Preparation of Wind Rose by ORIANA Software

Introduction

1. Data measured in the form of angle are to be found almost everywhere throughout Science. They arise commonly in Meteorology and Oceanography, Biology, Geography, Geology etc. and typical examples in Meteorology include prevailing wind, period of occurrence of severe thunderstorms, wind gust, tornados, waves, precipitation, fog etc. These analyses have gained much attention as they describe most of these environmental phenomena in the changing climate situation. The ORIANA Software is dedicated to the analysis of circular variables. The most common circular wind data can be analyzed by this Software as Wind Rose which would be an excellent tool to forecast the wind and associate weather by Met officers and to declare the runway-in-use well in advance by Air Traffic Control officer for landing and take-off.

The ORIANA Software

4. History. ORIANA, the statistical software dedicated to the analysis of circular variables, was first introduced on 31 December 2003 (Version 1), and was upgraded with the latest version issued on 03 May 2007 (Version 2) and finally further modified last on 22 April 2010 (Version 3). The software is available, with the demo version, at:

http://www.kovcomp.co.uk/oriana/index.html

5. Price of Registered Software. ORIANA may be bought directly via e-mail by paying through credit

card, or it may bought with manual & CD. The price is shown as:

Item Price (excluding VAT and shipping)Oriana 3.0 (e-mail only) Commercial - ₤250 / $400Oriana 3.0 (with manual & CD) Commercial - ₤270 / $435

6. Other Software for Circular Data. There are very few software for circular data analysis. The WRPLOT and AXIS are other two software.

7. Uses. In view of the scarcity of commercialize statistical software in the market, the software can be useful for students, researcher, scientists and also medical professional in areas which involve in analyzing circular data. It has a window-based environment with several options in the drop down menu. There are five windows in ORIANA including:

a. The main window.b. Status window.

c. Data editor.

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d. Results window.

e. Graph windows.f. Notepad.

8. Tutorial Guide. The tutorial guide is provided in ORIANA in order to help users become familiar with this software. It offers various graphical and analytical analysis as a well as to calculate a variety of the special types of statistics involving the data measured in degrees, time of day or other circular form. Some of the features that available in ORIANA include summary statistics for each sample, one sample test, multi sample test and also correlation between samples.

Data Used

9. In this study, 04 (four) following data sets have been used for different analysis and graphs:

a. Daily Wind Data. Daily averages of 10 years’ wind data have been used from Climate Register to prepare monthwise Wind Rose for Met Squadron, BAF Base Zahurul Haque which was distributed to all Met Squadron including Air Headquarters.

b. Hourly Wind Data. The hourly wind data along with special observation have been used for the month of July 2009 (as Southwest Monsoon data) and January 2010 (as Northeast Monsoon data).

c. Period of Prevailing Wind. Period of prevailing wind data during the month of January 2010.

d. Arrival Time of Precipitation. Arrival time of precipitation data for the month of March April and May for last 5 years.

Descriptive Statistics of Wind Data and Time Data

10. Circular Plot. Graphical representations are often used to summarize the data. ORIANA offers wide range of representation which included:

a. Rose diagram.b. Circular histogram.c. Raw data plot.d. Arrow data plot.e. Linear histogram.

However, the most commonly used types of graph for circular data is the rose diagram.

11. Rose Diagram. The rose diagram is a histogram displayed in a circle, similar to the pie chart for linear data. Rose diagram for wind is called Wind Rose. It is a

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graphic tool used by meteorologists to give a brief and clear view of how wind speed and wind direction are typically distributed at a particular station.

It is a grid made in a polar chart that shows how many times the wind blows in a certain direction. It has zero at the center and increases outward as spoke with the increased frequencies of the wind location. The length of each spoke around the circle is related to the frequency that the wind blows from a particular direction per unit time. The longest spoke shows the wind direction with the greatest frequency. There are some concentric circles, each represents a different frequency, emanating from zero at the center to increasing frequencies at the outer circles. A wind rose plot contains additional information, in that each spoke is broken down into colour-coded bands that show wind speed ranges. Wind roses typically use 16 cardinal directions, such as north (N), NNE, NE, etc., although they may be subdivided into as many as 32 directions.

Each sector of circular plot represents the frequency or number of observations which falls in the range of angles. The concentric circles show the frequency of the observations for each angular value.

8. Basic Statistics for each Sample. To complement the graphical analysis, summary statistics are often deployed with the Software. Similar to any window-based environment, the summary statistics in ORIANA can be obtained from the drop down menu. In other words, from the Analyses menu, drop down to choose Stats... and further to the Statistics dialog box, in which one can choose several summary statistics and statistical tests. Here, the monthwise wind rose are shown for apprehension of prevailing wind during each month. However, for the study, the summary statistics for the wind data of January 2010 and July 2009 are given as in Table 1. The summary statistics as shown in Table 1 depicts the following:

a. The numbers of observations for this study are 802 and 885 observations for January 2010 and July 2009 wind data respectively.

b. The mean direction (μ) is the direction of the resultant vectors with given corresponding angles and is defined by:

, S>0, C>0

µ = , C>0

, S<0, C>0

where and . For January 2010 wind data, the mean

angle is 351.6020, while for July 2009 wind data the mean angle is 159.020.

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c. Length of mean vector is defined by . It is the length of the

directions of the resultant vectors at given angles and the range is between 0 and 1. The larger value of r implies that the observations are closely clustered around the mean. For this data set, the value of r is 0.882 and 0.718 for January 2010 and July 2009 wind data set respectively. The value of r for January 2010 wind data is higher than July 2009 wind data and it closer to 1 meaning that the observations for January 2010 is clustered closely around the mean as compared to July 2009.

d. Median is defined as a direction that divides the data into two equal size groups and in ORIANA the median may be calculated. As opposed to linear data, where we can easily find the midpoint between observations as we arranged the data in increasing order. However, for circular data it is rather complicated since the data are in closed curve and can always be rotated around the circle. This has caused a problem on how to choose an appropriate axis on the circular scale. For the given data set, the calculated median is 0° for January 2010 wind data set and 160° for July 2009 wind data set.

e. Concentration is denoted by and is a parameter that related to von Mises distribution. It is also related to the length of mean vector and the value of given by ORIANA is the maximum likelihood estimation of population concentration. A large value of r will imply the large value of κ. For this data set, the concentrations are 4.534 and 2.124 for January 2010 and July 2009 wind data set respectively.

f. Circular variance is the measures of dispersion of circular data. Variance is related to length of mean vector and calculated by using V = 1 - r. The values of circular variance for the January 2010 and July 2009 wind data set are 0.118 and 0.282 respectively.g. Circular standard deviation is an analogue to linear counterpart but it is calculated in a much different way and is given by . The values are 28.722° and 46.617° for January 2010 and July 2009 wind data set respectively.

h. Standard error of mean are calculated based on the length of mean vector and concentration parameters as well as assuming that the data set follows a von Mises distribution. For the given data set, the standard error of mean is 1.012° and 1.559° for January 2010 and July 2009 wind data set respectively.

j. Finally, the 95% and 99% confidence intervals are derived from the standard error as for the normal distribution. It is defined as 95% or 99% probability that the true mean vector is greater and less than this value. At 95% confidence interval, the values are between 349.619° and 353.586° for January 2010 wind data set whereas 155.963° and 162.077° for July 2009 wind data set. While at 99% confidence interval, the value is between 348.996° and 354.209° for January 2010 wind data set whereas 155.003° and 163.037° for July 2009 wind data set.

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Basic Statistics: January 2010 and July 2009 Wind DataVariable Angles Angles

Data Type Angles Angles

Number of Observations 802 885

Data Grouped? Yes Yes

Group Width (& Number of Groups) 10° (36) 22.5° (16)

Mean Vector (µ) 351.602° 159.02°

Length of Mean Vector (r) 0.882 0.718

Median 0° 160°

Concentration 4.534 2.124

Circular Variance 0.118 0.282

Circular Standard Deviation 28.722° 46.617°

Standard Error of Mean 1.012° 1.559°95% Confidence Interval (-/+) for µ 349.619° 155.963°

353.586° 162.077°99% Confidence Interval (-/+) for µ 348.996° 155.003°

Table 1: Basic statistics for January 2010 and July 2009 wind data.

9. Testing for Uniformity. The samples can be tested whether they are uniformly distributed or otherwise, that is to test whether all directions are equal likely. By using one sample test such as Rayleigh’s Uniformity Test where the Z value is calculated simply as Z = nr2, with n is the number of observations and r is the length of the mean vector. A longer mean vector will give larger value of Z and greater concentration of the data around the mean. Thus, the likelihood of the data being uniformly distributed is less. From the test statistics, it gives a Z value of 623.793 with p-value < 1E-12 for Northeast data set and Z value of 456.503 with p-value < 1E-12 for Southwest data set. Hence at 5% significant level, we reject the null hypothesis that the samples were uniformly distributed.

Conclusion

10. The meteorological data are mostly by nature circular. Analysis of circular data by ORIANA would change the conventional method of averaging. I have found that ORIANA is user friendly software, and proves to be a useful package in analyzing circular data. It offers a wide selection of graphical display and descriptive statistics which deemed sufficient in statistical analysis of circular data.

Recommendations

11. Analysis of circular data by ORIANA and use of results by Met officers would have great impact on forecasting. Many uses of ORIANA would provide Met officers a scope of critical thinking about the Met elements and their behavior at a particular location. The preparation of wind rose, arrival time of a particular weather is paramount important in forecasting. The different Met elements like wind, temperature, humidity

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etc. may be correlated with the different weather phenomena like thunderstorms, fog, etc. by using ORIANA. Some uses of Wind Rose may be as follows:

a. Meteorological information during take-off and landing of aircrafts.

b. Preparation of runway and other infrastructures using prevailing wind direction.

c. Preparation of chimney or cowl in a building using prevailing wind direction.

d. Identifying appropriate location of smoke/gas generated mills/factories or brickfields for avoiding air pollution. e. Preparation of wind rose for different height of a particular location to prepare upper wind atlas for subsequent forecast during the absence of wind.

f. To identify relationship, with the wind of the morning and subsequent wind in the afternoon associated with norwester or thunderstorm particularly during norwester.

g. Wind mill may be installed with the prevailing wind direction and speed to generate renewable energy.

h. Identify the changes in the frequency of wind direction and speed to comment for the aspect of global warming or climate change by finding out year to year wind rose, particularly for costal area of Bangladesh like Chittagong.

j. Finding out the monthwise prevailing wind direction and frequencies and validate the data with the intensity of monsoon according to the definition given by Ramage.

12. Proposal. The ORIANA Software that was used to draw the graphical representation and analysis of circular data. The analysis was done by downloading the demo version which remains valid for 30 days and only for 15 uses. As such, many features of the Software could not be explored. Registered version software may be procured and distributed to all Met Squadron to analyse the Met data for better forecasting to maintain our moto “FORECAST FOR OP SAFETY”.

11. Limitations. Nevertheless it has some limitations. For example, other features that is available for linear data set such as measure of skewness and kurtosis. Further analysis such as statistical inference, probability distribution function and predictive modeling such as regression are also not available in the statistical package. Thus, there is much to be done in developing a more comprehensive analysis of circular data which can be incorporated into the statistical package.

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9. Comparison between Samples. Watson-William F-Test can be used to compare two or more samples to determine if their mean angles differ significantly. The F statistic is the same as Fisher’s variance ratio statistic which is commonly used in linear statistics. This test assumes that the two samples are independent and drawn at random from a population with a von Mises distribution. It also assumes that the concentrations of the two samples are similar and that they are sufficiently large, normally greater than 2. For this data set, the test statistics give the value of 254.151 and the probability value associated with the null hypothesis is less than 0.001. Hence, null hypothesis can be rejected at 5% significant level implying that the mean directions for the two monsoons are not the same.

Data file - I:\Key Note jan\January 2010 Wind Data.oriJanuary 2010 Wind DataAnalysis begun: Tuesday, June 08, 2010 11:35:41 PM

Variable Angles AnglesData Type Angles AnglesNumber of Observations 802 0Data Grouped? Yes NoGroup Width (& Number of Groups) 10° (36)Length of Mean Vector (r) 0.882 *****Rayleigh Test (Z) 623.793 *****Rayleigh Test (p) < 1E-12 *****Rao's Spacing Test (U) ----- *****Rao's Spacing Test (p) ----- *****Watson's U² Test (Uniform, U²) ----- *****Watson's U² Test (p) ----- *****Kuiper's Test (Uniform, V) ----- *****Kuiper's Test (p) ----- *****Chi-Squared Test (Uniform, X²) 15843.466 *****Chi-Squared Test (p) < 1E-12 *****V Test (V; expected mean 0.00°) 0.872 *****V Test (u) 34.942 *****V Test (p) < 1E-12 *****

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***** indicates that a result could not be calculated. ----- indicates that a result could not be calculated because the data are grouped.

BASIC STATISTICSData file - I:\Key Note jan\July 2009 Wind Data.oriJuly 2009 Wind DataAnalysis begun: Tuesday, June 08, 2010 11:38:44 PM

The data in variable "Angles" do not appear to fit the requested group width of 22.5. A value of 0 seems to be a better fit.

Variable Angles AnglesData Type Angles AnglesNumber of Observations 885 0Data Grouped? Yes NoGroup Width (& Number of Groups) 22.5° (16)Length of Mean Vector (r) 0.718 *****Rayleigh Test (Z) 456.503 *****Rayleigh Test (p) < 1E-12 *****Rao's Spacing Test (U) ----- *****Rao's Spacing Test (p) ----- *****Watson's U² Test (Uniform, U²) ----- *****Watson's U² Test (p) ----- *****Kuiper's Test (Uniform, V) ----- *****Kuiper's Test (p) ----- *****Chi-Squared Test (Uniform, X²) 2415.972 *****Chi-Squared Test (p) < 1E-12 *****V Test (V; expected mean 0.00°) -0.671 *****V Test (u) -28.213 *****V Test (p) 1 *****

***** indicates that a result could not be calculated. ----- indicates that a result could not be calculated because the data are grouped.

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