Meteo Module

The METEO module was initially developed for simulations of meteotsnamis. It now includes subroutines for simulating the wind effects on waves, storm surges, landslide-generated tsunamis and processes related to atmospheric pressure effects.

  • Wind effect on waves

Wind effects are modeled using the wind stress forcing proposed by Chen et al. (2004). The wind stress is expressed by

(1)\[{\bf R}_w = \frac{\rho_a}{\rho} C_{dw} |{\bf U}_{10} - {\bf C}| ({\bf U}_{10} - {\bf C})\]

where \(\rho_a\) and \(\rho\) represent air density and water density, respectively, \(\bf C\) is wave celerity. The wind stress is only applied on wave crests. A free parameter representing a ratio of the forced crest height to maximum surface elevation is implemented in the model.

  • Holland model

Holland model is an analytic model of wind and pressure profiles described based on Hurricanes. The pressure distribution can be expressed by

(2)\[p = p_c + (p_n-p_c) exp(-A/r^B)\]

where \(p\) is the pressure at radius \(r\), \(p_c\) and \(p_n\) are the central pressure and the ambient pressure, respectively. \(A\) and \(B\) are scaling paramters from the model input. The velocity distribution can be described by

(3)\[V_c = [AB(p_n-p_c)exp(-A/r^B)/\rho_a r^B]^{1/2}\]

Based on the formulations above, it is easy to obtain the following storm parameters

The radius of maximum winds (RMW) is

(4)\[R_w = A^{1/B}\]

The maximum wind speed

(5)\[V_m = C(p_n-p_c)^{1/2}\]

where

(6)\[C = (B/\rho_a e)^{1/2}\]
  • Storm surge

To calculate storm surges, wind stress is applied

(7)\[{\bf R}_w = \frac{\rho_a}{\rho} C_{dw} |{\bf U}_{10}| ({\bf U}_{10})\]

Note that \(\bf C\) is not used, compared to the formula for ‘Wind effect on waves’.

  • Meteotsunami

Meteotsunami is modeled using a pressure source of two-dimensional Gausian distribution:

(8)\[P = dP exp \left(-(\frac{(x^\prime - x_0)^2}{2\sigma_x^2} + \frac{(y^\prime - y_0)^2}{2\sigma_y^2}) \right)\]

where \(dP\) is the pressure anomaly in mb, \((x^\prime,y^\prime)\) are the coordinates rotated to the pressure moving direction (angle is \(\theta\) as indicated in the figure). \(\sigma_x\) and \(\sigma_y\) are paramters representing the length of the width of the pressure source.

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  • Landslide-generated tsunami

Landslide-generated tsunami can be calculated using the same approach as the meteotsunami. Details will be reported by Woodruff (2017).