CARIBBEAN METOCEAN CLIMATE STATISTICS (CARIMOS) Vincent J. Cardone, President Oceanweather Inc. Cos Cob, CT, USA Specification of the extreme and normal.

CARIBBEAN METOCEAN CLIMATE STATISTICS

(CARIMOS)

Vincent J. Cardone, PresidentOceanweather 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

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°

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.

Hindcast Model Attributes Swell Grid

GRID SWELL

Coarse Grid

GRID COARSE

Fine Grid

GRID FINE

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4°N

4°N

6°N

6°N

8°N

8°N

10°

N

10°

N

12°

N

12°

N

14°

N

14°

N

16°

N

16°

N

18°

N

18°N

64°W

64°W

62°W

62°W

60°W

60°W

58°W

58°W

56°W

56°W54°W 54°W

Tracks of Tropical Cyclones

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

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

• Holland’s profile peakedness parameter

Snapshot Solutions

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

Wind Fields in Tropical Cyclones

Tropical Wind Field

Methodology

Model InputsModel Inputs

Tropical ModelTropical Model

WWSWWS

Wave ModelWave Model

Aircraft Reconnaissance

• North Atlantic1944 – present

• Western North Pacific 1944-1986

Image Courtesy of TPC

Bi

r

Rpin

i

i edpprp)(

1

0)(

Pressure Profile Fit to Aircraft Data

35/50 Knot Radii

Image Courtesy of JTWC

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

Input Output

QUIKSCAT Scatterometer

Winds

http://winds.jpl.nasa.gov/news/new_oceans.html

Possible Model Solutions for Dp=90, B=1.00

Sample QUIKSCAT Fit

Wind Analysis

Distributed Application

(HWind)

HWind vs. Tropical Model Winds

Winds on Sept 15th, 2000 15GMT

HWind: 37.3 m/s NHC: 45.4 m/s TC96/QuikScat: 43.3 m/s

TC96HWind

Sample Workstation Rp Fit in CARIMOS Hurricane

Sample CARIMOS Hurricane Wind Hindcast

Sample CARIMOS Wave Hindcast

Continuous Wind Fields

• NOAA NCEP Reanalysis 10-m winds• First iteration revealed biases• Interactive Objective Kinematic Analysis

(IOKA)

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

Model Validation - Buoy Data

Hindcast vs Buoy 41018

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

Model Distributional Validation vs. Buoy

Model Validation - Altimeter Data

Data Set 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94

CARIMOS Continuous Hindcast

GEOSAT - Geodetic Mission

GEOSAT - Exact Repeat Mission

ERS-1

TOPEX/POSEIDON

Model Distributional Validation - Altimeter

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

Model Validation Altimeter

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

CARIMOS Wind and Wave Fields Definitions

Field Description

Date Julian format (where Jan 1 1900 = 1, Jan 2 1900 = 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.

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 4.000 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 .32157 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).

First Spectral Moment Following Haring and Heideman (OTC 3280, 1978) the first and second moments contain powers of = 2f; 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 = 2f; 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.

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 cosn spreading as follows:n = (2*ANGSPR)/(1-ANGSPR)

In-Line Variance Ratio Directional spreading by Haring and Heideman, p 1542. 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 = 1.00 . According to Haring and Heideman, cos^2 spreading corresponds to Rat = 0.75.

Wave Partition Fields (Sea/Swell):

Total Variance of “Sea” PartitionPeak Spectral Period of “Sea” PartitionVector Mean Direction of “Sea” PartitionTotal Variance of “Swell” PartitionPeak Spectral Period of “Swell” PartitionVector 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 cos3 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.

Sample Storm Peak TableStorm Peaks

23 Peaks found > 4 within a window of 72 hours.

CS Gpt 3106, Lat 15.0n, Long 75.0w, Depth 4024.333mDefined Period: Storms

Date Ranges: 9/8/1921 01:00 to 10/2/2000 18:00

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 195509 252300 80.9 26.93 4.863 11.742 258.1 3.457 2.837 8.821 264.5 0.8032 0.7198 10.9 0.2 282.6 15.101 8.358 1.7120 0.9476195109 041500 316.3 19.98 4.370 12.223 200.6 3.089 2.567 8.362 213.1 0.7204 0.6252 16.1 0.3 180.6 14.552 8.028 1.7402 0.9601199911 151700 165.0 22.58 4.237 11.753 27.1 3.037 2.537 8.234 40.3 0.6990 0.6007 28.2 0.2 22.5 14.162 7.830 1.7199 0.9510194109 261300 49.7 23.15 4.211 11.552 244.1 3.024 2.510 8.209 250.0 0.7953 0.6994 8.2 0.3 233.0 14.654 8.135 1.7851 0.9910194208 241200 254.0 21.04 3.259 11.768 177.3 2.417 2.112 7.221 208.7 0.6100 0.5681 12.4 0.5 147.3 12.860 7.105 1.7809 0.9839193309 192100 223.2 16.67 2.798 12.663 189.0 2.029 1.782 6.691 219.7 0.5800 0.6305 8.0 0.4 131.5 11.855 6.528 1.7718 0.9756196007 130300 337.4 12.84 2.479 11.439 209.8 1.889 1.693 6.297 218.8 0.7640 0.6685 9.1 0.1 147.8 11.030 6.085 1.7517 0.9664196107 220300 58.0 18.37 2.409 10.859 250.3 1.868 1.705 6.208 256.3 0.7980 0.7000 1.2 0.1 254.6 11.080 6.143 1.7847 0.9896198008 060100 288.9 7.49 2.183 15.563 226.9 1.367 1.108 5.910 238.2 0.7859 0.7633 6.1 0.1 127.7 10.556 5.807 1.7861 0.9826198809 120900 224.1 13.68 1.778 14.382 193.5 1.422 1.428 5.334 230.8 0.3029 0.7310 1.8 0.2 120.8 9.777 5.335 1.8330 1.0002194408 200400 276.1 11.65 1.707 13.778 195.0 1.261 1.170 5.227 218.4 0.6766 0.6707 2.9 0.3 139.7 9.742 5.361 1.8638 1.0256193211 041800 44.5 16.05 1.596 10.357 250.8 1.332 1.295 5.054 255.7 0.7443 0.6334 1.6 0.2 218.1 9.687 5.396 1.9168 1.0677196908 302100 156.2 8.24 1.546 10.026 230.6 1.273 1.216 4.974 237.4 0.7818 0.6863 10.1 0.0 222.7 8.731 4.833 1.7553 0.9716197809 160000 53.9 16.07 1.425 9.660 248.2 1.233 1.235 4.775 253.2 0.8026 0.7042 2.8 0.1 248.2 8.737 4.851 1.8298 1.0159193808 231300 159.6 17.91 1.277 9.414 236.4 1.129 1.147 4.520 243.8 0.7691 0.6784 11.8 0.1 285.6 7.829 4.332 1.7321 0.9584197909 010000 38.3 6.23 1.236 16.425 239.0 0.815 0.706 4.447 242.5 0.8933 0.8501 0.7 0.1 97.8 8.246 4.510 1.8542 1.0141195410 101100 102.7 19.92 1.194 8.139 283.8 1.140 1.213 4.371 283.3 0.8151 0.7283 4.5 0.4 265.5 8.310 4.635 1.9011 1.0605197108 211800 86.5 7.04 1.190 11.861 227.4 0.960 0.935 4.363 233.9 0.8277 0.7494 1.1 0.1 105.3 7.715 4.235 1.7682 0.9707193808 112300 193.3 8.65 1.176 11.520 215.1 0.901 0.837 4.338 228.2 0.6592 0.6869 1.1 0.2 123.2 7.647 4.220 1.7627 0.9729197109 081400 65.1 15.12 1.175 8.943 253.4 1.063 1.112 4.336 258.3 0.8063 0.7073 1.5 0.1 267.5 7.845 4.357 1.8093 1.0049193108 130900 250.5 12.18 1.164 10.660 208.0 1.009 1.040 4.315 226.9 0.6919 0.6768 3.8 0.2 133.5 7.587 4.173 1.7582 0.9672193307 010100 73.6 15.24 1.143 8.956 261.2 1.039 1.084 4.277 264.7 0.8170 0.7199 2.9 0.1 297.1 7.997 4.451 1.8697 1.0407195108 171700 227.1 3.90 1.100 12.848 230.7 0.726 0.575 4.196 234.4 0.8790 0.8235 0.7 0.2 120.9 7.566 4.189 1.8031 0.9984

Computation of Maximum Individual Wave Height in a Storm

The program evaluates Borgman's (1973) integral:

where H is the largest wave height; a2 is the mean square height taken as a function of time, t; ta and tb 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 = M0/M1

M8h1.08311- = h} > {H Pr

0

2 1.063

exp

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.

0 = f

S2

2

Extremal Analysis

• Storm Peak Table• Issues Peaks over threshold vs annual

maximum Selection of distribution Selection of fitting threshold Site averaging

Algorithm - Return-Period ExtremesCalculation 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. 34 - 36) was followed for Gumbel, Borgmanand Galton, with plotting positions based in i/(n+1), often called Weibull plotting position.

b

h - a - = } h H { Pr1

1expexp

b

h - a - = } h H { Pr2

22expexp

dt 2t-

2

1 = } h H { Pr

2x

exp b

a-h = x

3

3log, where

Climate Variability - Impact on Design Wave Criteria

Cold Years

100-year Hs 7.4m (Gumbel)

100-year Hs 7.9m (Weibull)

Warm Years



Overall



Tropical Cyclone Variability

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

Significant Wave Height Interannual Variability of Exceedence Value

Significant Wave Height Interannual Variability of Exceedence Value

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

CARIBBEAN METOCEAN CLIMATE STATISTICS (CARIMOS) Vincent J. Cardone, President Oceanweather Inc. Cos Cob, CT, USA Specification of the extreme and normal.

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