Report

Development and Initial Evaluation of A Generalized Asymmetric Tropical Cyclone Vortex Model in ADCIRC Jie Gao, Rick Luettich University of North Carolina at Chapel Hill Jason Fleming Seahorse Coastal Consulting ADCIRC Users Group Meeting, USACE Vicksburg, MS, April 29, 2013 Introduction Goal: use tropical cyclone storm parameters provided in NHC ATCF Best Track or Forecast Advisories to generate dynamically consistent pressure and wind fields for storm surge predictions. Storm Parameters lon, lat of center of eye Vmax R64 , R50 , R34 in 4 storm quadrants Pc - ATCF BT only Storm forward motion NW SW NE SE Pn , Rmax - estimated separately Schematic cross section of a hurricane wind field Holland (1980) Wind Model (ADCIRC: NWS=8) Hurricane Isabel of 2003 showing the circular, symmetric eye associated with annular hurricanes at Sept 13 2013 1710Z. The Holland Wind Model produces a symmetric hurricane vortex with the spatially constant Rmax. Hyperbolic hurricane pressure profile (Schloemer 1954): = + − − (1) Substitute into the gradient wind equations, the vortex wind velocity is: = − − + 2 2 − 2 (2) Holland (1980) Wind Model (ADCIRC: NWS=8) Derive relationships for scaling parameters A, B • Assume V=Vmax @ r =Rmax (dV/dr = 0 @ r =Rmax) • Assume Rmax<< Vmax = cyclostrophic wind balance @ r =Rmax • Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms: = (3) 2 − = (4) Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations: = + − − = 2 1− + 2 2 (5) − 2 (6) Holland (1980) Wind Model (ADCIRC: NWS=8) Derive relationships for scaling parameters A, B • Assume V=Vmax @ r =Rmax (dV/dr = 0 @ r =Rmax) • Assume Rmax<< Vmax = cyclostrophic wind balance @ r =Rmax • Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms: = (3) 2 − = Holland “B” (4) Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations: = + − − = 2 1− + 2 2 (5) − 2 (6) Asymmetric Holland Wind Model (ADCIRC: NWS=19) Hurricane Bob of 1991 was extremely asymmetrical, having uneven distribution of the wind radii at Aug 19 1991 1226Z. The asymmetrical characteristic of a hurricane can be addressed in AHW with spatially varying Rmax. • Holland Equations (4), (5), (6) • Use either R64 , R50 , or R34 distance to strongest wind isotach (64kt, 50kt, 34kt) to solve for a different Rmax in each storm quadrant (NE, NW, SW, SE) Holland (1980) Wind Model (ADCIRC: NWS=8) Derive relationships for scaling parameters A, B • Assume V=Vmax @ r =Rmax (dV/dr = 0 @ r =Rmax) • Assume Rmax<< Vmax = cyclostrophic wind balance @ r =Rmax • Setting dV/dr = 0 from Eq. (2) after dropping Corriolis terms: = (3) 2 − = Holland “B” (4) Substitute Eqs. (3) & (4) into Eqs. (1) & (2) - final Holland equations: e.g., Vg=64 kt r=R64 Solve for Rmax = + − − = 2 1− + 2 2 (5) − 2 (6) Asymmetric Holland Wind Model (ADCIRC: NWS=19) Hurricane Bob of 1991 was extremely asymmetrical, having uneven distribution of the wind radii at Aug 19 1991 1226Z. The asymmetrical characteristic of a hurricane can be addressed in AHW with spatially varying Rmax. • Holland Equations (4), (5), (6) • Use either R64 , R50 , or R34 distance to strongest wind isotach (64kt, 50kt, 34kt) to solve for a different Rmax in each storm quadrant (NE, NW, SW, SE) • Interpolate Rmax around storm Rmax (θ) Asymmetric Holland Wind Model (ADCIRC: NWS=19) Hurricane Bob of 1991 was extremely asymmetrical, having uneven distribution of the wind radii at Aug 19 1991 1226Z. The asymmetrical characteristic of a hurricane can be addressed in AHW with spatially varying Rmax. • Holland Equations (4), (5), (6) • Use either R64 , R50 , or R34 distance to strongest wind isotach (64kt, 50kt, 34kt) to solve for a different Rmax in each storm quadrant (NE, NW, SW, SE) • Interpolate Rmax around storm Rmax (θ) , = + − − , = 2 1− + 2 2 (5) − 2 (6) Asymmetric Holland Wind Model (ADCIRC: NWS=19) Problems with Asymmetric Holland Model (AHM) • Inconsistency between Rmax ,Vmax and full gradient wind velocity, Vg , Eq. (6) when Rmax ≮≮ Vmax • In some cases unable to compute Rmax • B is constant in space Eq. (4) • Only uses single (strongest) isotach in each quadrant Generalized Asymmetric Wind Model (GAM) • Start again with the initial pressure and gradient wind equations from Holland (1980) • Do not assume cyclostropic balance dVg/dr = 0 @ r =Rmax , = + − − , = 2 + 1− (7) + 2 2 2 = + − 2 + = 1 + − 2 (8) (9) (10) Comparison of Wind Formulations AHM NWS=19 , = + − − , = 2 1− + 2 2 − 2 2 − = , = + − − 2 + 1− Pressure (6) Wind (4) Holland B GAM , = (5) (7) + 2 2 − 2 (8) 2 () = + − (9) 2 + () = 1 + (10) Implementation of GAM • Procedures B0 , ψ0 • Guess initial values without considering coriolis force ASWIP ADCIRC B,ψ Rmax • Use brute-force marching to solve for Rmax in each quadrant • Re-calculate B and ψ using the latest Rmax in each quadrant Spatial Interpolation • Spatially interpolate Rmax, B, and ψ at each ADCIRC node. converge ? Inputs • Storm center locations, Vmax, Pn, Pc, multiple Isotachs and their radii, etc Output Fort.22 Vg(r, θ), P(r, θ) • Calculate dynamic wind and pressure fields Weighted Composite Wind Field NE Isot 34 Isot 50 Isot 64 Composite SE SW NW Weighted Composite Wind Field NE Isot 34 Isot 50 Isot 64 Composite SE SW NW Weighted Composite Wind Field NE Isot 34 Isot 50 Isot 64 Composite SE SW NW Weighted Composite Wind Field in GAM AHM (NWS = 19) only uses the highest isotach in each quadrant to generate its wind/pressure field. GAM uses a linear weighting of parameter sets computed from all available isotachs in each quadrant. R64 R50 R34 Weighted Composite Wind Field NE Isot 34 Isot 50 Isot 64 Composite SE SW NW Comparison of Spatial Wind Fields (Strong Wind) AHM NWS=19 GAM Comparison of Spatial Wind Fields (Weak Wind) AHM NWS=19 GAM Conclusions • A new “Generalized Asymmetric vortex Model" is implemented in ASWIP / ADCIRC, that solves the full gradient wind equation, and utilizes all available isotachs to generate composite wind fields. • The new formulation allows the model to (i) faithfully represent weaker and larger storms and (ii) to exactly fit multiple wind isotachs that are typically specified in each storm quadrant in either forecast or best track input. • Because GAM is still a parametric model, it lacks complexity when compared to reanalysis H*Wind. Does best available job of representing available ATCF BT / forecast parameters. NWS = 19 GAM H*Wind Thank you! NWS = 19 NWS = 20 H*Wind Comparison of Spatial Wind Fields (Strong Wind) Cont. AHM NWS=19 GAM Comparison of Spatial Wind Fields (Weak Wind) Cont. AHM NWS=19 GAM