GRAVITY WAVES, RAINBANDS, AND DEEP CONVECTION INDUCED BY TRADE WIND FLOW PAST PUERTO RICO

 

Shawn P. Bennett
National Weather Service

Vanda Grusbisic and Roy M. Rasmussen
National Center for Atmospheric Research, Boulder, Colorado

INTRODUCTION

Studies based on data collected during the 1985 Joint Hawaii Warm Rain Project and the 1990 Hawaiian Rainband Project (Austin et al. 1996; Smith and Grusbii 1993; Rasmussen et al. 1989; Smolarkiewicz et al. 1988) show that gravity waves, rainbands, and deep convection may form as a result of trade wind flow over a tropical island. These mesoscale phenomenon: gravity waves and rainbands are the source of deep convection that results in frequent heavy rains and flooding in Puerto Rico. Carter and Elsner (1997) describe Puerto Rico has having the greatest recurring threat to life and property due to flash flooding of any U.S. state or territory. Thus, a thorough understanding of the interaction of the trade winds with the topography of Puerto Rico is key to accurate warnings and forecasts. In this paper we will present a comparison of high resolution numerical model results with the Puerto Rico's climatological rainfall pattern and the climatological diurnal wind regimes at San Juan, Mayagüez and Ponce.

GEOGRAPHICAL AND CLIMATOLOGICAL CONTEXT

2.1 Geographical Context

The Commonwealth of Puerto Rico is situated in the northeastern Caribbean Sea (ref. Fig.1). It is the smallest and easternmost island of the Greater Antilles chain. The U.S. Virgin Islands lie just to the east. Puerto Rico stretches about 180 kilometers (112 miles) from west to east and about 65 kilometers (40 miles) from north to south.

Map of Puerto Rico, the Greater Antilles, and the eastern Caribbean Sea



The interior of the island is defined by the Cordillera Central which rises to 1,338 meters (4,389 feet) above sea level at Cerro de Punta (ref. Fig. 2). The northeastern end of the island features the Sierra de Luquillo which contains the Caribbean National Forest.

Smoothed elevation contours (meters) of Puerto Rico



Up to 610 centimeters (240 inches) of annual rainfall have been recorded in the highest peaks of this tropical rainforest, known locally as El Yunque. The highest peaks in the Sierra de Luquillo are El Toro at 1,074 meters (3510 feet), El Yunque at 1065 meters (3494 feet) and Pico del Este at 1051 meters (3448 feet). The north coast is described by a broad coastal plain which rises in a gentle slope toward the interior, while the south coast is marked by a narrow coastal plain that rises steeply toward the Cordillera Central.

2.2 Climatological Patterns: Wind

Puerto Rico's wind regime is characterized by two principal factors: diurnal land and sea breezes, and persistent 10 ms-1 northeasterly trade wind flow. Figure 3 shows a weak nighttime offshore southeasterly land breeze followed by a daytime onshore northeasterly sea breeze at San Juan. Figure 4 shows a weak nighttime offshore easterly land breeze followed by a westerly onshore sea breeze at Mayagüez. Figure 5 shows a weak nighttime offshore northeasterly land breeze followed by a daytime onshore southeasterly sea breeze at Ponce.

Climatology pattern of diurnal winds at San Juan.

 

Climatological pattern of diurnal winds at Mayaguez.

 

Climatological pattern of diurnal winds at Ponce.

 

2.3 Climatological Patterns: Rainfall

Carter et al. (1997) present a study of the Puerto Rico monthly rainfall climatology based on data collected from the National Weather Service cooperative observation network. Daily rainfall totals from 1980-1989 were used. Rainfall from tropical storms and hurricanes were excluded. The 95th percentile values of daily precipitation that were calculated and are shown in Figure 6.

 

95%-ile values of daily precipitation derived from a composite of monthly average rainfall.

 

MODEL SETUP AND DESCRIPTION

We conducted our numerical experiment with a model developed by Smolarkiewicz and described by Smolarkiewicz and Margolin (1996). The model resolution was set at 5 kilometers in the horizontal and 150 meters in the vertical. The model uses a finite difference approximation to the anelastic, non-hydrostatic fluid dynamics equations. Our numerical simulation was initialized with the 1200 UTC 1 October 1995 sounding at San Juan and the diurnal solar cycle for 1 October 1995 and was allowed to run for 24 hours. The island of Puerto Rico was represented in the model by an idealized island geometry and terrain, roughly equivalent to the actual island dimensions (ref. Fig. 8). An average ridge line elevation of 930 meters (3051 feet) was used to represent the Cordillera Central.

3.1 The Froude Number: Flow Reversal, Gravity Waves, Lee Vorticies

Smolarkiewicz and Rotunno (1990), hereafter, SR90, present a numerical study of the flow of an inviscid, non-rotating, density stratified fluid past a three-dimensional obstacle with a Froude number of 0.33. Conceptually, the Froude number is proportional to the ratio of the kinetic energy to potential energy (Fr = U/Nh, where U is the mean upstream flow speed, N is the Brunt-Väisälä frequency, and h is the height of the obstacle). The Froude number calculated from the San Juan sounding used in our numerical simulation was 0.6. Figure 7 (adapted from the first panel of SR90 Fig. 11) shows that in the case where the aspect ratio ß = 0.5, this is the case most closely representing Puerto Rico, lee vortices form without an upwind flow reversal and a standing gravity wave forms just downstream of the ridge axis of the obstacle. We expect that the results of our numerical simulations should be similar to the results presented in Figure 7.

Low Froude number, flow past an idealized obstacle.

 

DISCUSSION

4.1 Model Results: Wind, Theta, qc

Figure 8 shows a daytime xy vector plot of the u wind and u wind perturbation. Wind vectors indicate an onshore northeasterly flow along the north and east coasts and an onshore southeasterly flow along the south coasts and an onshore westerly flow along the west coast where the hint of lee vortices and a flow reversal zone are evident. The wind is decelerating as it encounters the mountain slopes on the east coast and in the flow reversal zone off the west coast. The wind is accelerating as it flows down the slope from the windward (north and east) sides of the island toward the leeward (south and west) sides of the island. Figure 9 shows a nighttime xy vector plot of the u wind and u wind perturbation. This plot shows the diurnal wind reversal in the offshore southeasterly flow along the north coast and in the offshore northeasterly flow along the south coast. An increase in the magnitude of the deceleration of the u wind along the east and west coasts can be seen at night. This may be indicative of the offshore flow associated with the land breeze generated by the diurnal wind reversal opposing the persistent onshore trade wind flow along the east coast and the persistent onshore westerly wind on the west coast. This westerly wind is the manifestation of the flow reversal created by a cyclonic lee vortex off the northwest coast and a anticyclonic lee vortex off the southwest coast of the island. Figure 10 shows the theta perturbation field associated with the flow past the island: a positive theta perturbation along the leeward side of the island and a negative theta perturbation along the windward side. This positive theta perturbation coincides with the regions of flow subsidence on the leeward side of the island while the negative theta perturbation coincides with the region of ascent due to orographic lift on the windward side of the island.

Daytime plot of the u wind an u wind perturbation.

 

Nighttime plot of u wind and u wind perturbation.

 

Morning theta perturbation plot.

 

Figures 11, 12, and 13 are west to east (left to right) cross sections of the island. Figure 11 shows a high amplitude gravity wave anchored over the western slope of the island. A low amplitude gravity wave is anchored just over the crest of the eastern slope of the island. Figure 12 shows the vertical velocity field, w, associated with these gravity waves: a strong positive w over the western slope and weak positive w over the eastern slope. Figure 13 depicts the cloud water field, qc. Two areas should be noted: 1) atop the eastern slope and crest of the ridge, and 2) between 1.5 to 2.5 kilometers altitude just above the maximum intensity of the gravity wave over the western slope. These are the areas that coincide with the highest annual and daily average rainfall. In addition, the area over the western slope is where deep convection regularly occurs in Puerto Rico.

Daytime isentropic cross section plot showing gravity waves over the western and eastern ends of Puerto Rico

 

Daytime plot of vertical velocity.

 

Daytime plot of cloud water.

 

SUMMARY AND CONCLUSIONS

The model simulated wind, cloud water, vertical velocity, and theta perturbation fields were quite similar to the climatological daily wind and rainfall patterns. Although, we do not present model rainfall, we can infer the rainfall pattern, from the theta perturbation , w, and qc plots. Perhaps the most significant finding is that standing gravity waves develop over western and eastern Puerto Rico because of the islands spatial geometry, topography, as well as its typical tropical atmospheric moisture, instability, and trade wind flow regime. These gravity waves are manifested in the form of deep convection and very heavy rainfall that often leads to flash flooding. Other significant findings include: 1) the lack of an upwind flow reversal zone offshore from the eastern end of the island, instead, it appears that flow reversal takes place onshore over the Sierra de Luquillo, in the form of persistent rainshowers and occasional rainbands, 2) cyclonic and anti-cyclonic lee vortices offshore from the western end of the island, 3) a positive theta perturbation on the windward side of the island.

In short, the model simulations have led to improved weather forecasts and warnings through an increase in our understanding of the interaction of the trade winds with the topography of Puerto Rico, and by providing us with a quantitative physical explanation for several interesting hydrometeorological phenomena: the El Yunque tropical rainforest, persistent deep convection and thunderstorm occurrence maxima over western Puerto Rico, the semi-arid southwest coast, and the high average wind speed over the northwest coast.

REFERENCES

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Carter, M.M., and J.B. Elsner, 1997: A statistical method for forecasting rainfall over Puerto Rico, Wea. Forecasting, 9, 265-278.

, S.P. Bennett, J.B. Elsner, 1997: Monthly rainfall climatology for Puerto Rico, submitted to NWS Southern Region, Technical Attachment to Southern Topics, in process.

, and J.B. Elsner, 1996: Convective rainfall regions of Puerto Rico, Int. J. of Climatol. , 16, 1033-1043.

Galianes, M.T., Editor, 1977: Geovisión de Puerto Rico, Universidad de Puerto Rico, 59-62.

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Smolarkiewicz, P.K. and R. Rotunno, 1990: Low Froude number flow past three dimensional obstacles. Part II: Upwind flow reversal zone. J. Atmos. Sci., 47, 1498-1511.

Smolarkiewicz, P.K, and L.G. Margolin, 1996: On Forward-in-Time Differencing for Fluids: an Eulerian/Semi-Lagrangian Non-Hydrostation Model for Stratified Flows, Numerical Methods in Atmospheric and Oceanic Modelling. The Andre J. Robert Memorial Volume (C.Lin, R. Laprise, H. Ritchie, Eds.), Canadian Meteorological and Oceanographic Society, Ottawa, Canada.


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