3.1. Spin-Up Period
Kinetic energy spectra were determined for each day in April 2003 at every 6 h interval of the integration period. Figure 3
and Figure 4
show the corresponding kinetic energy spectra for only two days, 2 April 2003 and 6 April 2003, as other days show similar spectra. Figure 3
spectra were derived from model simulations that ingested FNL data as initial while those in Figure 4
were from simulations initialized with NCEP reanalysis. The spin-up period is determined by comparing the slope of the kinetic energy spectra with the
is the wavenumber) dependence which has been observed at the mesoscale scales [63
]. At initialization, that is, zero hours into the forecast, no smaller-scale information is present and the energy content is low (Figure 3
and Figure 4
). Substantial mesoscale information develops by 6 h into the simulation. Spectra for 12 h and 18 h are similar to the 6 h spectra for 2 April 2003. However, for 6 April 2003 the 6 h forecast has not developed sufficiently; by 12 h into the run mesoscale information seems to have fully developed. We therefore chose the first 12 h as the spin-up period for generation of mesoscale information. Thus, the simulation of one diurnal period is a 36 h run with the first 12 h discarded for the development of mesoscale information.
The WRF model develops sufficient mesoscale information 12 h from model initialization thereby providing a spin-up time configuration of 12 h. In addition, the spin-up period of 12 h is in keeping with the corresponding timescales associated with typical mesoscale features. We note that the modelling of some days require a shorter spin-up time of 6 h, and that spin-up time may be dependent on the large-scale atmospheric conditions driving mesoscale phenomena. Therefore, errors between the simulated wind speeds and corresponding observations may be introduced by using a fixed spin-up period of 12 h for all synoptic conditions. However, such errors may be smoothed out when deriving average wind statistics relevant for wind maps. We also found that Skamarock’s spectral method [22
] in which the kinetic energy spectra of model simulations were compared with the typical spectra of mesoscale features is useful for model configuration for regions with limited data sets.
3.3. Sensitivity to PBL Schemes
WRF was run for seven PBL schemes for the month of April 2003 on a grid of 5 km horizontal resolution which is nested within a 25 km resolution parent grid. The mean error statistics in wind speed and wind direction at each site, Table 2
for Piarco and Table 3
for Crown Point, are based on hourly averaged wind speed data from the only two WMO meteorological stations in the southernmost Caribbean islands of Trinidad and Tobago. The comparisons are performed for the 5 km horizontal resolution and we expect that comparative results among the various PBL schemes to hold at the 1 km horizontal resolution as preliminary tests indicate that there is little improvement in error statistics in increasing horizontal resolution from 5 km to 1 km. The results focus on wind speeds rather than wind directions because the main application of the sensitivity tests of this work is in mapping the wind resources of the Trinidad and Tobago.
and Table 3
have two significant features: firstly, against most wind speed error statistics, the TEMF PBL scheme performed the worst at the two sites, and secondly, with the exception of TEMF, no one PBL scheme seems to perform better than any other PBL scheme. The TEMF scheme produced the largest RMSE, MABE, STDE, second largest MBE, smallest R2
coefficient and IOA in wind speed. With the exception of TEMF, the RMSE, MABE, and STDE in wind speed for the other PBL schemes lie within a small range: the RMSE in wind speed was 1.28–1.47 m/s at Piarco and 1.76–2.11 m/s at Crown Point, the MABE was 1.02–1.16 m/s at Piarco and 1.39–1.52 m/s at Crown Point, and STDE was 1.26–1.34 m/s at Piarco and 1.67–1.81 m/s at Crown Point. No one PBL scheme produced the smallest bias error in wind speed at both stations. MYNN 2.5 and UW-TK both produced the smallest RMSE at Piarco and ACM2 had the smallest RMSE at Crown Point. The smallest MABE at Piarco was from the MYNN 2.5 PBL scheme while the smallest MABE at Crown Point resulted from the use of YSU-TOPO. YSU and UW-TK produced the highest R2
coefficient and IOA at Piarco. QNSE gave the highest
at Crown Point and UW-TK, the highest IOA at Crown Point. As no PBL outperforms the other at each station, the mean errors were calculated, which are shown in Table 4
YSU-TOPO provides the smallest overestimation of approximately 0.16 m/s with MYNN 2.5 giving the smallest underestimation of about −0.16 m/s. The RMSE is smallest for ACM2, YSU-NO-TOPO and YSU-TOPO. These PBL schemes also produced the smallest MABE. With the exception of TEMF, the STDE are similar for all PBL schemes tested with PBLs YSU-TOPO, ACM2, UW-TK, and QNSE having approximately the smallest values. The average spatial error statistics therefore indicate that the YSU-TOPO scheme gives the smallest overall spatial errors. PBL schemes were also assessed in their abilities to model the diurnal variation in wind speed. Most PBL schemes were able to replicate the smaller diurnal amplitude at Crown Point (Figure 14
) relative to Piarco (Figure 15
) with the exception of TEMF which significantly underestimates the diurnal amplitude at both sites. Although the YSU-TOPO was chosen as the PBL scheme with best overall spatial performance, it should be noted that YSU overestimates the night-time wind speeds from 10 p.m. to 7 a.m. at both sites with small positive biases from 8 a.m. to 5 p.m. (Figure 14
and Figure 15
In addition, YSU-NO-TOPO and YSU-TOPO produced similar magnitudes in diurnal variation at both sites and along with MYNN 2.5, UW-TK, QNSE and ACM2, these schemes generated daytime maximum wind speeds similar to the observed maximum. For the two sites considered QNSE, TEMF, and UW-TK gave similar nighttime wind speeds and have smaller biases for nighttime winds than other PBL schemes. The diurnal variation at the Piarco site for all PBLs (Figure 15
) show large positive biases for wind speeds less than 2 m/s which occur at night. The PBL schemes do not capture the mean nighttime wind speeds. This has been observed in several other studies [16
] and may be linked to the stable conditions and low turbulence that persist during the night but with the PBL schemes producing too much vertical mixing at night [16
]. The PBL ensemble, however, captures the hourly wind speeds between 8 a.m. and 7 p.m. at Crown Point and 9 a.m. and 5 p.m. at Piarco. Various PBL schemes perform better for each hour. For example, at Piarco, UW-TK best represented the mean hourly wind speeds from 10 p.m.to a.m., MYNN 2.5 from 8 a.m. to 1 p.m., YSU-TOPO from 2 p.m. to 4 p.m., MYJ from 5 p.m.to 6 p.m., and TEMF from 7 p.m. to 9 p.m.
An accurate prediction of the wind speeds is crucial in determining the wind power density (WPD) of each site. The WPD is taken as a measure of the wind potential or resource of a site. Sites with higher wind potential are of greater interest to developers. In this study, the WPD was determined using the standard air density to compare the impact of the PBL-SL predictions of wind speed on WPD. Although the YSU PBL scheme was found to have a positive bias in the wind speed, it provides a conservative estimate and reasonable magnitude of the WPD at the two measurement sites. The YSU-TOPO PBL scheme underestimates the WPD by 2.5 W m−2 at Piarco, even though it predicts a small positive bias in mean monthly wind speed. Although the MYNN 2.5 provides a more conservative estimate for mean wind speed over YSU, it underestimates the mean WPD by 22.1 W m−2. At Crown Point, MYNN 2.5 underestimates the WPD by 32.9 W m−2 compared with YSU’s underestimate of 18.0 W m−2. In contrast, ACM2 overestimates the mean WPD by 4.0 W m−2 at Piarco and 2.9 W m−2 at Crown Point.
In addition to accurately predicting the diurnal evolution of wind speeds, the selected PBL model has to be able to simulate wind speed histograms as wind speed distributions directly impact on the estimate of the WPD. The wind speed distributions are often approximated by probability frequency distributions to estimate the energy output of wind turbines. The two sites, Crown Point and Piarco, are characterized by bimodal wind speed distributions as denoted by the red lines on Figure 16
and Figure 17
. The TEMF and QNSE PBL schemes do not capture the bimodal distribution at Crown Point and Piarco. The MYNN 2.5 also shows such undesired behavior at Crown Point. At Crown Point, YSU-NO-TOPO, YSU-TOPO, and ACM2 underestimate the frequency of the low wind speed intervals 0–1 m/s and 1–2 m/s and overestimate the 5–6 m/s interval at the Crown Point site (Figure 16
). The MYJ better represents the 2–3 m/s and 5–6 m/s intervals. MYJ, YSU, YSU-TOPO, ACM2 captures the wind speed intervals in which the peaks occur. UW-TK overestimates the frequency of wind speed bins less than 4 m/s at Crown Point. At Piarco, ACM2 and UW-TK overestimates the 2–3 m/s interval and underestimates the 4–5 m/s interval frequency. Of the remaining PBL schemes, the MYJ PBL scheme captures the intervals that give the observed frequency distribution its bimodal nature, but underestimates the occurrence of the 0–1 m/s and 1–2 m/s intervals (Figure 17
). The YSU-NO-TOPO, YSU-TOPO, and the MYJ accurately estimate the frequency of the 6–7 m/s wind speed interval, which constitutes the second peak in the wind speed frequency distribution. MYJ overestimates the frequency of the 7–8 m/s while the YSU schemes estimate its frequency more accurately. The YSU schemes tend to overestimate the frequency of the 2–3 m/s, 3–4 m/s, and 5–6 m/s interval frequencies and underestimate the frequency of the 4–5 m/s interval.
In summary, the sensitivity tests to PBL schemes showed that most PBL schemes were able to model the mean wind speed at both stations as well as the diurnal cycle even though all schemes generally overestimated nighttime wind speeds. The YSU-TOPO scheme however, had the smallest spatial average for mean bias error, root-mean-square error and mean absolute error. YSU-TOPO, along with MYJ and ACM2 PBL schemes, provided conservative estimates for the WPD at both sites. One key aspect of this analysis was a qualitative one in which PBLs were assessed in whether they were able to capture the bimodal feature of the wind speed distribution. The bimodal feature is due to the high occurrence of low wind speeds at the 10 m level. Although this qualitative assessment was performed for 10 m level wind speed distributions, it is here hypothesized that schemes capable of capturing the bimodal wind speed distribution at the surface would most likely be able to capture the typical unimodal wind speeds at higher levels above ground.