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CARIBBEAN METOCEAN CLIMATE STATISTICS (CARIMOS) Vincent J. Cardone, President Oceanweather Inc. Cos Cob, CT, USA Specification of the extreme and normal wind and wave climate and basin scale storm surge and 2-D currents by a hindcast approach

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CARIMOS Hindcast Approach Hindcast 109 tropical cyclones 1921 – 1999 Hindcast 15-continuous years 1981 – 1995 Winds and waves: triple nested approach to account for North Atlantic swell input, complex basin morphology, shallow water and island sheltering: 1.25°/.25°/.065° Basin storm surge with 2D hydro model:.25°

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Tropical Cyclones NOAA National Hurricane Center HURDAT Tape. Tropical Cyclone Deck Aircraft Reconnaissance Data. Annual Tropical Storm Reports and Summaries. Published Accounts of Caribbean Storms. Continuous Wind Fields Northern Hemisphere Surface Analysis Final Analysis Series NOAA Tropical Strip surface analyses NOAA NCDC TDF-11 format ship report files Climatological summaries Gridded pressure fields (NCDC Global Historical Fields CD) Global so-called WMO 1000-mb wind fields Gridded digital products of the new NOAA NCEP Global Reanalysis Project, specifically the 6-hourly 1000 mb and 10m surface wind fields.

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Hindcast Model Attributes Swell Grid GRIDSWELL

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Coarse Grid GRIDCOARSE

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Fine Grid GRIDFINE

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Tracks of Tropical Cyclones

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Tropical Wind Model (TC96) Diagnostic PE PBL Model Wind field snapshots Buoy/Rig comparisons show accuracy of +/- 20º in wind direction and +/- 2 m/s in wind speed Applied in worldwide tropical basins

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Tropical Model Snapshot Inputs Speed and direction of vortex motion Equivalent geostrophic flow of the ambient PBL pressure field in which the vortex propagates Central Pressure Scale radius of exponential radial pressure profile Hollands profile peakedness parameter

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Snapshot Solutions

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Wind WorkStation (WWS) Graphical analysis tool for the analysis of marine surface wind fields Blending tropical wind field into synoptic scale Direct analysis of tropical winds

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Wind Fields in Tropical Cyclones

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Tropical Wind Field Methodology Model Inputs Tropical Model WWS Wave Model

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Aircraft Reconnaissance North Atlantic 1944 – present Western North Pacific Image Courtesy of TPC

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Pressure Profile Fit to Aircraft Data

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35/50 Knot Radii Image Courtesy of JTWC

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Tropical Cyclone Snap Database Dp: 2 to 120 mb every 2 mb Rp 5 to 120 Nmi every 4 Nmi B 1 to 2.5 every.1 Maximum Surface Wind Radius of Maximum Wind Azimuthally Averaged Wind Speed in 5 Nmi Bins Radius of 35/50 Knots InputOutput

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QUIKSCAT Scatterometer Winds

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Possible Model Solutions for Dp=90, B=1.00

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Sample QUIKSCAT Fit

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Wind Analysis Distributed Application (HWind)

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HWind vs. Tropical Model Winds Winds on Sept 15 th, GMT HWind: 37.3 m/s NHC: 45.4 m/s TC96/QuikScat: 43.3 m/s TC96HWind

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Sample Workstation Rp Fit in CARIMOS Hurricane

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Sample CARIMOS Hurricane Wind Hindcast

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Sample CARIMOS Wave Hindcast

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Continuous Wind Fields NOAA NCEP Reanalysis 10-m winds First iteration revealed biases Interactive Objective Kinematic Analysis (IOKA)

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Validation Tropical Cyclones – rely on extensive prior validation in tropical regimes such as Gulf of Mexico, South China Sea… Continuous – utilize buoy and satellite altimeter measured winds and sea states

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Model Validation - Buoy Data

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Hindcast vs Buoy 41018

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Wind and Wave Statistics for CARIMOS Operational Hindcast vs. Buoy 41018

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Model Distributional Validation vs. Buoy

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Model Validation - Altimeter Data

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Model Distributional Validation - Altimeter

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Wind and Wave Statistics for CARIMOS Operational Hindcast vs. Altimeter Data

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Model Validation Altimeter

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CARIMOS Derivative Products Continuous Hindcast - site specific Time series 15 years, 3-hourly Bivariate distributions (HS-TP, HS-VMD, WS-WD) Duration/persistence distributions Extremes Time series in storms, hourly Return period extremes of WS, HS, HM, HC, TP, Va, Sh 1 year to 100 years

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CARIMOS Wind and Wave Fields Definitions FieldDescription Date Julian format (where Jan = 1, Jan = 2, etc.) Wind Direction From which the wind is blowing, clockwise from true north in degrees (meteorological convention). Wind Speed 1-hour average of the effective neutral wind at a height of 10 meters, units in meters/second.

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Total Spectrum Wave Fields: Total Variance The sum of the variance components of the hindcast spectrum, over the 552 bins of the wave model, in meters squared. Significant Wave Height times the square root of the total variance, in meters. Peak Spectral Period Peak period is the reciprocal of peak frequency, in seconds. Peak frequency is computed by taking the spectral density in each frequency bin, and fitting a parabola to the highest density and one neighbor on each side. If highest density is in the Hz bin, the peak period reported is the peak period of a Pierson-Moskowitz spectrum having the same total variance as the hindcast spectrum. Vector Mean Direction To which waves are traveling, clockwise from north in degrees (oceanographic convention).

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First Spectral Moment Following Haring and Heideman (OTC 3280, 1978) the first and second moments contain powers of = 2 f; thus: where dS is a variance component and the double sum extend over 552 bins. Second Spectral Moment Following Haring and Heideman (OTC 3280, 1978) the first and second moments contain powers of = 2 f; thus: where dS is a variance component and the double sum extend over 552 bins. Dominant Direction Following Haring and Heideman, the dominant direction is the solution of the equations The angle is determined only to within 180 degrees. Haring and Heideman choose from the pair (, +180) the value closer to the peak direction.

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Angular Spreading The angular spreading function (Gumbel, Greenwood & Durand) is the mean value, over the 552 bins, of cos( -VMD), weighted by the variance component in each bin. If the angular spectrum is uniformly distributed over 360 degrees, this statistic is zero; if uniformly distributed over 180 degrees, 2/ ; if all variance is concentrated at the VMD, 1. For the use of this statistic in fitting an exponential distribution to the angular spectrum, see Pearson & Hartley, Biometrika Tables for statisticians, 2:123 ff. Angular spreading (ANGSPR) is related to cos n spreading as follows: n = (2*ANGSPR)/(1-ANGSPR) In-Line Variance Ratio Directional spreading by Haring and Heideman, p Computed as: If spectral variance is uniformly distributed over the entire compass, or over a semicircle, Rat = 0.5; if variance is confined to one angular band, or to two band 180 degrees apart, Rat = According to Haring and Heideman, cos^2 spreading corresponds to Rat = 0.75.

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Wave Partition Fields (Sea/Swell): Total Variance of Sea Partition Peak Spectral Period of Sea Partition Vector Mean Direction of Sea Partition Total Variance of Swell Partition Peak Spectral Period of Swell Partition Vector Mean Direction of Swell Partition Explanation of sea/swell computation: The sum of the variance components of the hindcast spectrum, over the 552 bins of the wave model, in meters squared. To partition sea (primary) and swell (secondary) we compute a P-M (Pierson-Moskowitz) spectrum, with a cos 3 spreading, from the adopted wind speed and direction. For each of the 552 bins, the lesser of the hindcast variance component and P-M variance component is thrown into the sea partition; the excess, if any, of hindcast over P-M is thrown into the swell partition.

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Sample Storm Peak Table Storm Peaks 23 Peaks found > 4 within a window of 72 hours. CS Gpt 3106, Lat 15.0n, Long 75.0w, Depth m Defined Period: Storms Date Ranges: 9/8/ :00 to 10/2/ :00 CCYYMM DDHHmm WD WS ETOT TP VMD MO1 MO2 HS DMDIR ANGSPR INLINE HSUR CS CD MaxWAVE CREST W/HS C/HS deg m/s m^2 sec deg m^2/s m2/s2 m deg cm cm/s deg m m

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Computation of Maximum Individual Wave Height in a Storm The program evaluates Borgman's (1973) integral: where H is the largest wave height; a 2 is the mean square height taken as a function of time, t; t a and t b are the beginning and end of the storm; and T(t) is the wave period, taken here is the significant wave period. Maximum Individual Wave Height (Forristall, 1978): T = M 0 /M 1

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Computation of Maximum Individual Crest Height in a Storm Maximum Crest Height (Haring and Heideman, 1978): where h is elevation and d is water depth T =.74 TP TP is the reciprocal of fpeak, found by solving by inverse interpolation The median of the resulting distribution was taken as the maximum expected single peak in the storm.

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Extremal Analysis Storm Peak Table Issues Peaks over threshold vs annual maximum Selection of distribution Selection of fitting threshold Site averaging

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Algorithm - Return-Period Extremes Calculation of Return-Period Extremes The distributional assumptions used are: 1.Gumbel distribution of extremes: 2.Borgman distributions of extremes, i.e., Gumbel distribution of squared extremes: 3.Galton distribution of height, i.e. normal distribution of log heights: 4.Weibull distribution described in next section The fitting procedure of Gumbel (1958, pp ) was followed for Gumbel, Borgman and Galton, with plotting positions based in i/(n+1), often called Weibull plotting position., where

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Climate Variability - Impact on Design Wave Criteria Cold Years 100-year Hs7.4m (Gumbel) 100-year Hs7.9m (Weibull) Warm Years 100-year Hs9.9m (Gumbel) 100-year Hs10.3m (Weibull) Overall 100-year Hs9.0m (Gumbel) 100-year Hs9.2m (Weibull)

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Tropical Cyclone Variability (From Goldberg et al., Science, 293, 20 July, 2001)

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Significant Wave Height Interannual Variability of Exceedence Value

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Conclusions Demonstration that CARIMOS provides a very skillful model for normal conditions Importance of due consideration to decadal climatic trends, 25% difference in extreme wave heights Importance of due consideration in inter- annual variability upto 100% difference in values of 90% and 99% exceedences

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