and A can be explained by a single metric Nconv, which itself depends in part on the island CAPE. With a larger high-CAPE area, there is more chance of an island-forced convergence zone coinciding with high CAPE and generating deep convection. To evaluate the sensitivity of the trend to the chosen DCI threshold, we evaluated alternative thresholds of 50 and 200 J kg−1 min−1 for each of the simulation suites. The results were consistent with those shown in Fig. 11.

c. Origin of CAPE variations

The decrease of CAPE with h in both the TRMM observations and the WRF simulations stems from the general decrease of specific humidity and temperature with height in the atmosphere. Due to this decrease, islands that protrude deeper into the troposphere are characterized by drier environmental air. As a result, both equivalent potential temperature (θe) and CAPE tend to decrease over high terrain, at least in horizontally homogeneous atmospheres. Orographic processes like increased evapotranspiration over forested mountains, or thermally forced upslope flow converging moisture over the summit, can partially overcome this trend in some cases (Kirshbaum et al. 2018). However, humidifying the ridge-top atmosphere becomes increasingly difficult at larger h, where turbulent mixing with dry air aloft is highly effective at reducing specific humidity.

To illustrate this trend, we evaluate 2-m θe distributions in selected members of the MCAPE200W suite (Fig. 12). In general, potentially (and, usually, conditionally) unstable layers tend to exhibit vertically decreasing θe profiles (∂θe/∂z < 0), and hence, the air over the high terrain tends to have lower θe than that over the lower terrain.

Fig. 12.
Fig. 12.

Snapshots of surface equivalent potential temperature taken 30 min before deep convection occurred for three different HI simulations with MCAPE200W. Other quantities plotted include height contours and the coastline (gray boundary).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

Figures 12a–c, respectively, compare θe 30 min before deep convection initiation in three simulations in the MCAPE200W suite, one with both high intensity and high frequency (h = 1 km and U = 2 m s−1), one with low intensity and low frequency (h = 3 km and U = 2 m s−1), and one with high intensity and low frequency (h = 1 km and U = 8 m s−1). Corresponding distributions of CAPE (Fig. 13) reveal that, for the most part, near-surface θe and CAPE correlate strongly; hence, the former is a reasonable proxy for the latter. The areal coverage of high θe and CAPE is the greatest for lower h and U, with a major decrease at larger h and a modest decrease at larger U. Not coincidentally, lower values of h and U also exhibit the largest intensities and frequencies (Figs. 6 and 7).

Fig. 13.
Fig. 13.

Snapshots of CAPE taken at the same time and for the same HI simulations as in Fig. 12. Other quantities plotted are height contours, wind vectors, and the coastline (gray boundary).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

The relations between CAPE, Nconv, intensity, and frequency can be appreciated from the distributions of CAPE and surface divergence. The low-U, low-h case shows a large area of high CAPE coinciding with numerous surface-based convergence lines (Figs. 13a and 14a), yielding relatively large island-averaged CAPE and Nconv. This combination favors both high intensity and high frequency. In contrast, the high-h, low-U case (Figs. 13b and 14b) has much a smaller island-averaged CAPE, implying smaller Nconv and sharply decreased intensity and frequency. Finally, the high-U, low-h case has similar peak CAPE values to the first case but a smaller areal coverage of high CAPE and less prevalent sharp surface convergence lines (Figs. 13c and 14c), resulting in relatively high intensity but lower frequency (due to reduced Nconv). The reason there are still high CAPE values even for strong winds (Fig. 13c) is that the low-level flow is blocked by the mountain and deflects around it. Heat is only ventilated by the wind in places where the winds are offshore, but they are mostly onshore.

Fig. 14.
Fig. 14.

Snapshots of surface velocity divergence taken at the same time and for the same HI simulations as in Fig. 12. Other quantities plotted are wind vectors and the coastline (gray boundary).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

Altogether, the ideal conditions for vigorous convection are modest h and weak ambient winds. Both of these trends relate to moist instability (CAPE) in some fashion. Taller islands have weaker and less frequent convection because elevated air is colder and drier, thus reducing CAPE. Modestly tall islands have high CAPE and relatively intense storms, which is superior to flat islands that lack the terrain-anchored surface convergence to facilitate deep convection initiation. The presence of strong winds reduces storm frequency primarily by disrupting the formation of strong near-surface convergence zones and secondarily by transporting lower-CAPE maritime air onto the island.

5. The importance of terrain complexity

One robust feature of the WRF simulations is an initial increase in both intensity and frequency as h increases from zero to around 500 m, bucking the broader inverse trends between h and each metric (Figs. 6a,c,e and 7a,c,e). Although there is a hint of similar behavior in the TRMM climatology, with the negative intensity and frequency trends both stalling or reversing at low h, few real islands are this low-lying, and thus, the sampling is limited. Given that CAPE generally decreases monotonically as h increases (Figs. 9a,c,e), the cause of the reversal of the intensity and frequency trends at small h cannot be explained by CAPE or Nconv.

Near-surface preconvective convergence fields for the MCAPE200W simulations suggest that the flows transition from more cellular and disorganized, Rayleigh–Bénard-like convection at smaller h to a more organized set of 3–4 quasi-linear convergence zones aligned with smaller-scale ridges at larger h (Fig. 15). Whereas the more cellular convective boundary layer (CBL) convection pattern at lower h induces the formation of numerous weak, short-lived convective cells (Fig. 15a), the more organized and persistent convergence pattern at larger h initiates stronger, more sustained cells along the convergence zones and their intersections (Fig. 15b).

Fig. 15.
Fig. 15.

Velocity vectors and divergence field for the same configuration in Fig. 12, but for (a) h = 62 m and (b) 500 m, and taken 30 min after convection had initiated. The plots include contours of vertically integrated hydrometeor content with five contour levels, 0–30 g kg−1 (using a green–white scale).

Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-23-0204.1

Although the model horizontal grid spacing used herein is too coarse to adequately resolve CBL turbulence, the clear transition from disorganized dry convection to organized convergence zones in Fig. 15 is consistent with previous large-eddy simulations employing much higher grid resolution. For example, Fig. 6 of Kirshbaum (2017) shows organized convergence lines becoming dominant over CBL turbulence over sufficiently steep terrain slopes.

To understand why the CBL dynamics transition between these two regimes as h is increased, we note that thermally forced circulations over heated land are generally driven by horizontal buoyancy gradients (e.g., Kirshbaum 2013). Over relatively flat and homogeneous land surfaces, these gradients are associated with small-scale, and usually small-amplitude, random variations in air density. Over mountains, by contrast, low-level buoyancy gradients are created by the vertical tilting of surface-based superadiabatic layers over sloping terrain. We hypothesize that this tilting, which is responsible for the formation of anabatic and katabatic winds, induces the transition from disorganized cells at very low h to organized convergence zones at larger h.

To evaluate this hypothesis, we compare the characteristic horizontal buoyancy gradient over flat terrain (the “turbulent” term) with the estimated horizontal buoyancy gradient generated by the tilting of the surface superadiabatic layer (the “tilting” term). Both are estimated using preconvective (30 min before the first RPF40) conditions from the flat (h = 0 m) cases of the MCAPE200W suite. The turbulent term is evaluated as the root-mean-square (RMS) near-surface horizontal virtual potential temperature (θυ) gradient (‖∇hθυRMS), and the tilting term is the product of the mean island vertical θυ gradient at the lowest model level and the mean terrain slope (h/R×θυ¯/z, where R=A/π).

If the tilting term is larger than the turbulent term, we expect organized, terrain-forced convergence lines to dominate the CBL flow. We define ht as the value of h at which the ratio of the tilting term to the turbulent term is unity. Thus, h > ht implies a dominant tilting term for which organized convergence lines are expected to develop.

In Figs. 11a and 11b, we show all the cases where h < ht with blue filled circles. These cases are uniquely characterized by lower intensities and frequencies, even where Nconv is relatively large. The range of ht values lies between h = 125 and 500 m, the same range of values over which both intensity and frequency tend to increase, rather than decrease, with increasing h. Thus, this simple analysis helps explain the positive intensity and frequency trends at modest values of h (Figs. 6 and 7). When h > ht, the formation of quasi-stationary convergence lines favors stronger, wider, and longer-lived updrafts at the cloud base. This, in turn, favors more vigorous and surface-rooted moist convection.

In light of these results, one limitation of our experiments is the assumption of homogeneous surface cover. In reality, mesoscale variations in land cover, soil moisture, and/or albedo create θυ gradients that may also organize CBL circulations into more focused convergence lines. Thus, the sharp simulated decrease in intensity and frequency at very small h likely results from the simplifications of our modeling setup, which probably explains why the decrease is less evident in the TRMM observations than in the simulations. Because orographic effects on the CBL tend to dominate over surface cover effects for even modest h values (e.g., Kirshbaum et al. 2016; Imamovic et al. 2017), this limitation is likely confined to the very low end of the simulated range of h.

6. Conclusions

Islands are well known to trigger and modify atmospheric convection by some combination of orographic and thermal forcing. In this study, we have exploited this notion to examine trends (sensitivities) in convective properties with island and environmental characteristics, both in TRMM observations near 272 islands over 22 years, and via the WRF convection-permitting model with a TRMM simulator (or forward model). The island characteristic of concern was the peak terrain height h (and, to a lesser extent, island area A); the environmental parameters were horizontal wind speed U as well as CAPE, CIN, and surface heat fluxes over the island. Previous studies have found convection becoming more intense with increasing A (e.g., Robinson et al. 2011), but previous studies of impacts of h and U are few and have reached different conclusions. The convective characteristics studied here were a measure of the frequency or likelihood that precipitating convection will be strong (how often does a feature with a 20-dBZ echo attain a 40-dBZ echo?) and one of the intensities of strong convection (what is the average maximum 40-dBZ echo height among storms attaining a 40-dBZ echo?). These dual measures break the usual question of what conditions will cause strong deep convection into two parts, which turn out to have different environmental controls.

Our approach compares observed trends found by statistical regression with model trends found in controlled experiments, each focusing on afternoon convection influenced by daytime heating. A fundamental assumption of this approach is that we have a large enough sample of islands to obtain reasonable statistics and that there is no systematic relationship between island characteristics and environmental ones. We have tested this assumption to the extent possible by looking at trends in the environmental parameters with the island ones and have not found any significance; a map of islands (Fig. 1) shows that the various sizes are quasi-randomly distributed geographically among the island population although this population itself is clustered in certain regions and so cannot be (and is not) taken as an unbiased sample of the tropical atmosphere. While some observed environmental parameters are correlated with others (i.e., CAPE and U due to their climatological distributions), this can be accounted for in model–observation comparisons once it is identified since the environmental factors are varied independently in the simulations. Thus, we find that our approach should be sound for isolating the impacts of different influences on the convection in a way comparable between observation and simulation.

Using the above approach, we found herein that observed strong convective intensity (with maximum echoes exceeding 40 dBZ) increases with A (confirming previous results), decreases modestly with both h and U on average, and increases strongly with CAPE. These negative trends with both h and U broadly disagree with the predictions of linear theories of orographic precipitation (e.g., Smith and Barstad 2004).

All of the above trends were reproduced reasonably accurately by the WRF simulations except for the absence of a systematic trend when U was varied alone. The observed decrease with U was instead explained by noting that higher U in nature tends to occur at lower CAPE and that it is this covariation of CAPE and U that likely explains the decrease. Indeed, our overall result was that all of the systematic variations in strong convective intensity seen were well explained by CAPE, including the downward trend with h above a few hundred meters, which stems from island-averaged CAPE decreasing with h owing to the protrusion of higher mountains into the drier free troposphere. In other words, CAPE variations lurked behind nearly all other trends seen in strong convective intensity. The slope and intercept of the regression line of intensity (km) versus CAPE (J kg−1) for all the TRMM RPFs are 6.8 × 10−4 ± 5.1 × 10−6 (kg km J−1) and 2.6 ± 0.067 (km), respectively.

Convective frequency likewise depended not only on CAPE but also on surface convergence, a proxy for the strength and intensity of boundary layer updrafts. The coexistence of these two factors was captured here by a simple “deep convective index” defined as the product of CAPE and near-surface convergence. The simulated frequency correlated well with the total area over which this index exceeded a threshold value. Thus, successful initiation of deep convection was favored by larger coverage of strong updrafts lifting air to saturation within higher-CAPE regions. This areal dependence largely explains the increase in convective vigor with A.

In the simulations, the above results held only for h down to a threshold of around 200 m, below which convection weakened sharply. A similar but weaker change was also found in the observations. In WRF, this reversal of the h trends corresponded to a transition in the simulated CBL morphology from quasi-linear, quasi-stationary mesoscale convergence lines for h > 200 m to disorganized, cellular, and transient dry convection over flatter islands. The stronger convergence lines emerging with significant topography apparently favor stronger convection, modulated by other conditions (CAPE in particular) as noted above. This threshold was tentatively accounted for by a simple theoretical analysis that compares the terrain-induced tilting of near-surface vertical buoyancy gradients (which scales with h) to the near-surface horizontal buoyancy gradients (which does not), with a predicted crossover scale of around 200 m.

There are a few caveats with this study that must be noted. Although a clear midafternoon maximum appears in the observed convective measures, RPFs were observed by TRMM at all times of the day. Hence, a large fraction of precipitation events may not have been directly associated with diurnal heating or cooling over the islands. The WRF simulations were quasi idealized in that they combined some realistic elements (initial soundings and terrain geometries) with major simplifications (horizontally homogeneous initial state and sinusoidally varying surface heat fluxes over land). Furthermore, the simulations did not consider larger-scale, non-island-forced precipitation systems that originate upstream and cross the island, nor did they include vertical wind shear; possibly for this reason, deep convection initiation required a certain terrain height (as noted above) and a surface heat flux of at least 20 W m−2. Thus, the simulations did not capture the full range of mechanisms behind the observed RPFs, and the effects of each of the simulation parameters on the overall trends merit further attention. Also, due to computational costs, this study did not allow for varying island terrain other than experimenting with two islands, again invoking the assumption that island shapes will vary quasi randomly and will not affect statistical trends.

Nonetheless, by separating the overall question of convective vigor into a frequency of occurrence of “strong” convection (40-dBZ echoes present) and intensity of this strong convection, this work has clarified the relative roles of CAPE and low-level convergence in controlling convective vigor. These results may be of use in developing simple models and parameterizations of convection. Provided there is enough surface heterogeneity for intense convergence lines to develop over the island, CAPE controls intensity and Nconv controls frequency. It is encouraging that systematic variations in observed island convection can be qualitatively captured by the idealized setup used here. The interesting transition seen here at very low topography, and its applicability to reality, deserves further study.

Acknowledgments.

This work was supported by the NSF Physical and Dynamical Meteorology program, Grant 1926078. We would like to acknowledge high-performance computing support from Cheyenne (https://doi.org/10.5065/D6RX99HX) provided by NCAR’s Computational and Information Systems Laboratory, sponsored by the National Science Foundation. S. C. S. was funded by the Australian Research Council, FL150100035, and D. J. K.’s contributions were supported by the Canadian Natural Science and Engineering Research Council (Grant RGPIN 418372-17).

Data availability statement.

All of the data used for the present analysis were downloaded from http://atmos.tamucc.edu/trmm/data and are freely available to interested researchers. The Weather Research and Forecasting Model used for all the simulations is also freely available at https://www.mmm.ucar.edu/models/wrf. The IDL codes used to analyze all the data are all archived locally and available upon request to the corresponding author.

REFERENCES

  • Barthlott, C., B. Adler, N. Kalthoff, J. Handwerker, M. Kohler, and A. Wieser, 2016: The role of Corsica in initiating nocturnal offshore convection. Quart. J. Roy. Meteor. Soc., 142, 222237, https://doi.org/10.1002/qj.2415.

    • Search Google Scholar
    • Export Citation
  • Cecil, D. J., 2009: Passive microwave brightness temperatures as proxies for hailstorms. J. Appl. Meteor. Climatol., 48, 12811286, https://doi.org/10.1175/2009JAMC2125.1.

    • Search Google Scholar
    • Export Citation
  • Cronin, T. W., K. A. Emanuel, and P. Molnar, 2015: Island precipitation enhancement and the diurnal cycle in radiative-convective equilibrium. Quart. J. Roy. Meteor. Soc., 141, 10171034, https://doi.org/10.1002/qj.2443.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1990: Mountain waves and downslope winds. Atmospheric Processes over Complex Terrain, Meteor. Monogr., No. 23, Amer. Meteor. Soc., 59–81, https://link.springer.com/chapter/10.1007/978-1-935704-25-6_4.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation
  • Iguchi, T., T. Kozu, R. Meneghini, J. Awaka, and K. Okamoto, 2000: Rain-profiling algorithm for the TRMM precipitation radar. J. Appl. Meteor., 39, 20382052, https://doi.org/10.1175/1520-0450(2001)040<2038:RPAFTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Imamovic, A., L. Schlemmer, and C. Schär, 2017: Collective impacts of orography and soil moisture on the soil moisture-precipitation feedback. Geophys. Res. Lett., 44, 11 68211 691, https://doi.org/10.1002/2017GL075657.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., 2013: On thermally forced circulations over heated terrain. J. Atmos. Sci., 70, 16901709, https://doi.org/10.1175/JAS-D-12-0199.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., 2017: On upstream blocking over heated mountain ridges. Quart. J. Roy. Meteor. Soc., 143, 5368, https://doi.org/10.1002/qj.2945.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., and R. B. Smith, 2009: Orographic precipitation in the tropics: Large-eddy simulations and theory. J. Atmos. Sci., 66, 25592578, https://doi.org/10.1175/2009JAS2990.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., and C.-C. Wang, 2014: Boundary layer updrafts driven by airflow over heated terrain. J. Atmos. Sci., 71, 14251442, https://doi.org/10.1175/JAS-D-13-0287.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., F. Fabry, and Q. Cazenave, 2016: The Mississippi valley convection minimum on summer afternoons: Observations and numerical simulations. Mon. Wea. Rev., 144, 263272, https://doi.org/10.1175/MWR-D-15-0238.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., B. Adler, N. Kalthoff, C. Barthlott, and S. Serafin, 2018: Moist orographic convection: Physical mechanisms and links to surface-exchange processes. Atmosphere, 9, 80, https://doi.org/10.3390/atmos9030080.

    • Search Google Scholar
    • Export Citation
  • Kummerow, C., W. Barnes, T. Kozu, J. Shiue, and J. Simpson, 1998: The Tropical Rainfall Measuring Mission (TRMM) sensor package. J. Atmos. Oceanic Technol., 15, 809817, https://doi.org/10.1175/1520-0426(1998)015<0809:TTRMMT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Liu, C., and E. J. Zipser, 2015: The global distribution of largest, deepest, and most intense precipitation systems. Geophys. Res. Lett., 42, 35913595, https://doi.org/10.1002/2015GL063776.

    • Search Google Scholar
    • Export Citation
  • Liu, C., E. J. Zipser, D. J. Cecil, S. W. Nesbitt, and S. Sherwood, 2008: A cloud and precipitation feature database from nine years of TRMM observation. J. Appl. Meteor. Climatol., 47, 27122728, https://doi.org/10.1175/2008JAMC1890.1.

    • Search Google Scholar
    • Export Citation
  • Markowski, P., and Y. Richardson, 2011: Mesoscale Meteorology in Midlatitudes. Vol. 2. John Wiley and Sons, 432 pp.

  • Masunaga, H., and Coauthors, 2010: Satellite data simulator unit: A multisensor, multispectral satellite simulator package. Bull. Amer. Meteor. Soc., 91, 16251632, https://doi.org/10.1175/2010BAMS2809.1.

    • Search Google Scholar
    • Export Citation
  • Mohr, K. I., and E. J. Zipser, 1996: Mesoscale convective systems defined by their 85-GHz ice scattering signature: Size and intensity comparison over tropical oceans and continents. Mon. Wea. Rev., 124, 24172437, https://doi.org/10.1175/1520-0493(1996)124<2417:MCSDBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nicolas, Q., and W. R. Boos, 2022: A theory for the response of tropical moist convection to mechanical orographic forcing. J. Atmos. Sci., 79, 17611779, https://doi.org/10.1175/JAS-D-21-0218.1.

    • Search Google Scholar
    • Export Citation
  • Nugent, A. D., R. B. Smith, and J. R. Minder, 2014: Wind speed control of tropical orographic convection. J. Atmos. Sci., 71, 26952712, https://doi.org/10.1175/JAS-D-13-0399.1.

    • Search Google Scholar
    • Export Citation
  • Qian, J.-H., 2008: Why precipitation is mostly concentrated over islands in the Maritime Continent. J. Atmos. Sci., 65, 14281441, https://doi.org/10.1175/2007JAS2422.1.

    • Search Google Scholar
    • Export Citation
  • Robinson, F. J., S. C. Sherwood, and Y. Li, 2008: Resonant response of deep convection to surface hot spots. J. Atmos. Sci., 65, 276286, https://doi.org/10.1175/2007JAS2398.1.

    • Search Google Scholar
    • Export Citation
  • Robinson, F. J., S. C. Sherwood, D. Gerstle, C. Liu, and D. J. Kirshbaum, 2011: Exploring the land–ocean contrast in convective vigor using islands. J. Atmos. Sci., 68, 602618, https://doi.org/10.1175/2010JAS3558.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W., and Coauthors, 2008: A description of the advanced research WRF version 3. NCAR Tech. Rep. NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

  • Smith, R. B., 1989: Hydrostatic Airflow over Mountains. Advances in Geophysics Series, Vol. 31, Elsevier, 41 pp.

  • Smith, R. B., and I. Barstad, 2004: A linear theory of orographic precipitation. J. Atmos. Sci., 61, 13771391, https://doi.org/10.1175/1520-0469(2004)061%3C1377:ALTOOP%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., P. Schafer, D. J. Kirshbaum, and E. Regina, 2009: Orographic precipitation in the tropics: Experiments in Dominica. J. Atmos. Sci., 66, 16981716, https://doi.org/10.1175/2008JAS2920.1.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., and Coauthors, 2012: Orographic precipitation in the tropics: The Dominica Experiment. Bull. Amer. Meteor. Soc., 93, 15671579, https://doi.org/10.1175/BAMS-D-11-00194.1.

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., C. D. Burleyson, and S. E. Yuter, 2011: Rain on small tropical islands. J. Geophys. Res., 116, D08102, https://doi.org/10.1029/2010JD014695.

    • Search Google Scholar
    • Export Citation
  • Spencer, R. W., H. M. Goodman, and R. E. Hood, 1989: Precipitation retrieval over land and ocean with the SSM/I: Identification and characteristics of the scattering signal. J. Atmos. Oceanic Technol., 6, 254273, https://doi.org/10.1175/1520-0426(1989)006<0254:PROLAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Surcel, M., I. Zawadzki, and M. K. Yau, 2015: A study on the scale dependence of the predictability of precipitation patterns. J. Atmos. Sci., 72, 216235, https://doi.org/10.1175/JAS-D-14-0071.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 50955115, https://doi.org/10.1175/2008MWR2387.1.

    • Search Google Scholar
    • Export Citation
  • Van Nguyen, H., Y.-L. Chen, and F. Fujioka, 2010: Numerical simulations of island effects on airflow and weather during the summer over the island of Oahu. Mon. Wea. Rev., 138, 22532280, https://doi.org/10.1175/2009MWR3203.1.

    • Search Google Scholar
    • Export Citation
  • Wang, C.-C., and D. J. Kirshbaum, 2015: Thermally forced convection over a mountainous tropical island. J. Atmos. Sci., 72, 24842506, https://doi.org/10.1175/JAS-D-14-0325.1.

    • Search Google Scholar
    • Export Citation
  • Wang, S., and A. H. Sobel, 2017: Factors controlling rain on small tropical islands: Diurnal cycle, large-scale wind speed, and topography. J. Atmos. Sci., 74, 35153532, https://doi.org/10.1175/JAS-D-16-0344.1.

    • Search Google Scholar
    • Export Citation
  • Williams, E., and S. Stanfill, 2002: The physical origin of the land–ocean contrast in lightning activity. C. R. Phys., 3, 12771292, https://doi.org/10.1016/S1631-0705(02)01407-X.

    • Search Google Scholar
    • Export Citation
  • Zhu, L., L. Bai, G. Chen, Y. Q. Sun, and Z. Meng, 2021: Convection initiation associated with ambient winds and local circulations over a tropical island in South China. Geophys. Res. Lett., 48, e2021GL094382, https://doi.org/10.1029/2021GL094382.

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., D. J. Cecil, C. Liu, S. W. Nesbitt, and D. P. Yorty, 2006: Where are the most intense thunderstorms on Earth? Bull. Amer. Meteor. Soc., 87, 10571072, https://doi.org/10.1175/BAMS-87-8-1057.

    • Search Google Scholar
    • Export Citation
Save
  • Barthlott, C., B. Adler, N. Kalthoff, J. Handwerker, M. Kohler, and A. Wieser, 2016: The role of Corsica in initiating nocturnal offshore convection. Quart. J. Roy. Meteor. Soc., 142, 222237, https://doi.org/10.1002/qj.2415.

    • Search Google Scholar
    • Export Citation
  • Cecil, D. J., 2009: Passive microwave brightness temperatures as proxies for hailstorms. J. Appl. Meteor. Climatol., 48, 12811286, https://doi.org/10.1175/2009JAMC2125.1.

    • Search Google Scholar
    • Export Citation
  • Cronin, T. W., K. A. Emanuel, and P. Molnar, 2015: Island precipitation enhancement and the diurnal cycle in radiative-convective equilibrium. Quart. J. Roy. Meteor. Soc., 141, 10171034, https://doi.org/10.1002/qj.2443.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1990: Mountain waves and downslope winds. Atmospheric Processes over Complex Terrain, Meteor. Monogr., No. 23, Amer. Meteor. Soc., 59–81, https://link.springer.com/chapter/10.1007/978-1-935704-25-6_4.

  • Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 23182341, https://doi.org/10.1175/MWR3199.1.

    • Search Google Scholar
    • Export Citation
  • Iguchi, T., T. Kozu, R. Meneghini, J. Awaka, and K. Okamoto, 2000: Rain-profiling algorithm for the TRMM precipitation radar. J. Appl. Meteor., 39, 20382052, https://doi.org/10.1175/1520-0450(2001)040<2038:RPAFTT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Imamovic, A., L. Schlemmer, and C. Schär, 2017: Collective impacts of orography and soil moisture on the soil moisture-precipitation feedback. Geophys. Res. Lett., 44, 11 68211 691, https://doi.org/10.1002/2017GL075657.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., 2013: On thermally forced circulations over heated terrain. J. Atmos. Sci., 70, 16901709, https://doi.org/10.1175/JAS-D-12-0199.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., 2017: On upstream blocking over heated mountain ridges. Quart. J. Roy. Meteor. Soc., 143, 5368, https://doi.org/10.1002/qj.2945.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., and R. B. Smith, 2009: Orographic precipitation in the tropics: Large-eddy simulations and theory. J. Atmos. Sci., 66, 25592578, https://doi.org/10.1175/2009JAS2990.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., and C.-C. Wang, 2014: Boundary layer updrafts driven by airflow over heated terrain. J. Atmos. Sci., 71, 14251442, https://doi.org/10.1175/JAS-D-13-0287.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., F. Fabry, and Q. Cazenave, 2016: The Mississippi valley convection minimum on summer afternoons: Observations and numerical simulations. Mon. Wea. Rev., 144, 263272, https://doi.org/10.1175/MWR-D-15-0238.1.

    • Search Google Scholar
    • Export Citation
  • Kirshbaum, D. J., B. Adler, N. Kalthoff, C. Barthlott, and S. Serafin, 2018: Moist orographic convection: Physical mechanisms and links to surface-exchange processes. Atmosphere, 9, 80, https://doi.org/10.3390/atmos9030080.

    • Search Google Scholar
    • Export Citation
  • Kummerow, C., W. Barnes, T. Kozu, J. Shiue, and J. Simpson, 1998: The Tropical Rainfall Measuring Mission (TRMM) sensor package. J. Atmos. Oceanic Technol., 15, 809817, https://doi.org/10.1175/1520-0426(1998)015<0809:TTRMMT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Liu, C., and E. J. Zipser, 2015: The global distribution of largest, deepest, and most intense precipitation systems. Geophys. Res. Lett., 42, 35913595, https://doi.org/10.1002/2015GL063776.

    • Search Google Scholar
    • Export Citation
  • Liu, C., E. J. Zipser, D. J. Cecil, S. W. Nesbitt, and S. Sherwood, 2008: A cloud and precipitation feature database from nine years of TRMM observation. J. Appl. Meteor. Climatol., 47, 27122728, https://doi.org/10.1175/2008JAMC1890.1.

    • Search Google Scholar
    • Export Citation
  • Markowski, P., and Y. Richardson, 2011: Mesoscale Meteorology in Midlatitudes. Vol. 2. John Wiley and Sons, 432 pp.

  • Masunaga, H., and Coauthors, 2010: Satellite data simulator unit: A multisensor, multispectral satellite simulator package. Bull. Amer. Meteor. Soc., 91, 16251632, https://doi.org/10.1175/2010BAMS2809.1.

    • Search Google Scholar
    • Export Citation
  • Mohr, K. I., and E. J. Zipser, 1996: Mesoscale convective systems defined by their 85-GHz ice scattering signature: Size and intensity comparison over tropical oceans and continents. Mon. Wea. Rev., 124, 24172437, https://doi.org/10.1175/1520-0493(1996)124<2417:MCSDBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Nicolas, Q., and W. R. Boos, 2022: A theory for the response of tropical moist convection to mechanical orographic forcing. J. Atmos. Sci., 79, 17611779, https://doi.org/10.1175/JAS-D-21-0218.1.

    • Search Google Scholar
    • Export Citation
  • Nugent, A. D., R. B. Smith, and J. R. Minder, 2014: Wind speed control of tropical orographic convection. J. Atmos. Sci., 71, 26952712, https://doi.org/10.1175/JAS-D-13-0399.1.

    • Search Google Scholar
    • Export Citation
  • Qian, J.-H., 2008: Why precipitation is mostly concentrated over islands in the Maritime Continent. J. Atmos. Sci., 65, 14281441, https://doi.org/10.1175/2007JAS2422.1.

    • Search Google Scholar
    • Export Citation
  • Robinson, F. J., S. C. Sherwood, and Y. Li, 2008: Resonant response of deep convection to surface hot spots. J. Atmos. Sci., 65, 276286, https://doi.org/10.1175/2007JAS2398.1.

    • Search Google Scholar
    • Export Citation
  • Robinson, F. J., S. C. Sherwood, D. Gerstle, C. Liu, and D. J. Kirshbaum, 2011: Exploring the land–ocean contrast in convective vigor using islands. J. Atmos. Sci., 68, 602618, https://doi.org/10.1175/2010JAS3558.1.

    • Search Google Scholar
    • Export Citation
  • Skamarock, W., and Coauthors, 2008: A description of the advanced research WRF version 3. NCAR Tech. Rep. NCAR/TN-475+STR, 113 pp., https://doi.org/10.5065/D68S4MVH.

  • Smith, R. B., 1989: Hydrostatic Airflow over Mountains. Advances in Geophysics Series, Vol. 31, Elsevier, 41 pp.

  • Smith, R. B., and I. Barstad, 2004: A linear theory of orographic precipitation. J. Atmos. Sci., 61, 13771391, https://doi.org/10.1175/1520-0469(2004)061%3C1377:ALTOOP%3E2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., P. Schafer, D. J. Kirshbaum, and E. Regina, 2009: Orographic precipitation in the tropics: Experiments in Dominica. J. Atmos. Sci., 66, 16981716, https://doi.org/10.1175/2008JAS2920.1.

    • Search Google Scholar
    • Export Citation
  • Smith, R. B., and Coauthors, 2012: Orographic precipitation in the tropics: The Dominica Experiment. Bull. Amer. Meteor. Soc., 93, 15671579, https://doi.org/10.1175/BAMS-D-11-00194.1.

    • Search Google Scholar
    • Export Citation
  • Sobel, A. H., C. D. Burleyson, and S. E. Yuter, 2011: Rain on small tropical islands. J. Geophys. Res., 116, D08102, https://doi.org/10.1029/2010JD014695.

    • Search Google Scholar
    • Export Citation
  • Spencer, R. W., H. M. Goodman, and R. E. Hood, 1989: Precipitation retrieval over land and ocean with the SSM/I: Identification and characteristics of the scattering signal. J. Atmos. Oceanic Technol., 6, 254273, https://doi.org/10.1175/1520-0426(1989)006<0254:PROLAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Surcel, M., I. Zawadzki, and M. K. Yau, 2015: A study on the scale dependence of the predictability of precipitation patterns. J. Atmos. Sci., 72, 216235, https://doi.org/10.1175/JAS-D-14-0071.1.

    • Search Google Scholar
    • Export Citation
  • Thompson, G., P. R. Field, R. M. Rasmussen, and W. D. Hall, 2008: Explicit forecasts of winter precipitation using an improved bulk microphysics scheme. Part II: Implementation of a new snow parameterization. Mon. Wea. Rev., 136, 50955115, https://doi.org/10.1175/2008MWR2387.1.

    • Search Google Scholar
    • Export Citation
  • Van Nguyen, H., Y.-L. Chen, and F. Fujioka, 2010: Numerical simulations of island effects on airflow and weather during the summer over the island of Oahu. Mon. Wea. Rev., 138, 22532280, https://doi.org/10.1175/2009MWR3203.1.

    • Search Google Scholar
    • Export Citation
  • Wang, C.-C., and D. J. Kirshbaum, 2015: Thermally forced convection over a mountainous tropical island. J. Atmos. Sci., 72, 24842506, https://doi.org/10.1175/JAS-D-14-0325.1.

    • Search Google Scholar
    • Export Citation
  • Wang, S., and A. H. Sobel, 2017: Factors controlling rain on small tropical islands: Diurnal cycle, large-scale wind speed, and topography. J. Atmos. Sci., 74, 35153532, https://doi.org/10.1175/JAS-D-16-0344.1.

    • Search Google Scholar
    • Export Citation
  • Williams, E., and S. Stanfill, 2002: The physical origin of the land–ocean contrast in lightning activity. C. R. Phys., 3, 12771292, https://doi.org/10.1016/S1631-0705(02)01407-X.

    • Search Google Scholar
    • Export Citation
  • Zhu, L., L. Bai, G. Chen, Y. Q. Sun, and Z. Meng, 2021: Convection initiation associated with ambient winds and local circulations over a tropical island in South China. Geophys. Res. Lett., 48, e2021GL094382, https://doi.org/10.1029/2021GL094382.

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., D. J. Cecil, C. Liu, S. W. Nesbitt, and D. P. Yorty, 2006: Where are the most intense thunderstorms on Earth? Bull. Amer. Meteor. Soc., 87, 10571072, https://doi.org/10.1175/BAMS-87-8-1057.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Islands in TRMM dataset.

  • Fig. 2.

    Maps of terrain height and areal coverage of HI and Oahu (inset) (m).

  • Fig. 3.

    Variation with island area and terrain height of convective metrics averaged over (a)–(c) 24 h and (d)–(f) from 1000 to 1800 LT: intensity measured via (a),(d) Z40max; (b),(e) PCT85min; and (c),(f) frequency. The number of islands in each area-height bin is given in the top inset box; at least five islands were required for a point to be included in the plot. The error bar for each bin represents the standard error (1-σ uncertainty), taking the number of islands as the sample size. Note that the vertical axes in (b) and (e) have been flipped to show a decrease in intensity with height.

  • Fig. 4.

    Number of RPFs vs LT of day. The upper (blue) bars show RPFs, while the lower (red) bars show RPF40s.

  • Fig. 5.

    Simulated maximum height of RPFs and RPF40s vs time of day; (top) two with h = 1 km, U = 2 m s−1, or 8 m s−1 and (bottom) two with h = 2 km, U = 2 m s−1, or 8 m s−1. For each simulation, the intensity is given by the average height of a cluster of large filled circles and the frequency by the number of large circles divided by the number of small circles.

  • Fig. 6.

    Intensity of convection versus h and U for full- and half-sized HI and Oahu, compared to TRMM observations in the nearest respective size category (black). The number of islands in each height bin is given in brackets for islands in TRMM3 and TRMM4, with the error bars being defined in the same way as in Fig. 3. Data points are shown only for WRF simulations that had more than a total of 20 min of deep convection.

  • Fig. 7.

    As in Fig. 6, but for frequency of convection and without requiring the 20-min duration.

  • Fig. 8.

    TRMM: Mean CAPE and CIN vs h and U for all TRMM area bins (compared to Fig. 3d and Fig. 6).

  • Fig. 9.

    Island-averaged CAPE versus h and U in WRF simulations over full HI, half HI, and Oahu (resized to match the area of fullHI) (compared to Fig. 6).

  • Fig. 10.

    WRF: Frequency and intensity versus CAPE and CIN for a range of conditions (all full HI with h = 1 km and U = 2 m s−1, unless otherwise stated). As with Fig. 9, CAPE and CIN have been averaged over land and over the 30-min period before the occurrence of the first RPF40. The black dots represent additional simulations designed to sample a range of CAPE and CIN values (see Table 2). The respective size of each color symbol represents the magnitude of the quantity (with values given in the inset box).

  • Fig. 11.

    Frequency and intensity versus Nconv, the number of grid points where DCI > 100 J kg−1 min−1. The blue and black circles are for individual simulations with heights below and above the threshold, respectively (see text). The green triangles and red squares are averages over h and U, respectively. The golden filled circles are averages over all the simulations in the full HI or half HI bins. The respective size of each color symbol represents the magnitude of the quantity (with values given in the inset box). These simulations are from the MCAPE200W suite.

  • Fig. 12.

    Snapshots of surface equivalent potential temperature taken 30 min before deep convection occurred for three different HI simulations with MCAPE200W. Other quantities plotted include height contours and the coastline (gray boundary).

  • Fig. 13.

    Snapshots of CAPE taken at the same time and for the same HI simulations as in Fig. 12. Other quantities plotted are height contours, wind vectors, and the coastline (gray boundary).

  • Fig. 14.

    Snapshots of surface velocity divergence taken at the same time and for the same HI simulations as in Fig. 12. Other quantities plotted are wind vectors and the coastline (gray boundary).

  • Fig. 15.

    Velocity vectors and divergence field for the same configuration in Fig. 12, but for (a) h = 62 m and (b) 500 m, and taken 30 min after convection had initiated. The plots include contours of vertically integrated hydrometeor content with five contour levels, 0–30 g kg−1 (using a green–white scale).

All Time Past Year Past 30 Days
Abstract Views 24603 24603 0
Full Text Views 2625 2625 1418
PDF Downloads 310 310 91