Changes to regional-scale flow change the climate on the islands, and the islands themselves have their own impact on the regional-scale circulation (as evident in Figure 4). The most obvious impacts of the islands on the regional climate are the introduction of diurnal variability and the increased surface roughness of the island to the otherwise unobstructed easterlies over the open Caribbean Sea. The prescribed RSM Caribbean SSTs are daily averaged. However, the simulated air-sea interface still has diurnal variability due to diurnal varying surface atmospheric conditions and energy budgets. For brevity, the discussion here will concentrate on the ERA-40 downscaling.
 It is only natural to begin with a discussion that contrasts the diurnal variabilities over the islands with the nearby water. That information is presented in Figure 5: the RSM-simulated diurnal variability of the 2 m temperature (T2m), PBL depth (HPBL), and 10 m wind speed (WS10m). Since it is evident from Figure 4 that there is a distinction between the east (upwind, where the mean flow originates) and the west (downwind, where the mean flow is going) of the islands, our composite in Figure 5 is also further divided into downwind and upwind waters. The island average is normalized by total surface area covered by the islands. In other words, the value is biased toward the large islands.
Figure 5. The composite hourly diurnal variability of the (a) 2 m temperature (T2m), (b) PBL depth (HPBL), and (c) 10 m wind speed (WS10m) for all land (“Lesser Antilles Isles”) and water points (“East Caribbean Waters”) within the box (11°N–18°N, 58°W–62.5°W, Trinidad excluded), and water points that are west (downwind “Lee Waters”) and east (upwind “Windward Waters”) of 61°W. Above the plots, (left) S denotes small AWP, (right) L denotes large AWP, and numbers denote years.
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 The simulated diurnal T2m variability over water is much weaker than it is over the islands. During the daytime (nighttime), islands are warmer (colder) than the surrounding waters. Temperatures are highest over the island shortly after noon and are lowest in the dawn hours, with a typical diurnal range of about 5°C. The T2m over water shows signs of a subdiurnal cycle: temperatures are moderately lower (∼0.5°C) during the afternoon hours and are highest during the overnight hours and at dawn. The simulated diurnal variability of HPBL is also higher over the islands than over water, consistent with the diurnal variations of T2m.
 The composite island nighttime/dawn T2m minimum is slightly higher during the large AWP years (<0.3°C). The early afternoon T2m maximum shows a much larger change (∼0.7°C). The simulated island temperature anomalies responding to the surrounding SST anomalies are reflected mostly in the daytime.
 The simulated diurnal variations of WS10m over water are consistent with the lower troposphere wind diurnal cycle as analyzed by M08: surface/lower tropospheric winds are strongest overnight and are weakest during the afternoon. Over the islands, WS10m are much lower; wind speeds are about one fourth of the wind speeds over open waters. Curiously, the wind speed is strongest over the islands during the daytime, when the open water wind speeds are lowest. We will discuss this in further detail in section 4.2.
 The WS10m (T2m) is lower (higher) on the downwind-leeward side of the islands than on the upwind-windward side, but the difference itself is diurnally varying and is largest during the afternoon. Air that is warmed over the island is being advected westward. Therefore, T2m over water west of the islands remains elevated by about 0.1–0.2°C until about 2200 local standard time (LST).
4.2. The Richardson Number Problem
 The question is then “How do the islands modulate the climate in the open water around them”? This is fundamentally tied to how the islands can impact the flow surrounding environment. At first order, the problem is essentially a gradient (derivative)/bulk (finite-differencing) Richardson number (Ri) problem. That is, how do the vertically sheared CLLJ easterlies, strongest in the lower troposphere and weakening toward the surface, respond to the islands' diurnal heating?
where Fr, g, u, v, Tv, and θv take on their usual meanings: the Froude Number, the approximate gravitational acceleration near the Earth's surface (g ≈ 9.81 m s−2), zonal and meridional wind speeds (u, v), virtual temperature (Tv ≈ T(1 + 0.6q)), and virtual potential temperature (θv). The CLLJ is dominated by the zonal component (M08); however, diurnal variations of the meridional component are significant (CV10). During the daytime, the growth of HPBL over the islands (Figure 5b) leads to vertical mixing of potential temperature, moisture (specific humidity, q), and momentum (which leads to the reduction of the vertical shear).
 The impact of the widening of the boundary layer and vertical mixing over the islands is clearly illustrated in Figure 6, where we have plotted the diurnal variability of the vertical differences of q, wind shear, and θv between the 1000 hPa and 925 hPa isobars over the islands. The shear between 925 hPa and 1000 hPa isobars is highest during the nighttime and is reduced during the daytime when stronger easterlies mix down toward the surface (Figure 6b) and strengthen the surface wind speeds (as seen in Figure 5c). The opposite applies with moisture: air is drier aloft, and mixing reduces the negative difference (Figure 6a).
Figure 6. Similar to Figure 5 but for the different islands (labeled) and the difference of (a) specific humidity (q925-q1000), (b) wind shear (squared) (u925 − u1000)2 + (v925 − v1000)2, and (c) virtual potential temperature (θv,925-θv,925) between 925 hPa and 1000 hPa isobars.
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 The reduction of wind shear between 925 hPa and 1000 hPa is associated with a reduction of average wind speed of the lower troposphere. Shown in Figure 7a is the average wind speed (WS) between 925 hPa and 1000 hPa. The average WS is lowest during the daytime (∼0.5 m s−1 less than the nighttime/dawn maximum) as kinetic energy of the mean flow is lost to turbulent kinetic energy (TKE) through diurnal vertical mixing [Holton, 2004].
Figure 7. Same as in Figure 6 but for the 925 hPa and 1000 hPa average WS (1/2(WS925+WS1000)), average Tv (1/2(Tv,925+Tv,1000)), and the difference of 925 hPa and 1000 hPa geopotential height (“thickness,” Z925-Z1000).
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 Considerable PBL variations are observed between the different islands. Some of the individual islands stand out: the small islands have weaker diurnal variations, and Trinidad has a distinctly large variation. All the one-grid-point islands (Nevis, Barbuda, and Montserrat; boldface in Table 1) and some of the smaller islands (Marie Galante and Antigua) have weaker diurnal variability in the vertical wind shear and θv differences.
 The one-grid-point islands, Marie Galante, and Antigua have T2m diurnal variabilities that are comparable to those of the other islands. In Figure 8, we have shown the diurnal variability of the same three variables used in Figure 5 over the individual islands. With the exception of Trinidad, T2m varies between 26°C and 30°C. The three one-grid-point islands stand out in terms of the daily average WS10m, which is higher by about 0.5 m s−1 compared to that of all other “bigger” islands. Unlike the WS10m of the one-grid-point islands, the WS10m of Marie Galante and Antigua is generally comparable to that of the other Lesser Antilles islands (except Trinidad).
Figure 8. Similar to Figure 6 but for the diurnal variability for the ERA-40 downscaled (a) T2m, (b) HPBL, and (c) WS10m over the resolved individual Lesser Antilles isles.
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 Trinidad's diurnal mean and variability are particularly notable. Trinidad is not only the largest of the islands, but it's location, close to the South American coast with far less open water downwind to the west, is unique. Because of its geographical location and its relatively large size among the other Lesser Antilles islands, Trinidad warrants a study specifically focusing on it alone.
 Unlike Trinidad, the one-grid-point islands are crowded toward the northern end of the Lesser Antilles and are the farthest away from the South American coast. We will discuss the location of the one-grid-point islands in detail in section 5 under interannual variability, especially in comparison with Antigua, a “larger” island that is in proximity to the three one-grid-point islands.
 The other islands between Trinidad and the one-grid-point islands have varying degrees of diurnal variability in the 925 hPa and 1000 hPa vertical difference of Tv, θv, q. Using Figure 8 as a reference, we have plotted u925 at the time HPBL are deepest (∼1400 local time) and shallowest (∼0500 local time) in Figure 9. The local 1400 local time u925 is characterized by alternating stronger easterlies between and behind the islands and weaker easterlies in front of (windward side) and behind (leeward side) the islands, a classic signature of lee waves. The feature is simulated regardless of whether the AWP is anomalously large or small. The feature is absent at the northern end of the islands near the one-grid-point islands. At 0500 local time (Figures 9b and 9d), the easterlies are stronger over the open water, and lee wave features are actually less prominent. Easterlies remain relatively weak upwind of the islands in large AWP years as compared to the small AWP years.
Figure 9. The (a, b) small and (c, d) large AWP composite u925 at (left) 1400 local standard time (1800 UT) and (right) 0500 local standard time (0900 UT) over the eastern Caribbean. Contour intervals are 0.5 m s−1.
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 Equation (1) tells us how the island modifies the mean flow when it crosses over the islands. During the daytime, wind speeds increase near the land surface, and vertical shear is reduced as island thermals mix momentum downward. If the islands are “flat,” the diurnal cycle of lower troposphere is controlled only by the diurnal thermals (Ri increases). For “hilly” islands, increased terrain interaction leads to increased mechanical turbulence and gravity waves (Ri decreases).
 The diurnal variations of thickness (Δz) and average Tv between 925 hPa and 1000 hPa isobars are small (Figures 7b and 7c).
The Richardson number diurnal variations become diurnal variations of the vertical shear (squared) and θv differences in the lower troposphere.
where S is the shear term. The diurnal variations of S, Δθv, and Ri of the individual islands are shown in Table 4.
 Ri decreases during the daytime for larger and hillier islands. For smaller islands, Ri increases during the daytime. The hilly islands (such as Guadeloupe and Martinique) have especially low values in the third and sixth columns of Table 4. Terrain heating leads to higher θv on the 1000 hPa isobar through elevated sensible heating. This is the same as saying a smaller Δθv and a stronger reduction of reduced gravity (the Brunt-Väisälä frequency), and that drives Ri down. For the smaller islands with poorly resolved topographic features, the islands act as hot spots with their surface terrain comparatively unimportant. In Table 4, sixth column values are systematically lower than those of the third column. This difference is related to the preferential sensitivity of daytime temperatures to AWP anomalies (see section 5).
 Despite the increased mechanical-generated turbulence for the larger and hillier islands during the daytime, the increase of mechanical lee waves is still fundamentally connected with heating-induced reduction of vertical stability. The above results also show that the modeled island-atmosphere interaction is sensitive to the model-resolved island size and topography.