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نکته های کلیدی در آب و هواشناسی سینوپتیک - مطالب آذر 1393
 
نکته های کلیدی در آب و هواشناسی سینوپتیک
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مدیر وبلاگ : mehdi doostkamian
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سه شنبه 11 آذر 1393
mehdi doostkamian

What Is Covariance?
Covariance measures how two variables move together. It measures whether the two move in the same direction (a positive covariance) or in opposite directions (a negative covariance). In this article, the variables will usually be stock prices, but they can be anything.

In the stock market, a strong emphasis is placed on reducing the risk amount taken on for the same amount of return. When constructing a portfolio, an analyst will select stocks that will work well together. This usually means that these stocks do not move in the same direction.

Calculating Covariance
Calculating a stock's covariance starts with finding a list of previous prices. This is labeled as "historical prices" on most quote pages. Typically, the closing price for each day is used to find the return from one day to the next. Do this for both stocks, and build a list to begin the calculations.

For example:
 

Day ABC Returns (%) XYZ Returns (%)
1 1.1 3
2 1.7 4.2
3 2.1 4.9
4 1.4 4.1
5 0.2 2.5
Table 1: Daily returns for two stocks using the closing prices

From here, we need to calculate the average return for each stock:

For ABC it would be (1.1 + 1.7 + 2.1 + 1.4 + 0.2) / 5 = 1.30

For XYZ it would be (3 + 4.2 + 4.9 + 4.1 + 2.5) / 5 = 3.74

Now, it is a matter of taking the differences between ABC's return and ABC's average return, and multiplying it by the difference between XYZ's return and XYZ's average return. The last step is to divide the result by the sample size and subtract one. If it was the entire population, you could just divide by the population size.

This can be represented by the following equation:
 

Using our example on ABC and XYZ above, the covariance is calculated as:

= [(1.1 - 1.30) x (3 - 3.74)] + [(1.7 - 1.30) x (4.2 - 3.74)] + [(2.1 - 1.30) x (4.9 - 3.74)] + …
= [0.148] + [0.184] + [0.928] + [0.036] + [1.364]
= 2.66 / (5 - 1)
= 0.665

In this situation we are using a sample, so we divide by the sample size (five) minus one.

You can see that the covariance between the two stock returns is 0.665. Because this number is positive, it means the stocks move in the same direction. When ABC had a high return, XYZ also had a high return.

Using Microsoft Excel
In Excel, you can easily find the covariance by using one the following functions:

= COVARIANCE.S() for a sample
or
= COVARIANCE.P() for a population

You will need to set up the two lists of returns in vertical columns, just like in Table 1. Then, when prompted, select each column. In Excel, each list is called an "array," and two arrays ishould be nside the brackets, separated by a comma.

Meaning
In the example there is a positive covariance, so the two stocks tend to move together. When one has a high return, the other tends to have a high return as well. If the result was negative, then the two stocks would tend to have opposite returns; when one had a positive return, the other would have a negative return.


Uses of Covariance
Finding that two stocks have a high or low covariance might not be a useful metric on its own. Covariance can tell how the stocks move together, but to determine the strength of the relationship, we need to look at the correlation. The correlation should therefore be used in conjunction with the covariance, and is represented by this equation:

A correlation between two variables is the covariance between each divided by the product of each variables standard deviation

where cov (X,Y) = covariance between X and Y

σX = standard deviation of X

σY = standard deviation of Y

The equation above reveals that the correlation between two variables is simply the covariance between both variables divided by the product of the standard deviation of the variables X and Y. While both measures reveal whether two variables are positively or inversely related, the correlation provides additional information by telling you the degree to which both variables move together. The correlation will always have a measurement value between -1 and 1, and adds a strength value on how the stocks move together. If the correlation is 1, they move perfectly together, and if the correlation is -1, the stocks move perfectly in opposite directions. If the correlation is 0, then the two stocks move in random directions from each other. In short, the covariance just tells you that two variables change the same way, while correlation reveals how a change in one variable effects a change in the other.

The covariance can also be used to find the standard deviation of a multi-stock portfolio. The standard deviation is the accepted calculation for risk, and this is extremely important when selecting stocks. Typically, you would want to select stocks that move in opposite directions. If the chosen stocks move in opposite directions, then the risk might be lower given the same amount or potential return.






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جمعه 7 آذر 1393
mehdi doostkamian
تبدیل سانتیگراد به فارنهایت
F = C x 9/5 + 32

حرف اف F علامت فارنهایت و حرف سی C علامت سانتیگراد است و اگر بخواهیم بدانیم ۲۵۰ درجه سانتیگراد چند درجه فارنهایت می شود مقدار آن را در فرمول فوق به شرح ذیل می گذاریم و عمل می کنیم :

F = 250 x 5/9 = 450 + 32 = 482
بنابراین همیشه ۲۵۰ درجه سانتیگراد ۴۸۲ درجه فارنهایت می شود و بالعکس اگر بخواهیم بدانیم ۳۵۰ درجه فارنهایت چند درجه سانتیگراد می شود مقدار آنرا در فرمول :

C = (F- 32) 5/9
می گذاریم و نتیجه را به دست می آوریم

C=(350-32) =318×5/9 =176

بنابراین درجه حرارت مورد دستور را که به فارنهایت گفته شده است ابتدا منهای ۳۲ می کنیم و باقیمانده را بر ۵ ضرب و حاصل را بر ۹ تقسیم می نماییم نتیجه اینکه درجه حرارت لازم به سانتیگراد از فارنهایت به دست می آید.
چنانچه که در مثال فوق ۳۵۰ درجه فارنهایت را که منهای ۳۲ می کنیم حاصل ۳۱۸ می شود و این عدد را در ۵ ضرب و حاصل را که ۱۵۹۰ است به ۹ تقسیم میکنیم نتیجه آن ۱۷۶ درجه سانتیگراد می شود.

فرمول تبدیل واحد ها به یکدیگر


سیلیسیوس(سانتیگراد) به فارنهایت = ( – ۳۲) × ۵⁄۹
فارنهایت به سیلیسیوس
= ( × ۹⁄۵)+۳۲
کلوین به فارنهایت
K = ( + ۴۵۹٫۶۷) × ۵⁄۹
فارنهایت به کلوین
= K × ۹⁄۵ − ۴۵۹٫۶۷
منبع: http://pichak.net/crop




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پنجشنبه 6 آذر 1393
mehdi doostkamian

Heat Index, apparent temperature

The heat index and the summer simmer index are used to measure the amount of discomfort during the summer months when heat and humidity often combine to make it feel hotter than it actually is. The heat index is usually used for afternoon high temperatures while the summer simmer index is used for overnight low temperatures. Below are the detailed equations that are used to calculate the apparent temperatures in the heat index and the summer simmer index.

Heat Index: If you know the relative humidity and the dry air temperature, then you can use the following equation to calculate the heat index.

(1) Heat index(HI), or apparent temperature(AI)= -42.379 + 2.04901523(Tf) + 10.14333127(RH) - 0.22475541(Tf)(RH) - 6.83783x10**(-3)*(Tf**(2)) - 5.481717x10**(-2)*(RH**(2)) + 1.22874x10**(-3)*(Tf**(2))*(RH) + 8.5282x10**(-4)*(Tf)*(RH**(2)) - 1.99x10**(-6)*(Tf**(2))*(RH**(2))

Note: In order for the Heat Index formula to work correctly, you must use the relative humidity in percent form. In other words, if the relative humidity is 65%, use 65 for RH in the formula, not .65.

Summer Simmer Index: If you know the relative humidity and the dry air temperature, then you can use the following equation to calculate the summer simmer index.

(2) Summer simmer index(SSI)= 1.98(Tf - (0.55 - 0.0055(RH))(Tf-58)) - 56.83

Tf= air temperature in degrees Fahrenheit, RH= relative humidity expressed as a whole number



How altitude affects humidity calculations

As altitude is gained, air pressure decreases. The discussion here covers the affects of this pressure decrease on the humidity formulas on this page.

Pressure decreases with height in the first 100 kilometers above the earth's surface according to the formula P(z)=P(sea level)*exp(-z/H).

P(z)= pressure at height z, P(sea level)= sea level pressure(~1013 millibars), z= height in meters, H= scale height(~7 kilometers)

Our evaluation of the humidity formulas on this page using different altitudes, shows that the relative humidity remains constant with pressure changes. The actual vapor pressure and the saturated vapor pressure both change, but they change by the same factor. This keeps relative humidity constant. The pressure coefficient in the formulas below for the standard atmosphere is 6.11. Applying the pressure formula above for 7000 feet of altitude, yields a pressure coefficient of 4.5. This lower coefficient reduces both actual vapor pressure and saturation vapor pressure, but does not change relative humidity.

The dewpoint temperature is affected by the higher altitude since it is affected by pressure. Using the saturation vapor pressure values from the formula below, you can divide the formula value by the ratio of the sea level pressure coefficient to the modified coefficient. For example, at 7000 feet of altitude the ratio is 6.11/4.5, or 1.38. Before using the formula value for saturated vapor pressure in the dewpoint procedure, you divide the formula value by 1.38.


Relative humidity from temperature and dewpoint

If you know the temperature and the dewpoint, and want to obtain relative humidity, the formulas are as follows:

First, to convert the temperature and the dewpoint from Fahrenheit to Celsius, use the following formulas.

(3) Tc=5.0/9.0*(Tf-32.0)

(4) Tdc=5.0/9.0*(Tdf-32.0)

Tc=air temperature in degrees Celsius, Tf=air temperature in degrees Fahrenheit

Tdc=dewpoint temperature in degrees Celsius

Tdf=dewpoint temperature in degrees Fahrenheit

Note: If your temperature and dewpoint are already in degrees Celsius, you can skip the first step and proceed to the second.

The next set of formulas assumes a standard atmospheric pressure. These formulas will calculate saturation vapor pressure(Es) and actual vapor pressure(E) in millibars.

(5) Es=6.11*10.0**(7.5*Tc/(237.7+Tc))

(6) E=6.11*10.0**(7.5*Tdc/(237.7+Tdc))

Once you have the saturation vapor pressure and the actual vapor pressure, relative humidity can be computed by dividing the actual vapor pressure by the saturation vapor pressure and then multiplying by 100 to convert the quantity to a percent.

(7) Relative Humidity(RH) in percent =(E/Es)*100

For example, if you have a station report that included an air temperature of 85 degrees Fahrenheit and a dewpoint of 65 degrees Fahrenheit and you wanted to compute the relative humidity, you would proceed as follows.

First, convert the Fahrenheit values to Celsius using formulas (3) and (4). The values you get should be Tc=29.4 and Tdc=18.3

Next, calculate the saturation vapor pressure and the actual vapor pressure using formulas (5) and (6) respectively. The values you get should be Es=40.9 and E=21.0

Finally, calculate relative humidity using formula (7). The final answer should be RH=51.3 %(percent).

Note: Due to the rounding of decimal places, your answer may be slightly different from the above answer, but it should be within 2%.


Dewpoint from relative humidity and temperature

If you know the relative humidity and the air temperature, and want to calculate the dewpoint, the formulas are as follows.

First, if your air temperature is in degrees Fahrenheit, then you must convert it to degrees Celsius by using the Fahrenheit to Celsius formula.

(8) Tc=5.0/9.0*(Tf-32.0)

The next step is to obtain the saturation vapor pressure(Es) using formula (5) as before when air temperature is known.

(5) Es=6.11*10.0**(7.5*Tc/(237.7+Tc))

The next step is to use the saturation vapor pressure and the relative humidity to compute the actual vapor pressure(E) of the air. This can be done with the following formula.

(9) E=(RH*Es)/100

RH=relative humidity of air expressed as a percent.(i.e. 80%)

Now you are ready to use the following formula to obtain the dewpoint temperature.

Note: ln( ) means to take the natural log of the variable in the parentheses

(10) Tdc=(-430.22+237.7*ln(E))/(-ln(E)+19.08)

If you wish, you can convert the Celsius dewpoint back into the Fahrenheit scale using the following formula.

(11) Tdf=(9.0/5.0)*Tdc+32

For example, if you have a weather station that gave you an air temperature of 60 degrees Fahrenheit and a relative humidity of 47%(percent) and you wanted to compute the dewpoint temperature, you would proceed as follows.

First, convert the air temperature to degrees Celsius by using formula (8). You should get Tc=15.6

Next, using formula (5) again, compute the saturation vapor pressure for an air temperature of 15.6 degrees Celsius. You should get 17.7.

Next, compute the actual vapor pressure by using formula (9). You should get E=8.3

Finally, you can compute the dewpoint temperature by using formula (10). You should get Tdc=4.3

If you want to convert this dewpoint temperature back into degrees Fahrenheit, you can do so by using formula (11). You should get Tdf=39.7

Note: Due to the rounding of decimal places, your answer may be slightly different from the above answer, but it should be within two degrees.


Relative humidity from temperature and wet bulb temperature

If you know the air temperature and the wet bulb temperature, you first want to calculate the actual mixing ratio of the air(W) using the following formula.

(12) W=[(Tc-Twb)(Cp)-Lv(Eswb/P)]/[-(Tc-Twb)(Cpv)-Lv]

W=actual mixing ratio of air

Cp=specific heat of dry air at constant pressure(J/g)~1.005 J/g

Cpv= specific heat of water vapor at constant pressure(J/g)~4.186 J/g

Lv=Latent heat of vaporization(J/g)~2500 J/g

Tc=air temperature in degrees Celsius

Twb=wet bulb temperature in degrees Celsius

Eswb=saturation vapor pressure at the wet bulb temperature(mb)

P=atmospheric pressure at surface~1013 mb at sea-level

Once you have the actual vapor pressure, you can use the following formula to calculate the saturation mixing ratio for the air.

(13) Ws=Es/P

Once you have the actual mixing ratio and the saturation mixing ratio, you can use the following formula to calculate relative humidity.

(14) Relative Humidity(RH) in percent=(W/Ws)*100

Note: The latent heat of vaporization(Lv) varies slightly with temperature. The value given above is an approximate value for the standard atmosphere at 0 degrees Celsius.

Note: Due to the large numbers of approximations using these formulas, your final answer may vary by as much as 10 percent.


Air density and absolute humidity

In order to calculate air density, you will have to use the Ideal Gas Law equation. Before you can use the gas law equation, you must first convert your temperature in degrees Celsius to degrees Kelvin by simply adding 273 to the Celsius temperature reading. (Tk=Tc+273) Also, you must convert pressure in kPa to Pa by simply multiplying your reading in kPa by 1000. (1 kPa=1000 Pa). If your pressure reading or calculation is in millibars, then you convert it to Pa by multiplying the reading in millibars by 100. (1 mb=100 Pa)

(15) The gas law equation: D=P/(T*R)

P= pressure in Pascals (Pa)

D=density(kg/m3)

T=temperature in degrees Kelvin

R=gas constant for air=287 (J/kg*Kelvin)

Rw=gas constant for water vapor= 461.5 (J/kg*Kelvin)

This gas law formula will give you the air density for a given temperature and pressure.

Absolute humidity is the density of water vapor in the air (kg/m3). To calculate absolute humidity, you must first use the dewpoint temperature and formula number (6) to calculate vapor pressure in millibars. Then convert the vapor pressure in millibars to Pa by multiplying by 100. Once you have the vapor pressure in Pa, you can use the gas law discussed above to calculate water vapor density(i.e. absolute humidity) by substituting Rw in place of R and by using the vapor pressure in the gas law formula, rather than the total atmospheric pressure that you would use to calculate air density.





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چهارشنبه 5 آذر 1393
mehdi doostkamian
برای فرخوانی فایل در متلب به جای اینکه داده را به محیط workspace انتقال دهید می توانداز دستورات زیر استفاده کنید
[F,PathName,FilterIndex] = uigetfile({'*.*','All Files(*.*)'}, 'Select your File ');
loadimage = strcat(PathName,F);
input = importdata(loadimage);
سپس ادامه دستورا بر مبنای اینپوت خواهد بود




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سه شنبه 4 آذر 1393
mehdi doostkamian
در آدرس زیر بسیاری از اسکریپت های با کاربرد اقلیمی گذاشته شده است:
http://www.tech.plym.ac.uk/spmc/links/matlab/matlab_toolbox.html
and

https://stuff.mit.edu/afs/sipb.mit.edu/user/arolfe/matlab
----------------------------------------------------------------------------------------------
با مراجعه به آدرس زیر رگرسیون و انواع آن را مرحله به مرحه شرح داده است:

http://www.atmos.washington.edu/~breth/classes/AM582/matlab/html/regression_example.html




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سه شنبه 4 آذر 1393
mehdi doostkamian