Analysis of ocean dynamics during the impact of Hurricane Matthew using ocean-atmosphere coupling

2.1 COAWST

The Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modeling System (Warner et al., 2010Warner, J. C.; Armstrong, B.; He, R. & Zambon, J. B. 2010. “Development of a Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modeling System”. Ocean Modelling, 35(3): 230-244, ISSN: 14635003, DOI: 10.1016/j.ocemod.2010.07.010.) was used to study ocean-atmosphere interactions during Hurricane Matthew. In this application, the Regional Oceanic Modeling System (ROMS) (Shchepetkin & McWilliams, 2005Shchepetkin, A. F. & McWilliams, J. C. 2005. “The regional oceanic modeling system (roms): a split-explicit, free-surface, topography-following-coordinate oceanic model”. Ocean Modelling, 9(4): 347-404. DOI: 10.1016/j.ocemod.2004.08.002.; Haidvogel et al., 2008Haidvogel, D. B.; Arango, H.; Budgell, W. P.; Cornuelle, B. D.; Curchitser, E.; Di Lorenzo, E.; Fennel, K.; Geyer, W. R.; Hermann, A. J.; Lanerolle, L.; Levin, J.; McWilliams, J. C.; Miller, A. J.; Moore, A. M.; Powell, T. M.; Shchepetkin, A. F.; Sherwood, C. R.; Signell, R. P.; Warner, J. C. & Wilkin, J. 2008. “Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System”. Journal of Computational Physics, 227(7): 3595-3624, ISSN: 10902716, DOI: 10.1016/j.jcp.2007.06.016.) and the atmospheric model Weather Research and Forecast (Michalakes et al., 2005Michalakes, J.; Dudhia, J.; Gill, D.; Henderson, T.; Klemp, J.; Skamarock, W. & Wang, W. 2005. “The weather research and forecast model: software architecture and performance”. In: Eleventh ECMWF Workshop on the Use of High Performance Computing in Meteorology, World Scientific, pp. 156-168, DOI: 10.1142/9789812701831_0012. , [Consulted: May 12, 2021].) (WRF, as integrated to SisPI) components were two-way coupled using the Model Coupling Toolkit (MCT) (Larson et al., 2005Larson, J.; Jacob, R. & Ong, E. 2005. “The model coupling toolkit: A new Fortran90 toolkit for building multiphysics parallel coupled models”. International Journal of High Performance Computing Applications, 19(3): 277-292, ISSN: 10943420, DOI: 10.1177/1094342005056115.). Also, a method for regridding was used (Warner et al., 2010Warner, J. C.; Armstrong, B.; He, R. & Zambon, J. B. 2010. “Development of a Coupled Ocean-Atmosphere-Wave-Sediment Transport (COAWST) Modeling System”. Ocean Modelling, 35(3): 230-244, ISSN: 14635003, DOI: 10.1016/j.ocemod.2010.07.010.).

2.2 Hurricane Matthew

Hurricane Matthew was a major hurricane that impacted the eastern Cuban coast in October 2016. It is considered the most intense and deadliest system in that hurricane season. Coastal impacts were severe in the regions which the hurricane pass. In Haiti, it provoked significant loss of life and an economic crisis. In the Southwestern United States, the extreme waves and water level caused coastal erosion, in addition to flooding due to storm surge and rainfall (Hegermiller et al., 2019Hegermiller, C. A.; Warner, J. C.; Olabarrieta, M. & Sherwood, C. R. 2019. “Wave - Current Interaction between Hurricane Matthew Wave Fields and the Gulf Stream”. Journal of Physical Oceanography, 49: 2883-2900, DOI: 10.1175/JPO-D-19-0124.1.). In Cuba, material damages were due to strong winds, intense precipitations, storm surge and coastal flooding. (Ballester & Rubiera, 2016Ballester, M. & Rubiera, J. 2016. Temporada ciclónica de 2016 en el Atlántico Norte. Hurricane Season Report, Website of the Cuban Institute of Meteorology. Available: <https://www.insmet.cu/asp/genesis.asp?TB0=PLANTILLAS&TB1=TEMPORADA&TB2=/Temporadas/temporada2016.html>, [Consulted: June 02, 2021].)

2.3 Experiments Design

In order to evaluate the coupled system a 72-hour forecast was performed, initialized on October 4^th (0000 UTC). During this period, the hurricane Matthew directly affected Cuba.

Three numerical experiments were performed. First, using a dynamic SST in the WRF model (WRF(SST)), consistent in a daily upgrade in the atmospheric model; this is the actual configuration used in the SisPI. Second, the oceanic model Regional Ocean Modeling System (ROMS) was used, initializing and upgrading the forcing data with output fields of the Global Forecast System (ROMS(GFS)). Finally, a coupled WRF and ROMS models was performed (WRF-ROMS) using the COAWST Modeling System.

The configurations used in the atmospheric and oceanic models were selected according to the available computational resources.

2.4 Verification data

To evaluate the behavior of the coupled system during hurricane Matthew simulations, data for the minimum center pressure, maximum sustained wind and best track were obtained from Atlantic HURricane DATabase (HURDAT2) (Landsea & Franklin, 2013Landsea, C. W. & Franklin, J. L. 2013. “Atlantic hurricane database uncertainty and presentation of a new database format”. Monthly Weather Review, 141(10): 3576-3592, ISSN: 00270644, DOI: 10.1175/MWR-D-12-00254.1.). For track simulations, the submodule Cysearch, from the Detection, Report and Evaluation Module (MDRE) (Sierra Lorenzo et al., 2016Sierra Lorenzo, M.; Borrajero Montejo, I.; Hinojosa Fernández, M.; Roque Carrasco, A.; Genó Rodríguez, C. F.; Vázquez Proveyer, L. & Ferrer Hernández, A. L. 2016. “Herramientas de detección , reporte y evaluación para salidas de modelos de pronóstico numérico desarrollado en Cuba Detection , reporting and evaluation tools for outputs from numerical forecast models developed in Cuba Introducción”. Revista Cubana de Meteorología, 22(2): 150-163, DOI: ISSN: 0864-151X.) was used.

In the SST analysis, data derived from the geostationary satellite (GOES) were used as verification (Maturi et al., 2008Maturi, E.; Harris, A.; Merchant, C.; Mittaz, J.; Potash, B.; Meng, W. & Sapper, J. 2008. “Noaa’s sea surface temperature products from operational geostationary satellites”. Bulletin of the American Meteorological Society, 89(12): 1877-1888, Available: <https://journals.ametsoc.org/view/journals/bams/89/12/2008bams2528_1.xml.>.). To analyze the SST simulations in each experiment, respect to the GOES data, the Mean Error (ME), Mean-Squared Error (MSE) and Root-Mean-Squared Error (RMSE) were calculated. Those parameters are defined as:

Here n is the total grid points where SST data is obtained, 𝑓 is the SST field in each numerical experiment and 𝑜 is the GOES SST field. The termn $ME=\frac{1}{n}\sum _{i-1}^n(f-0)$ is defined as the absolute error in each grid point.

During the evaluation process, the python language was used (Oliphant, 2007Oliphant, T. E. 2007. “Python for Scientific Computing”. Computing in Science & Engineering, 9: 10-20. DOI: 10.1109/MCSE.2007.58.; Millman & Aivazis, 2011Millman, K. J. & Aivazis, M. 2011. “Python for Scientists and Engineers”. Computing in Science & Engineering, 13: 9-12. DOI: 10.1109/MCSE.2011.36.), mainly the packages Numpy (Van der Walt et al., 2011Van der Walt, S.; Colbert, S. C. & Varoquaux, G. 2011. “The NumPy Array: A Structure for Efficient Numerical Computation.”. Computing in Science & Engineering, 13: 22-30. DOI: 10.1109/MCSE.2011.37.), Scipy (Virtanen et al., 2020Virtanen, P.; Gommers, R.; Oliphant, T.E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; Van der Walt, S.J.; Brett, M.; Wilson, J.; Millman, K.J.; Mayorov, N.; Nelson, A.R.J.; Jones, E.; Kern, R.; Larson, E.; Carey, C.J.; Polat, I.; Feng, Y.; Moore, E.W.; VanderPlas, J.; Laxalde, D.; Perktold, J.; Cimrman, R.; Henriksen, I.; Quintero, E.A.; Harris, C.R.; Archibald, A.M.; Ribeiro, A.H.; Pedregosa, F.; Van Mulbregt, P. & SciPy 1.0 Contributors. 2020. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17(3), 261-272. DOI:10.1038/s41592-019-0686-2.) and Matplotlib (Hunter, 2007Hunter, J. D. 2007. “Matplotlib: A 2D Graphics Environment”. Computing in Science & Engineering, 9: 90-95. DOI: 10.1109/MCSE.2007.55 ).

3.1 Hurricane track simulations

Analyzing the behavior of the hurricane Matthew according to the verification data (best track), it was located at 16.6^o N and 74.6^o W on October 4th, 0000 UTC (when the experiments were initialized). In the first 24 hours it kept a movement to the north and then acquired a W-N component until October 7^th. During the simulation period the hurricane Matthew was considered a major hurricane (Category 3-4, in the Saffir-Simpson scale).

In the track analysis (Figure 2), during the first 12 hours of simulations, the three experiments are in good agreement; until the hurricane center is located inside the geographical area covered by the oceanic mesh. According to the best track, Matthew made landfall on October 5^th, 0000 UTC, in Guantanamo. In the numerical experiments, it made landfall at 20.69 km offset from the real position (best track) in the WRF(SST) and WRF-ROMS experiments and at 38.83 km in the ROMS(GFS) experiment.

Position error, shown in Figure 3, is defined as the difference between the best track and the hurricane center position in each experiment (computed using the Cysearch submodule) at 6 hour’s intervals. Figure 3 shows that the WRF(SST) and WRF-ROMS experiments are in good agreement during the first 24 hours of simulation. The differences between this experiments and the ROMS(GFS) ranges from 1.33 to 18.13 km, being maximum on October 5^th, 0000 UTC.

After 24 hours of forecast the ROMS(GFS) experiment has the lower position errors in track simulations. Also, during the coupling (WRF-ROMS experiment) the errors in track simulations are less than the position errors obtained using the SisPI configuration (WRF(SST) experiment). In general, the coupled system improves predictions with respect to SisPI from 8.51 to 25.92 km; being maximum at 48 hours of forecast (October 6^th at 0000 UTC).

The WRF configuration used in the WRF(SST) and WRF-ROMS numerical experiments is the same used in SisPI, which was evaluated for short term prediction in Cuba (Sierra Lorenzo et al., 2014Sierra Lorenzo, M.; Ferrer Hernández, A. L.; Hernández Valdés, R.; González Mayor, Y.; Cruz Rodríguez, R. C.; Borrajero Montejo, I. & Rodríguez Genó, C. F. 2014. Sistema automático de predicción a mesoescala de cuatro ciclos diarios. Informe de Resultado Científico. 71 p., DOI: 10.13140/RG.2.1.2888.1127 Available: <https://www.researchgate.net/publication/281555728_Sistema_automatico_de_prediccion_a_mesoescala_de_cuatro_ciclos_diarios>, [Consulted: March 12, 2021]., 2017Sierra Lorenzo, M.; Borrajero Montejo, I.; Ferrer Hernández, A. L.; Morfa Ávalos, Y.; Morejón Loyola, Y. & Hinojosa Fernández, M. 2017. Estudios de sensibilidad del SisPI a cambios de la PBL, la cantidad de niveles verticales y, las parametrizaciones de microfísica y cúmulos, a muy alta resolución. Informe de Resultado Científico. 26 p., DOI:10.13140/RG.2.2.29136.00005 .Available: <https://www.researchgate.net/publication/325050959_Estudios_de_sensibilidad_del_SisPI_a_cambios_de_la_PBL_la_cantidad_de_niveles_verticales_y_las_parametrizaciones_de_microfisica_y_cumulos_a_muy_alta_resolucion>, [Consulted: March 14, 2021].). By increasing the simulations period in these experiments, bigger position errors are obtained as is shown in Figure 3.

3.2 SST analysis

The cloudiness associated with the passing of the hurricane does not allow for estimation of SST in the GOES data. Two states are defined in the analysis of the SST field: the initial state of the sea surface thermal field, before the hurricane pass, using the SST data on October 1^st at 0400 UTC; and a final state, after the hurricane pass, with the data corresponding to 8^th at 0500 UTC. Figure 4 shows the SST simulations in the initial and final states (before and after the hurricane passes) in each numerical experiment and the verification (GOES) data.

The SST field behavior is analyzed in each experiment and it is compared with the SST simulation obtained from the GOES data (Figure 4 d)). Using the ROMS model, without and with coupling (Figure 4 b) and c) respectively), the SST simulations are more detailed, while in the WRF(SST) experiment (Figure 4 a)) is more smoothed. However, in both experiments where the ROMS model is used, in some areas the SST values are overestimated, fundamentally at south of Cuba (Figure 4 b) and c), second column); and in other areas (fundamentally in the region of the Bahamas) the SST values are below verification data (Figure 4 b) and c), first column). The differences between the ROMS(GFS) and WRF-ROMS experiments increases with the forecast time.

Figure 5 shows the absolute error field for each experiment, respect to the SST data obtained from the GOES satellite. In Figure 5 b) and c), is shown how the ROMS model configuration used induces that SST values are underestimated in the region of the Bahamas, before and after the hurricane passes. This values of absolute error are the basis in the calculation of the statistical parameters presented in Table 1.

The cooling of the sea surface in the area where the hurricane passes, phenomenon known as coldprint, is shown in Figure 4 for each numerical experiment and the GOES data. The study of this phenomenon depends on the best track (Figure 2). According to the track simulation in each numerical experiment, in the area where the hurricane passes, in the WRF(SST) experiment the SST variation is approximately 1°C while in the experiments which the ROMS model is used (ROMS(GFS) and WRF-ROMS) the SST values decrease approximately 3°C. According to the best track and the SST data obtained from the GOES satellite, the coldprint ranges from 2°C to 3°C.

In the final state, after the hurricane passes (Figure 4, second column), it is necessary to consider the position error in the track simulations (Figure 2 and 3). After going out to sea, at north of Cuba, the hurricane moved faster and its center was located further north in the numerical experiments with respect to the best track. Due to the position error in the last hours of simulation, the cooling of the sea surface in the numerical experiments is observed more to the north than that shown in the SST data obtained from the GOES satellite. Although quantitatively the coldprint phenomenon is better represented in the ROMS model simulations (region of the Bahamas), the position error causes the absolute error in this area to be greater (Figure 5 b) and c)) and therefore the statistics parameters showed in Table 3.

Table 3 shows the Mean Error, the Mean-Squared Error (MSE) and the Root-Mean-Squared Error (RMSE) calculated for each numerical experiment respect to the SST data obtained from the GOES satellite. In the analysis of the sea thermic field, the Mean Error is smaller in the simulations where the ROMS model is used. In the experiment ROMS(GFS) the slightest mean error is obtained after the hurricane passes and in the coldprint simulation. Before the hurricane passes, the mean error is similar in the ROMS(GFS) and WRF-ROMS experiments.

The lowest values of MSE and RMSE are obtained in the WRF(SST) experiment. In the ROMS(GFS) and WRF-ROMS the big values of the absolute error, especially in the Bahamas region, are maximized in the MSE when squared so the highest values of the MSE and RMSE are obtained. However, the values of RMSE differ only in the decimal part.

In general, there are no big differences between the statistics calculated for each numerical experiment (Table 3). This differences are mainly due to the use of a first approximation (not validated) in the ROMS model configuration. For this reason, the statistics shown in Table 3 are a starting point to future sensibility studies.

3.3 Oceanic Mixed Layer

To analyze the behavior of forecast variables in oceanic mixed layer (until 100 meters deep) and the impact of the SST variations in the oceanic dynamic in water of different bathymetry, two points of interest are defined: S1, approximately 2778 meters deep and S2, in shallower waters, approximately 1245 meters deep (Figure 6). This analysis is performed using the numerical experiments which involve the ROMS model (ROMS(GFS) and WRF-ROMS numerical experiments).

In Figures 7 and 8, positive values of U means movement east, V movement north and W vertically upward.

In S1, the behavior of the oceanic variables simulated in both numerical experiments are similar. The net latent heat flux (positive toward ocean), in the first 12 hours of simulation, corresponds to the longwave radiation from the surface to atmosphere and the influences of the hurricane circulation. The next time steps, this output flux intensifies due to the hurricane wind effect. Approximately at 18 hours of simulation, a peak of maximum ascendant flux is reached, associated with the maximum wind velocities located in this point. The amount of heat transferred to the atmosphere begins to decrease after this time, because of the calm in the hurricane eye, and then starts to increase again due to the effect of the winds circulation of the hurricane. After the 30 hours of forecast, in the coupled system, the variations of the net heat flux are dominated by short wave solar radiation demonstrating a clear diurnal cycle throughout the model run.

SST values greater than 27ºC predominated at point S1 during initial forecast interval (0-12 hours) until a depth of 60 meters, which are favorable conditions for a hurricane intensification. After 12 hours of forecast, due to the strong winds and vorticity, the colder water mixes upward, the sea surface gets cold and salinity decreases. Also, there is a stronger upward W-velocity after 24 hours associated with the upwelling due to the hurricane influence, and the magnitude of velocity of the currents is maximum. The U and V currents clearly demonstrate an inertial oscillation after the hurricane’s passage.

At point S2 (Figure 8), where the water is shallower, the dynamics in the mixed layer is different. The thermal inertia is smaller. Due to the shallower depth, the SST varies more abruptly, under the effect of radiation diurnal cycle and the oceanic movements. It is important to take the position error into account in this analysis.

In S2 (Figure 8), after the 36 hours of simulation, the location begins to have influence from the hurricane winds, which causes a SST decrease, a maximum of the ascendant heat flux to the atmosphere, upwelling and a salinity decrease. The change in the surface net heat fluxes is more perceptible in the WRF-ROMS experiment (Figure 8 b)). The SST decreases below 26ºC in both experiments, which is disadvantageous for hurricane development and explains the hurricane weakening in this area observed during coupling simulations.

In general, the bigger differences between the two experiments are obtained in their prediction of the net heat fluxes, mainly in the representation of the diurnal cycle. In the coupled system, the variations of the heat fluxes are more perceptible. During coupling the heat fluxes as computed by the WRF model are used in the ocean model. In the ROMS(GFS) numerical experiment, the implemented surface scheme (COARE) computes turbulent heat fluxes (latent and sensible heat); but radiative fluxes (i.e., shortwave and longwave radiation flux) are not calculated and are provided in the forcing file from the GFS data. These differences in the estimation of the heat fluxes could account the differences observed in the SST simulations.