# 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.

• Landslide-generated tsunami

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