Python Code
import numpy as np
import matplotlib.pyplot as plt
from io import BytesIO
import base64
# Kinetiverse Hurricane Model Parameters for Hurricane Laura (2020)
CAPE = 2500 # Convective Available Potential Energy (J/kg)
updraft = 25 # Updraft velocity (m/s)
T_freeze = 0.6 # Freezing level temperature factor
S_sat = 0.9 # Saturation factor
UHI_norm = 0.4 # Urban Heat Island factor
V_storm = 6 # Storm translation speed (m/s)
PWAT = 65 # Precipitable water (mm)
shear = 12 # Wind shear (m/s)
slope = 0.1 # Topographic slope
runoff_norm = 0.6 # Normalized runoff factor
S_soil = 0.8 # Soil saturation factor
SST = 30 # Sea surface temperature (°C)
c = 49 # Orbital acceleration (m/s², from JPL Horizons)
SRH = 250 # Storm relative helicity (m²/s²)
shear_max = 22 # Maximum shear (m/s)
shear_std = 2.5 # Shear standard deviation
M_conv_base = 0.6 # Base convergence factor
D_200 = 1.2e-5 # 200 hPa divergence (s⁻¹)
V_LLJ_HAFS = 18 # Low-level jet velocity (m/s)
sigma_slope = 0.12 # Standard deviation of slope
U_drain = 0.5 # Urban drainage efficiency
I_surface = 0.7 # Impervious surface factor
# Reference values
CAPE_ref = 2000 # Reference CAPE (J/kg)
V_ref = 10 # Reference storm speed (m/s)
PWAT_ref = 50 # Reference PWAT (mm)
c_0 = 50 # Reference orbital acceleration (m/s²)
SRH_ref = 200 # Reference SRH (m²/s²)
shear_max_ref = 20 # Reference max shear (m/s)
shear_std_ref = 2 # Reference shear std
D_ref = 1e-5 # Reference divergence (s⁻¹)
V_LLJ_ref = 10 # Reference LLJ velocity (m/s)
sigma_slope_ref = 0.1 # Reference slope std
# Constants
k_hail = 0.000269
k_rain = 0.00012
k_flood = 0.1
k_tornado = 0.0000098
k_hurricane = 8.1
k_wind_tornado = 0.055
k_surge = 10.0
k_topo = 0.1
k_burst = 1.3
nu = 0.15
pwat_scale = 0.0032
k_conv = 0.1
shear_max_scale = 0.05
soil_scale = 0.2
srh_scale = 0.0032
shear_std_scale = 0.02
ef_srh_scale = 0.1
ef_srh = 250
# Kinetiverse Equations
def cape_damp(CAPE, CAPE_ref):
return 1 - 0.1 * (CAPE - CAPE_ref) / CAPE_ref
def convergence_factor(M_conv_base, D_200, D_ref, V_LLJ_HAFS, V_LLJ_ref):
return M_conv_base * (1 + 0.25 * D_200 / D_ref) * (1 + 0.25 * V_LLJ_HAFS / V_LLJ_ref)
def topographic_complexity(sigma_slope, sigma_slope_ref):
return 1 + 0.1 * sigma_slope / sigma_slope_ref
def urban_drainage(U_drain, I_surface):
return 1 - 0.15 * U_drain + 0.2 * I_surface
def hail_size(CAPE, updraft, T_freeze, S_sat, k_hail, cape_damp_val):
return k_hail * np.sqrt(CAPE * updraft) * (1 + 0.2 * T_freeze) * (1 + 0.1 * S_sat) * cape_damp_val
def rainfall(CAPE, S_sat, UHI_norm, V_storm, V_ref, nu, PWAT, PWAT_ref, pwat_scale, k_rain, k_conv, M_conv, shear_max_scale, slope):
return k_rain * CAPE * (1 + 0.2 * S_sat) * (1 + 0.1 * UHI_norm) * (1 - 0.1 * V_storm / V_ref) * \
(1 + nu * V_ref / V_storm) * (1 + pwat_scale * (PWAT - PWAT_ref)**2) * \
(1 + k_conv * M_conv) * (1 + shear_max_scale * slope)
def flooding_index(R_rain, slope, k_flood, k_topo, runoff_norm, soil_scale, S_soil, T_complex, D_urban):
return k_flood * R_rain * (1 + k_topo * slope) * (1 + 0.1 * runoff_norm) * (1 + soil_scale * S_soil) * T_complex * D_urban
def tornado_number(CAPE, shear, UHI_norm, c, c_0, S_sat, k_tornado, k_hurricane, k_burst, SRH, SRH_ref, srh_scale, shear_max, shear_max_ref, shear_max_scale, shear_std, shear_std_ref, shear_std_scale):
srh_factor = 1 + srh_scale * (SRH - SRH_ref)
shear_max_factor = 1 + shear_max_scale * (shear_max - shear_max_ref)
shear_std_factor = 1 + shear_std_scale * (shear_std - shear_std_ref)
return k_tornado * k_hurricane * CAPE * shear * (1 + k_burst * UHI_norm) * (c / c_0) * (1 + 0.1 * S_sat) * srh_factor * shear_max_factor * shear_std_factor
def tornado_speed(CAPE, shear, slope, S_sat, k_wind_tornado, k_topo, SRH, SRH_ref, srh_scale, shear_max, shear_max_ref, shear_max_scale, shear_std, shear_std_ref, shear_std_scale, ef_srh, ef_srh_scale):
srh_factor = 1 + srh_scale * (SRH - SRH_ref)
shear_max_factor = 1 + shear_max_scale * (shear_max - shear_max_ref)
shear_std_factor = 1 + shear_std_scale * (shear_std - shear_std_ref)
ef_factor = 1 + ef_srh_scale * (SRH - ef_srh)
return k_wind_tornado * np.sqrt(CAPE * shear) * (1 + k_topo * slope) * (1 + 0.05 * S_sat) * srh_factor * shear_max_factor * ef_factor * shear_std_factor
def storm_surge(SST, M_conv, slope, c, c_0, k_surge):
SST_norm = (SST - 27) / 27
return k_surge * SST_norm * (1 + 0.3 * M_conv) * (1 + 0.2 * slope) * np.sqrt(c / c_0)
# Calculate predictions
cape_damp_val = cape_damp(CAPE, CAPE_ref)
M_conv = convergence_factor(M_conv_base, D_200, D_ref, V_LLJ_HAFS, V_LLJ_ref)
T_complex = topographic_complexity(sigma_slope, sigma_slope_ref)
D_urban = urban_drainage(U_drain, I_surface)
D_hail = hail_size(CAPE, updraft, T_freeze, S_sat, k_hail, cape_damp_val)
R_rain = rainfall(CAPE, S_sat, UHI_norm, V_storm, V_ref, nu, PWAT, PWAT_ref, pwat_scale, k_rain, k_conv, M_conv, shear_max_scale, slope)
I_flood = flooding_index(R_rain, slope, k_flood, k_topo, runoff_norm, soil_scale, S_soil, T_complex, D_urban)
N_tornado = tornado_number(CAPE, shear, UHI_norm, c, c_0, S_sat, k_tornado, k_hurricane, k_burst, SRH, SRH_ref, srh_scale, shear_max, shear_max_ref, shear_max_scale, shear_std, shear_std_ref, shear_std_scale)
V_tornado = tornado_speed(CAPE, shear, slope, S_sat, k_wind_tornado, k_topo, SRH, SRH_ref, srh_scale, shear_max, shear_max_ref, shear_max_scale, shear_std, shear_std_ref, shear_std_scale, ef_srh, ef_srh_scale)
S_surge = storm_surge(SST, M_conv, slope, c, c_0, k_surge)
# Observed values (approximated from NOAA, NWS, and ABC News reports for Hurricane Laura)
observed = {
'Hail Size (cm)': 2.5, # Approximate, as hail was less prominent
'Rainfall (inches)': 12.0, # 10–15 inches reported
'Flooding Index': 8.0, # Estimated based on severe flooding reports
'Tornado Number': 5.0, # Multiple tornadoes reported
'Tornado Speed (m/s)': 40.0, # EF1–EF2 tornadoes, ~40 m/s
'Storm Surge (ft)': 12.0 # 9–15 ft reported
}
# Predicted values
predicted = {
'Hail Size (cm)': D_hail,
'Rainfall (inches)': R_rain,
'Flooding Index': I_flood,
'Tornado Number': N_tornado,
'Tornado Speed (m/s)': V_tornado,
'Storm Surge (ft)': S_surge
}
# Create comparison table
metrics = list(observed.keys())
table_data = [[metric, f"{observed[metric]:.2f}", f"{predicted[metric]:.2f}", f"{((predicted[metric] - observed[metric]) / observed[metric] * 100):.2f}%"]
for metric in metrics]
# Plot predicted vs actual
fig, ax = plt.subplots(figsize=(8, 6))
for metric in metrics:
ax.scatter(observed[metric], predicted[metric], label=metric)
ax.plot([0, max(max(observed.values()), max(predicted.values()))],
[0, max(max(observed.values()), max(predicted.values()))], 'k--')
ax.set_xlabel('Actual Values')
ax.set_ylabel('Predicted Values')
ax.set_title('Hurricane Laura: Predicted vs. Actual')
ax.legend()
ax.grid(True)
# Save plot to base64 string for HTML embedding
buf = BytesIO()
plt.savefig(buf, format='png', bbox_inches='tight')
plt.close()
img_data = base64.b64encode(buf.getvalue()).decode('utf-8')
# Print results for verification
print("Metric | Actual | Predicted | Error (%)")
for row in table_data:
print(f"{row[0]} | {row[1]} | {row[2]} | {row[3]}")
Equations
The following equations from the Kinetiverse model are implemented in the code above:
\( \langle D_{\text{hail}} \rangle = k_{\text{hail}} \cdot \sqrt{\text{CAPE} \cdot \text{updraft}} \cdot (1 + 0.2 \cdot \text{T}_{\text{freeze}}) \cdot (1 + 0.1 \cdot S_{\text{sat}}) \cdot \text{cape}_{\text{damp}} \)
\( \langle R_{\text{rain}} \rangle = k_{\text{rain}} \cdot \text{CAPE} \cdot (1 + 0.2 \cdot S_{\text{sat}}) \cdot (1 + 0.1 \cdot \text{UHI}_{\text{norm}}) \cdot \left(1 - 0.1 \cdot \frac{V_{\text{storm}}}{V_{\text{ref}}}\right) \cdot \left(1 + \nu \cdot \frac{V_{\text{ref}}}{V_{\text{storm}}}\right) \cdot (1 + \text{pwat}_{\text{scale}} \cdot (\text{PWAT} - \text{PWAT}_{\text{ref}})^2) \cdot (1 + k_{\text{conv}} \cdot \text{M}_{\text{conv}}) \cdot (1 + \text{shear}_{\text{max,scale}} \cdot \text{slope}_{\text{max}}) \)
\( I_{\text{flood}} = k_{\text{flood}} \cdot \langle R_{\text{rain}} \rangle \cdot (1 + k_{\text{topo}} \cdot \text{slope}) \cdot (1 + 0.1 \cdot \text{runoff}_{\text{norm}}) \cdot (1 + \text{soil}_{\text{scale}} \cdot S_{\text{soil}}) \cdot \text{T}_{\text{complex}} \cdot \text{D}_{\text{urban}} \)
\( \langle N_{\text{tornado}} \rangle = k_{\text{tornado}} \cdot k_{\text{hurricane}} \cdot \text{CAPE} \cdot \text{shear} \cdot (1 + k_{\text{burst}} \cdot \text{UHI}_{\text{norm}}) \cdot \left(\frac{c}{c_0}\right) \cdot (1 + 0.1 \cdot S_{\text{sat}}) \cdot \text{srh}_{\text{factor}} \cdot \text{shear}_{\text{max,factor}} \cdot \text{shear}_{\text{std,factor}} \)
\( \langle V_{\text{tornado}} \rangle = k_{\text{wind,tornado}} \cdot \sqrt{\text{CAPE} \cdot \text{shear}} \cdot (1 + k_{\text{topo}} \cdot \text{slope}) \cdot (1 + 0.05 \cdot S_{\text{sat}}) \cdot \text{srh}_{\text{factor}} \cdot \text{shear}_{\text{max,factor}} \cdot \text{ef}_{\text{factor}} \cdot \text{shear}_{\text{std,factor}} \)
\( S_{\text{surge}} = k_{\text{surge}} \cdot \text{SST}_{\text{norm}} \cdot (1 + 0.3 \cdot \text{M}_{\text{conv}}) \cdot (1 + 0.2 \cdot \text{slope}) \cdot \sqrt{\frac{c}{c_0}} \)
Supporting equations for convergence factor, topographic complexity, and urban drainage are also included in the code.
