Friday, September 12, 2014

calculus introduction

This site seems to be best site introducing calculus.

http://www.wyzant.com/resources/lessons/math/calculus/integration/ftoc

algebra : 代数 is the study of operations
calculus : 积分 is the mathematical study of change : the branch of mathematics that
         deals with the finding and properties of derivatives and integrals of
         functions, by methods originally based on the summation of infinitesimal
         differences. The two main types are differential calculus(微分) and
         integral calculus (积分).
geometry : 几何 is the study of shape : the branch of mathematics concerned
        with the properties and relations of points, lines, surfaces, solids, and
        higher dimensional analogs.
dividend : number to be divided

Wednesday, September 10, 2014

Math expresssion pronunciation

Tuesday, September 9, 2014

Hurricane forecast models

Hurricane forecast models

Refer to here: http://www.nhc.noaa.gov/modelsummary.shtml

http://derecho.math.uwm.edu/models/models.html

Official Forecasts

These five identifiers represent forecasts issued by NOAA's National Hurricane Center (NHC), Central Pacific Hurricane Center (CPHC), Weather Prediction Center (formerly Hydrometeorological Prediction Center), and Ocean Prediction Center. While derived from official sources of information, they should NOT be considered to be official.

OFCL	Official NHC/CPHC Forecast
OFCI	Official NHC/CPHC Forecast Interpolated Ahead 6 hr
OHPC	Official Hydrometeorological Prediction Center Forecast
OOPC	Official Ocean Prediction Center Forecast

Dynamical Models

These identifiers represent forecasts obtained from weather forecast models that solve mathematical equations that describe how wind, temperature, and moisture evolve within the atmosphere. Most of these models forecast the weather over the entire globe and are not specifically designed for tropical storm and hurricane forecasting.

AVNO / GFSO	Global Forecast System Model Forecast
AVNI / GFSI	Previous GFS Forecast Interpolated Ahead 6 hr
AP##	GFS Ensemble Member Forecast (## = 01 to 20)
AEMN	GFS Ensemble Mean Forecast
AEMI	Previous AEMN Forecast Interpolated Ahead 6 hr
CMC	Canadian Global Model Forecast
CMCI	Previous CMC Forecast Interpolated Ahead 6 hr
COTC	U.S. Navy COAMPS-TC Model Forecast
COTI	U.S. Navy COAMPS-TC Model Forecast Interpolated Ahead 6 hr
COAL	U.S. Navy COAMPS-TC Model Forecast, Atlantic Basin
COAI	Previous COAMPS-TC Atlantic Forecast Interpolated Ahead 6 hr
COCE	U.S. Navy COAMPS-TC Model Forecast, E. Pacific Basin
COEI	Previous COAMPS-TC E. Pacific Forecast Interpolated Ahead 6 hr
EGRR / UKX	UKMET Model Forecast
EGRI / UKXI	Previous UKMET Forecast Interpolated Ahead 6 hr
EMX / ECMF	ECMWF Model Forecast (rare)
EMXI	Previous ECMWF Forecast Interpolated Ahead 6 hr (rare)
NAM	North American Mesoscale Model Forecast
NAMI	Previous NAM Forecast Interpolated Ahead 6 hr
NGPS / NGX	U.S. Navy NOGAPS Model Forecast
NGPI / NGXI	Previous NOGAPS Forecast Interpolated Ahead 6 hr
NVGM	U.S. Navy NAVGEM Model Forecast
NVGI	Previous NAVGEM Forecast Interpolated Ahead 6 hr

Limited-Area Dynamical Models

These identifiers represent forecasts obtained from weather forecast models that solve mathematical equations that describe how wind, temperature, and moisture evolve within the atmosphere. Unlike the "Dynamical Models" above, however, these models forecast the weather only over a small portion of the globe and are specifically developed to forecast tropical storms and hurricanes.

GFDL	GFDL Hurricane Model Forecast Track/Intensity
GFDI	Previous GFDL Forecast Interpolated Ahead 6 hr
GHMI	Previous Intensity-Modified GFDL Forecast Interpolated Ahead 6 hr
GFDT	GFDL Forecast Using a Different Vortex Tracking Algorithm
GFTI	Previous GFDT Forecast Interpolated Ahead 6 hr
GFDN	Navy-Initialized Version of the GFDL Hurricane Model
GFNI	Previous Navy-Initialized GFDL Forecast Interpolated Ahead 6 hr
GFDE	Extrapolated GFDL Forecast
HWRF	HWRF Hurricane Model Forecast Track/Intensity
HWFI	Previous HWRF Forecast Interpolated Ahead 6 hr

Consensus Models

These identifiers represent forecasts obtained from the average, or consensus, of multiple weather forecast model track and/or intensity forecasts. Simple averaging, weighted averaging, and bias-corrected averaging procedures may be used, depending upon the consensus model in question.

IVCN	Variable Intensity Consensus of DSHP, LGEM, HWFI, GHMI, and GFNI Models
GUNA	Consensus of AVNI, GFDI, EGRI and NGPI Model Track Forecasts
CGUN	Bias-Corrected GUNA Forecast
TCON / TCOE	Consensus of AVNI, EGRI, NGPI, GHMI, and HWFI Model Track Forecasts
TCOA	Consensus of AVNI, EGRI, GHMI, and HWFI Model Track Forecasts
TCCN	Bias-Corrected TCON Forecast
TVCN	Variable Consensus of AVNI, EGRI, EMXI, NGPI, GHMI, HWFI Model Track Forecasts
TVCE	Variable Consensus of AVNI, EGRI, EMXI, NGPI, GHMI, GFNI, HWFI Model Track Forecasts
TVCA	Variable Consensus of AVNI, EGRI, EMXI, GHMI, GFNI, HWFI Model Track Forecasts
TVCC	Bias-Corrected TVCN Forecast
RYOC / MYOC	Forecaster-Generated Consensus Guidance (rare)

Statistical and Statistical-Dynamical Models

These identifiers represent forecasts obtained from weather forecast models that solve statistical equations that describe how a tropical storm or hurricane moves and/or changes intensity in response to climatology and/or present and forecast weather conditions in its proximity. These models are less complex than the "Dynamical Models" and "Limited-Area Dynamical Models" described above; however, many of them are as skillful, if not more skillful, than the more complex models.

A98E	NHC-98 Track Model (old, unreliable)
BAMD	Deep-Layer Beta and Advection Model Track Forecast
BAMM	Medium-Layer Beta and Advection Model Track Forecast
BAMS	Shallow-Layer Beta and Advection Model Track Forecast
CLIP	72-hr Climatology and Persistence Track Forecast
CLP5	120-hr Climatology and Persistence Track Forecast
LBAR	Limited Area Barotropic Model Track Forecast (old, unreliable)
LGEM	Logistical Growth Error Model Intensity Forecast
SHFR	72-hr SHIFOR Model Intensity Forecast
SHF5	120-hr SHIFOR Model Intensity Forecast
DSHF	120-hr Decay SHIFOR Model Intensity Forecast
SHIP	SHIPS Model Intensity Forecast
DSHP	Decay SHIPS Model Intensity Forecast
DRCL	DeMaria Climatology and Persistence Model Intensity Forecast
MRCL	McAdie Climatology and Persistence Model Intensity Forecast
RI##	Rapid Intensification Aid (## = 25, 30, 35, 40)

Experimental Models (HFIP Stream 1.5)

From time to time, additional models in the Hurricane Forecast Improvement Program, or HFIP, quasi-operational "Stream 1.5" may appear within the guidance products. The identifiers below represent forecasts from models that NHC forecasters are currently evaluating for possible future use in actual NHC forecast operations. The most up-to-date information on these experimental products may always be found at the HFIP Home Page.

FIM9	Finite-Volume Icosahedral Model Forecast
FM9I	Previous FIM9 Forecast Interpolated Ahead 6 hr
CTCX	Experimental U.S. Navy COAMPS-TC Model Forecast
CXTI	Previous Experimental COAMPS-TC Forecast Interpolated Ahead 6 hr
HWFH	Experimental NOAA/HRD HWRF Forecast
HWHI	Previous Experimental NOAA/HRD HWRF Forecast Interpolated Ahead 6 hr
GP##	GFDL Ensemble Member Forecast (## = 00 to 09)
GPMN	GFDL Ensemble Mean Forecast
GPMI	Previous GFDL Ens. Mean Forecast Interpolated Ahead 6 hr
HHYC	HWRF with HYCOM Ocean Model
HHYI	Previous HWRF with HYCOM Ocean Model Forecast Interpolated Ahead 6 hr
HW##	HWRF Ensemble Member Forecast (## = 00 to 20)
HWMN	HWRF Ensemble Mean Forecast
HWMI	Previous HWRF Ens. Mean Forecast Interpolated Ahead 6 hr
UWN4	University of Wisconsin NMS Model Forecast
UW4I	Previous UW NMS Forecast Interpolated Ahead 6 hr
TV15	Consensus of Available HFIP Stream 1.5 Model Forecasts
MMSE	FSU Multimodel Superensemble
SPC3	Statistical Prediction of Intensity Forecast (six members)

Early Versus Late Models

The National Hurricane Center and other official tropical cyclone forecast centers make use of two different forms of dynamical model guidance during the forecast process: "early" and "late" models. Numerical models are typically run four times per day: 0000, 0600, 1200, and 1800 UTC. These times correspond to 8 pm, 2 am, 8 am, and 2 pm EDT, respectively. However, National Hurricane Center official forecasts are issued at 0300, 0900, 1500, and 2100 UTC. These times correspond to 11 pm, 5 am, 11 am, and 5 pm EDT, respectively. Ideally, model forecasts from the 0000 UTC cycle would be available to help make the 0300 UTC forecast (for example); however, as modern numerical weather prediction models typically require several hours to complete a given forecast cycle, this is often not possible.
To alleviate this, model forecasts from the previous cycle, or 1800 UTC in our current example, are shifted forward in time by 6 hr. This results in what is known as an interpolated, or "early", model that is available at 0000 UTC for forecasters to use when preparing the 0300 UTC forecast. The actual 0000 UTC model forecast, arriving after the 0300 UTC forecast must be made, is known as a "late" model forecast. As you might expect, "late" model forecasts thus form the basis for the subsequent "early" model forecasts. In the lists above, "early" models are those whose designators end in an I (e.g., AVNI, CMCI, etc.). "Late" models have no such notation. Please note that all consensus, statistical, and statistical-dynamical guidance is classified as "early" guidance and is often derived from "early" model output.

Disclaimer: The data displayed here are informational only and should NOT be used for making life and death decisions. Always take the word of official sources - the National Hurricane Center and your local National Weather Service office - when preparing for any potential storm impact. If anything on these plots causes confusion, disregard the information in its entirety. The availability, timeliness, and reliability of these data are not guaranteed, and no liability is implied or expressed by your use of this website.

Friday, September 5, 2014

nabla ∇

Del, or nabla, is an operator used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.

In the Cartesian coordinate system R^$n$ with coordinates

(x_1, \dots, x_n)

and standard basis

\{ \mathbf{\hat e}_1, \dots, \mathbf{\hat e}_n \}

, del is defined in terms of partial derivative operators as

\nabla = \left( {\partial \over \partial x_1}, \cdots, {\partial \over \partial x_n} \right) = \sum_{i=1}^n \mathbf{\hat e}_i {\partial \over \partial x_i}

In three-dimensional Cartesian coordinate system R³ with coordinates

(x, y, z)

and standard basis

\{ \mathbf{\hat{x}}, \mathbf{\hat{y}}, \mathbf{\hat{z}} \}

, del is written as

\nabla = \left( {\partial \over \partial x}, {\partial \over \partial y}, {\partial \over \partial z} \right) = \mathbf{\hat{x}} {\partial \over \partial x} + \mathbf{\hat{y}} {\partial \over \partial y} + \mathbf{\hat{z}} {\partial \over \partial z}

Notational uses

Gradient

The vector derivative of a scalar field f is called the gradient, and it can be represented as:

\nabla f = {\partial f \over \partial x} \mathbf{\hat{x}} + {\partial f \over \partial y} \mathbf{\hat{y}} + {\partial f \over \partial z} \mathbf{\hat{z}}

In particular, this notation is powerful because the gradient product rule looks very similar to the 1d-derivative case:

\nabla(f g) = f \nabla g + g \nabla f

However, the rules for dot products do not turn out to be simple, as illustrated by:

\nabla (\vec u \cdot \vec v) = (\vec u \cdot \nabla) \vec v + (\vec v \cdot \nabla) \vec u + \vec u \times (\nabla \times \vec v) + \vec v \times (\nabla \times \vec u)

Divergence

The divergence of a vector field

\vec{v}(x, y, z) = v_x \mathbf{\hat{x}} + v_y \mathbf{\hat{y}} + v_z \mathbf{\hat{z}}

is a scalar function that can be represented as:

\mbox{div}\,\vec v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z} = \nabla \cdot \vec v

The power of the del notation is shown by the following product rule:

\nabla \cdot (f \vec v) = f (\nabla \cdot \vec v) + \vec v \cdot (\nabla f)

The formula for the vector product is slightly less intuitive, because this product is not commutative:

\nabla \cdot (\vec u \times \vec v) = \vec v \cdot (\nabla \times \vec u) - \vec u \cdot (\nabla \times \vec v)

Curl

The curl of a vector field

\vec{v}(x, y, z) = v_x\mathbf{\hat{x}} + v_y\mathbf{\hat{y}} + v_z\mathbf{\hat{z}}

is a vector function that can be represented as:

\mbox{curl}\;\vec v = \left( {\partial v_z \over \partial y} - {\partial v_y \over \partial z} \right) \mathbf{\hat{x}} + \left( {\partial v_x \over \partial z} - {\partial v_z \over \partial x} \right) \mathbf{\hat{y}} + \left( {\partial v_y \over \partial x} - {\partial v_x \over \partial y} \right) \mathbf{\hat{z}} = \nabla \times \vec v

Directional derivative

The directional derivative of a scalar field f(x,y,z) in the direction

\vec{a}(x,y,z) = a_x \mathbf{\hat{x}} + a_y \mathbf{\hat{y}} + a_z \mathbf{\hat{z}}

is defined as:

Laplacian

The Laplace operator is a scalar operator that can be applied to either vector or scalar fields; for cartesian coordinate systems it is defined as:

Tensor derivative

Del can also be applied to a vector field with the result being a tensor. The tensor derivative of a vector field

\vec{v}

is a 9-term second-rank tensor, but can be denoted simply as

\nabla \otimes \vec{v}

, where

\otimes

represents the dyadic product. This quantity is equivalent to the transpose of the Jacobian matrix of the vector field with respect to space.
For a small displacement

\delta \vec{r}

, the change in the vector field is given by:

Product rules

\nabla (fg) = f\nabla g + g\nabla f

\nabla(\vec u \cdot \vec v) = \vec u \times (\nabla \times \vec v) + \vec v \times (\nabla \times \vec u) + ( \vec u \cdot \nabla) \vec v + (\vec v \cdot \nabla )\vec u

\nabla \cdot (f \vec v) = f (\nabla \cdot \vec v) + \vec v \cdot (\nabla f

)

\nabla \cdot (\vec u \times \vec v) = \vec v \cdot (\nabla \times \vec u) - \vec u \cdot (\nabla \times \vec v

)

\nabla \times (f \vec v) = (\nabla f) \times \vec v + f (\nabla \times \vec v

)

\nabla \times (\vec u \times \vec v) = \vec u \, (\nabla \cdot \vec v) - \vec v \, (\nabla \cdot \vec u) + (\vec v \cdot \nabla) \, \vec u - (\vec u \cdot \nabla) \, \vec v

\delta \vec{v} = (\nabla \otimes \vec{v}) \sdot \delta \vec{r}

\Delta = {\partial^2 \over \partial x^2} + {\partial^2 \over \partial y^2} + {\partial^2 \over \partial z^2} = \nabla \cdot \nabla = \nabla^2

\vec{a}\cdot\mbox{grad}\,f = a_x {\partial f \over \partial x} + a_y {\partial f \over \partial y} + a_z {\partial f \over \partial z} = (\vec a \cdot \nabla) f

\mbox{div}\,\vec v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z} = \nabla \cdot \vec v

math symbol pronunciation

Wednesday, September 3, 2014

hurricane intensity and track.

Reference : http://agora.ex.nii.ac.jp/digital-typhoon/help/unit.html.en

1. Unit of Pressure and Wind

This page summarizes the unit of pressure and wind used in this web site.

Hecto Pascal (hPa)

Hecto Pascal is a unit for pressure, and, in this web site, used mainly for representing the central pressure of a typhoon. In Japan, the unit of "millibar" (mb) was used through November 1992, but since December 1992, the unit of "hectopascal" (hPa) has been used to comply with the International System of Units. Conversion between those two units is 1hPa = 1mb, however, so the value itself is the same as before.

Knot (kt)

Knot is a unit for speed. One knot means a speed of moving one nautical mile (nm) in one hour. Knot is used for representing the maximum wind speed at the center of a typhoon, or a movement speed of a typhoon on this website. Because 1nm = 1.852km, 1kt = 1.852km/h = 0.5144m/s. Roughly speaking, halving the knot makes the speed in meter per second, while doubling it makes the speed in kilometer per hour.

By the way, Japan Meteorological Agency publishes conversion tables of motion speed, wind speed and distance. This site refers to these conversion tables.

2. Classification of Typhoons

The Classification of Intensity of Typhoons

The intensity of a tropical cyclone is classified by the maximum sustained wind (10-min mean) according to World Meteorological Organization (WMO). The following table summarizes categories for tropical cyclones. Here "Tropical Depression" is a tropical cyclone weaker than a typhoon, and a tropical cyclone stronger than a typhoon, Japan Meteorological Agency (JMA) classification has four levels (previously five) and international classification has three levels.

Intensity Class	Maximum Sustained Wind (10-min Mean)			International Category	Class
Intensity Class	knots (kt)	meters per second (m/s)	kilometers per hour (km/h)	International Category	Class
Low Pressure Area	central position cannot be accurately identified			Low Pressure Area	-
Tropical Depression	- 33	- 17	- 62	Tropical Depression (TD)	2
Typhoon	34 - 47	18 - 24	63 - 88	Tropical Storm (TS)	3
Typhoon	48 - 63	25 - 32	89 - 118	Severe Tropical Storm (STS)	4
Strong Typhoon	64 - 84	33 - 43	119 - 156	Typhoon (TY) or Hurricane	5
Very Strong Typhoon	85 - 104	44 - 53	157 - 192
Violent Typhoon	105 -	54 -	193 -

Note that the definition of "typhoon" is different between the Japanese standard and the international standard. A tropical storm with the wind speed of more than 34 kt is called a "typhoon" in Japan, while in the international standard, that with the wind speed of more than 64 kt is called a "typhoon." Tropical cyclones in the world are called by different names in each basin, such as a "typhoon" and a "hurricane," but the standard to be called by such names is the same : more than 64 kt of wind.

The Classification of Intensity of Typhoons and Hurricanes (USA Standard)

Joint Typhoon Warning Center (JTWC) and other US meteorological organizations use Saffir-Simpson Scale to classify tropical storms stronger than the hurricane (or typhoon) intensity based on the maximum sustained wind (1-min mean).

International Category	Category (Saffir-Simpson Scale)	Maximum Sustained Wind (1-min Mean)
International Category	Category (Saffir-Simpson Scale)	knots (kt)	meters per second (m/s)	kilometers per hour (km/h)
Typhoon / Hurricane	1	64 - 82	33 - 42	119 - 153
Typhoon / Hurricane	2	83 - 95	43 - 48	154 - 177
Typhoon / Hurricane	3	96 - 113	49 - 58	178 - 209
Typhoon / Hurricane	4	114 - 135	59 - 69	210 - 249
Typhoon / Hurricane	5	135-	70-	249-

A typhoon with maximum sustained surface winds greather than or equal to 130 knots (approximately Category 5) is called a "super typhoon," and a hurricane of Category 3 and above is called a "major hurricane." A tropical cyclone weaker than Category 1 is not a "typhoon" in the international standard, but may be classified as a "typhoon" in the Japanese standard.

In mainland China and Hong Kong, a typhoon with maximum sustained surface winds greather than or equal to 100 knots are called Super Typhoon. However, maximum sustained winds are measured differently in mainland China and Hong Kong, where the former uses 2-min mean and the latter uses 10-min mean.

In addition to maximum wind, maximum gust is also used to represent the strength of winds in a shorter time scale. Japan Meteorological Agency defines maximum gust as the average of 3 seconds (the average of 12 measurements by the frequency of 0.25 seconds), in comparison to the average of 10 minutes for maximum wind. The ration of maximum gust divided by maximum wind is called "gust factor" and it is known to take some values between 1.5 and 2. This means that 50m/s maximum gust could happen within the storm-wind circle of 25m/s maximum wind.

For other regions than Japan and the United States, please refer to the classifiction of tropical cyclones in the world.

The Classification of Size of Typhoons

The size of a typhoon is classified by the radius of the area in which the wind speed exceeds 15 m/s. The intensity and size represents different aspect of a typhoon. That is, we could have a strong but not large typhoon, and also a large but not strong typhoon.

Size Class	Radius of the area with the wind speed of 15m/s and above
Large	500km - 799km
Super	800km-

Effect of Typhoons and Typhoon Classes

Before 2000, JMA has been using additional typhoon classes for intensity and size. The intensity class had "weak" (which corresponds to Tropical Storm) and "middle" (which corresponds to Severe Tropical Storm), and the size class had "very small," "small," and "middle." These classes, however, might have given unreasonable relief to the people's attitude, such as "this typhoon is OK because it's very small and weak."

In addition, these typhoon classes were regarded as one reason for a big accident at a river on 1999, when a weak tropical depression caused heavy rain resulted in more than 10 people died of increased water level. Difference between typhoons and tropical depressions is only in terms of winds, and it has nothing to do with rains, but the expression of "weak" might have given different impression for preparedness. Based on this reflection, these classes are removed after 2000.

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