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Classification of wind events

14 messages · Jeff Newmiller, Stefano Sofia, Jim Lemon +1 more

Stefano Sofia
# 
Dear R list users,
I am aware that this question is not strictly related, at the present moment, to R code and it is more general. Please forgive me, but I need to share my thoughts with you.

Foehn conditions on the southern slope of Alps happen with strong northerly flows that impact perpendicularly over the Apls. This situation triggers strong northerly leeward winds.
Given a single automatic weather station, I would like to identify these periods starting from wind direction and wind intensity data. Frequency of data is quarter of hour.
I would really find difficult to detect the moving windows of these events:
- I can't analyse data day by day;
- at the beginning and at the end of each event, when the process is not at full speed yet, the rotation is not always perfectly identifiable;
- I cannot claim in principle that the direction of each consecutive observation is costantly and strictly from the chosen direction.

Does anybody have a clue on how to start to build this process in the right way?

Thank you for your attention and your help
Stefano

         (oo)
--oOO--( )--OOo----------------
Stefano Sofia PhD
Civil Protection - Marche Region
Meteo Section
Snow Section
Via del Colle Ameno 5
60126 Torrette di Ancona, Ancona
Uff: 071 806 7743
E-mail: stefano.sofia at regione.marche.it
---Oo---------oO----------------

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Jeff Newmiller
# 
Please make a reproducible R example of input and output.
On May 12, 2020 1:11:41 AM PDT, Stefano Sofia <stefano.sofia at regione.marche.it> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Jim Lemon
    

    

      
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Hi Stefano,
Given only one observation point you will find it difficult. If your
automatic weather station is in the low area where the foehn wind is
felt, it can only be distinguished from a dry katabatic wind if the
upwind conditions are known. There is a similar but milder version of
this in eastern Australia, but it is usually of the latter sort. There
may be a way to measure turbulence above the peak of the high ground
with radar or something, but I'm not familiar with that.

Jim

On Tue, May 12, 2020 at 6:13 PM Stefano Sofia

        
<stefano.sofia at regione.marche.it> wrote:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    
3 days later

    

      
      

        


  

        

      Stefano Sofia
    

    

      
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Dear Jim and Jeff,
thank you for your comments. You are right, it is quite difficult to detect this process through a single observation point, I am awre of it.
I need to set up an automatic algorithm to filter 20 years of data, and I have to find an easy way to do it.
I know quite well my automatic stations, the wind direction is very stable during these situations, and therefore I would like to start from it. (I should use also wind speed, relative humidity and temperature, but I will introduce them only once I will be able to manage the direction).
In the case of the example below reported, I know that the directions of this particular automatic station must be only SW or WSW.

My biggest problem, obviously, is to find the beginning and the end of each event, when there is a change in the main direction.
Thinking about categorical data in general, is there a way to detect periods when one particular category is more frequent?

Here I reproduce a real example 24 hours long, where these Foehn condition start between 09 and 10 and finish after 19:

first_day_POSIX <- as.POSIXct("2020-02-19-00-00", format="%Y-%m-%d-%H-%M")
last_day_POSIX <- as.POSIXct("2020-02-20-00-00", format="%Y-%m-%d-%H-%M")
mydf <- data.frame(data_POSIX=seq(first_day_POSIX, last_day_POSIX, by="10 min"))

mydf$main_dir <- c(WSW, WSW, SW, SW, W, WSW, WSW, WSW, W, W, SW, WSW, SSW, S, SW, SW, WSW, WNW, W, WSW, WSW, SE, SE, SE, NW, NNE, ENE, SE, NNW, NW, NW, NW, NW, NW, NW, NE, NW, NW, NW, NW, NW, N, WNW, NW, NNW, NNW, NW, NW, NW, WNW, ESE, W, WSW, SW, SW, SW, WSW, SW, S, S, SSW, SW, WSW, WSW, WSW, WSW, WSW, WSW, WSW, SW, WSW, WSW, WSW, WSW, SW, SW, WSW, WSW, WSW, WSW, WSW, SW, SW, SW, SW, SW, SW, SW, SW, SW, WSW, WSW, WSW, WSW, SW, SW, SW, SW, WSW, SW, SW, SW, SW, SW, WSW, SW, SW, W, WSW, WSW, SSW, S, WNW, SW, W, WSW, WSW, SE, SE, SE, NW, NNE, ENE, SE, NNW, NW, NW, NW, NW, NW, NW, NE, NW, NW, NW, NW, NW, N, WNW, NW, NNW, NNW, NW, NW, NW)

mydf$max_speed <- c(4.60, 4.60, 3.40, 3.10, 4.80, 4.20, 4.10, 4.50, 4.70, 4.30, 2.40, 2.30, 2.20, 2.10, 2.90, 2.80, 1.80, 2.70, 4.30, 3.30, 2.30, 2.30, 3.20, 3.20, 2.90, 2.30, 1.50, 1.80, 2.90, 2.40, 1.80, 2.40, 2.30, 2.60, 1.80, 2.30, 1.90, 2.20, 2.80, 2.40, 1.00, 1.10, 1.60, 2.30, 2.50, 3.30, 3.40, 3.20, 4.50, 3.90, 3.10, 2.40, 6.00, 7.80, 6.30, 7.80, 8.10, 6.10, 7.40, 9.50, 8.90, 9.10, 10.10, 10.50, 11.10, 10.10, 10.90, 11.30, 13.40, 13.50, 12.80, 11.50, 13.10, 13.50, 11.10, 10.50, 8.50, 10.10, 10.70, 13.60, 11.90, 14.90, 10.90, 10.90, 12.80, 12.10, 9.10, 8.30, 8.80, 7.40, 8.40, 10.30, 10.00, 7.00, 8.50, 8.40, 8.60, 6.70, 7.30, 6.20, 5.90, 5.90, 5.10, 5.80, 5.60, 6.50, 6.60, 11.70, 11.30, 8.70, 7.10, 6.90, 4.30, 3.80, 4.30, 3.30, 2.30, 2.30, 3.20, 3.20, 2.90, 2.30, 1.50, 1.80, 2.90, 2.40, 1.80, 2.40, 2.30, 2.60, 1.80, 2.30, 1.90, 2.20, 2.80, 2.40, 1.00, 1.10, 1.60, 2.30, 2.50, 3.30, 3.40, 3.20, 4.50)


Thank you for your attention
Stefano


         (oo)
--oOO--( )--OOo----------------
Stefano Sofia PhD
Civil Protection - Marche Region
Meteo Section
Snow Section
Via del Colle Ameno 5
60126 Torrette di Ancona, Ancona
Uff: 071 806 7743
E-mail: stefano.sofia at regione.marche.it
---Oo---------oO----------------

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Jeff Newmiller
    

    

      
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Please run your code before posting it... you forgot the quotes in your main_dir column.

first_day_POSIX <- as.POSIXct("2020-02-19-00-00", format="%Y-%m-%d-%H-%M")
last_day_POSIX <- as.POSIXct("2020-02-20-00-00", format="%Y-%m-%d-%H-%M")
mydf <- data.frame(data_POSIX=seq(first_day_POSIX, last_day_POSIX, by="10 min"))

mydf$main_dir <- c("WSW", "WSW", "SW", "SW", "W", "WSW", "WSW", "WSW", "W", "W", "SW", "WSW", "SSW", "S", "SW", "SW", "WSW", "WNW", "W", "WSW", "WSW", "SE", "SE", "SE", "NW", "NNE", "ENE", "SE", "NNW", "NW", "NW", "NW", "NW", "NW", "NW", "NE", "NW", "NW", "NW", "NW", "NW", "N", "WNW", "NW", "NNW", "NNW", "NW", "NW", "NW", "WNW", "ESE", "W", "WSW", "SW", "SW", "SW", "WSW", "SW", "S", "S", "SSW", "SW", "WSW", "WSW", "WSW", "WSW", "WSW", "WSW", "WSW", "SW", "WSW", "WSW", "WSW", "WSW", "SW", "SW", "WSW", "WSW", "WSW", "WSW", "WSW", "SW", "SW", "SW", "SW", "SW", "SW", "SW", "SW", "SW", "WSW", "WSW", "WSW", "WSW", "SW", "SW", "SW", "SW", "WSW", "SW", "SW", "SW", "SW", "SW", "WSW", "SW", "SW", "W", "WSW", "WSW", "SSW", "S", "WNW", "SW", "W", "WSW", "WSW", "SE", "SE", "SE", "NW", "NNE", "ENE", "SE", "NNW", "NW", "NW", "NW", "NW", "NW", "NW", "NE", "NW", "NW", "NW", "NW", "NW", "N", "WNW", "NW", "NNW", "NNW", "NW", "NW", "NW")

mydf$max_speed <- c(4.60, 4.60, 3.40, 3.10, 4.80, 4.20, 4.10, 4.50, 4.70, 4.30, 2.40, 2.30, 2.20, 2.10, 2.90, 2.80, 1.80, 2.70, 4.30, 3.30, 2.30, 2.30, 3.20, 3.20, 2.90, 2.30, 1.50, 1.80, 2.90, 2.40, 1.80, 2.40, 2.30, 2.60, 1.80, 2.30, 1.90, 2.20, 2.80, 2.40, 1.00, 1.10, 1.60, 2.30, 2.50, 3.30, 3.40, 3.20, 4.50, 3.90, 3.10, 2.40, 6.00, 7.80, 6.30, 7.80, 8.10, 6.10, 7.40, 9.50, 8.90, 9.10, 10.10, 10.50, 11.10, 10.10, 10.90, 11.30, 13.40, 13.50, 12.80, 11.50, 13.10, 13.50, 11.10, 10.50, 8.50, 10.10, 10.70, 13.60, 11.90, 14.90, 10.90, 10.90, 12.80, 12.10, 9.10, 8.30, 8.80, 7.40, 8.40, 10.30, 10.00, 7.00, 8.50, 8.40, 8.60, 6.70, 7.30, 6.20, 5.90, 5.90, 5.10, 5.80, 5.60, 6.50, 6.60, 11.70, 11.30, 8.70, 7.10, 6.90, 4.30, 3.80, 4.30, 3.30, 2.30, 2.30, 3.20, 3.20, 2.90, 2.30, 1.50, 1.80, 2.90, 2.40, 1.80, 2.40, 2.30, 2.60, 1.80, 2.30, 1.90, 2.20, 2.80, 2.40, 1.00, 1.10, 1.60, 2.30, 2.50, 3.30, 3.40, 3.20, 4.50)
# mark candidate rows
mydf$foehn1a <- mydf$main_dir %in% c( "WSW", "SW" )
# mark unstable conditions
mydf$foehn1b <- with( mydf
                    , cumsum( !foehn1a )
                    )
# find minimum length of foehn conditions
mydf$foehn1c <- ave( rep( 1, nrow( mydf ) )
                   , mydf$foehn1b
                   , FUN=function(v) 10 < length( v )
                   )
# find starts of foehns
mydf$foehn1d <- with( mydf
                    , 0 < diff( c( 0, foehn1c ) )
                    )
# identify foehns distinctly (multiple days)
mydf$foehn1e <- with( mydf
                    , ifelse( foehn1c
                            , cumsum( foehn1d )
                            , 0
                            )
                    )
mydf[ , c( 1, 2, 8 ) ]

        
On May 16, 2020 3:21:24 AM PDT, Stefano Sofia <stefano.sofia at regione.marche.it> wrote:

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Abby Spurdle
    

    

      
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Hi Stefano,

I don't have any specific suggestions, but...

If you could convert your (character) direction vector into a
(numeric) time-ordered direction vector giving radians or degrees, and
provide the corresponding speed vector...
(i.e. North -> 90 degrees).

I'd be happy to try and plot the data in a variety of ways...
...and see if there's any obvious relationships, or anything else useful.


On Sat, May 16, 2020 at 10:23 PM Stefano Sofia

        
<stefano.sofia at regione.marche.it> wrote:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Abby Spurdle
    

    

      
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Sorry, please put my last post aside.
I mis-read your question.

I agree with Jim's comments.

        
On Sun, May 17, 2020 at 9:52 PM Abby Spurdle <spurdle.a at gmail.com> wrote:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Jim Lemon
    

    

      
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Hi Stefano,
I don't know whether this will help you, but here is a way to
visualize wind speed and direction using clock24.plot:

first_day_POSIX <- as.POSIXct("2020-02-19-00-00", format="%Y-%m-%d-%H-%M")
last_day_POSIX <- as.POSIXct("2020-02-20-00-00", format="%Y-%m-%d-%H-%M")
mydf <- data.frame(data_POSIX=seq(first_day_POSIX, last_day_POSIX, by="10 min"))
mydf$main_dir<-c("WSW","WSW","SW","SW","W","WSW","WSW","WSW","W","W","SW",
 "WSW","SSW","S","SW","SW","WSW","WNW","W","WSW","WSW","SE","SE","SE",
 "NW","NNE","ENE","SE","NNW","NW","NW","NW","NW","NW","NW","NE","NW","NW",
 "NW","NW","NW","N","WNW","NW","NNW","NNW","NW","NW","NW","WNW","ESE","W",
 "WSW","SW","SW","SW","WSW","SW","S","S","SSW","SW","WSW","WSW","WSW","WSW",
 "WSW","WSW","WSW","SW","WSW","WSW","WSW","WSW","SW","SW","WSW","WSW","WSW",
 "WSW","WSW","SW","SW","SW","SW","SW","SW","SW","SW","SW","WSW","WSW","WSW",
 "WSW","SW","SW","SW","SW","WSW","SW","SW","SW","SW","SW","WSW","SW","SW",
 "W","WSW","WSW","SSW","S","WNW","SW","W","WSW","WSW","SE","SE","SE","NW",
 "NNE","ENE","SE","NNW","NW","NW","NW","NW","NW","NW","NE","NW","NW","NW",
 "NW","NW","N","WNW","NW","NNW","NNW","NW","NW","NW")
mydf$max_speed <- c(4.60, 4.60, 3.40, 3.10, 4.80, 4.20, 4.10, 4.50,
4.70, 4.30, 2.40, 2.30, 2.20, 2.10, 2.90, 2.80, 1.80, 2.70, 4.30,
3.30, 2.30, 2.30, 3.20, 3.20, 2.90, 2.30, 1.50, 1.80, 2.90, 2.40,
1.80, 2.40, 2.30, 2.60, 1.80, 2.30, 1.90, 2.20, 2.80, 2.40, 1.00,
1.10, 1.60, 2.30, 2.50, 3.30, 3.40, 3.20, 4.50, 3.90, 3.10, 2.40,
6.00, 7.80, 6.30, 7.80, 8.10, 6.10, 7.40, 9.50, 8.90, 9.10, 10.10,
10.50, 11.10, 10.10, 10.90, 11.30, 13.40, 13.50, 12.80, 11.50, 13.10,
13.50, 11.10, 10.50, 8.50, 10.10, 10.70, 13.60, 11.90, 14.90, 10.90,
10.90, 12.80, 12.10, 9.10, 8.30, 8.80, 7.40, 8.40, 10.30, 10.00, 7.00,
8.50, 8.40, 8.60, 6.70, 7.30, 6.20, 5.90, 5.90, 5.10, 5.80, 5.60,
6.50, 6.60, 11.70, 11.30, 8.70, 7.10, 6.90, 4.30, 3.80, 4.30, 3.30,
2.30, 2.30, 3.20, 3.20, 2.90, 2.30, 1.50, 1.80, 2.90, 2.40, 1.80,
2.40, 2.30, 2.60, 1.80, 2.30, 1.90, 2.20, 2.80, 2.40, 1.00, 1.10,
1.60, 2.30, 2.50, 3.30, 3.40, 3.20, 4.50)
mydf$main_dir<-factor(mydf$main_dir,
 levels=c("N","NNE","NE","ENE","E","ESE","SE","SSE",
 "S","SSW","SW","WSW","W","WNW","NW","NNW"))
dir2degrees<-seq(0,337.5,by=22.5)
mydf$wind_dir<-dir2degrees[as.numeric(mydf$main_dir)]
library(plotrix)
png("SS_spd_dir.png")
clock24.plot(mydf$max_speed,minutes=TRUE,mar=c(4,2,3,2),
 line.col=rainbow(16)[as.numeric(mydf$main_dir)],
 main="Wind speed and direction (color)")
legend(0,-17.5,levels(mydf$main_dir),fill=rainbow(16),
 xjust=0.5,ncol=8,cex=0.8)
dev.off()

Jim

        
On Sun, May 17, 2020 at 8:07 PM Abby Spurdle <spurdle.a at gmail.com> wrote:

            

      
      
      
    

        

      
      
    

        
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      Stefano Sofia
    

    

      
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Sorry for my fault.
I am very grateful for such code, which is extremely efficient. I would have never been able to reach these results.

In order to preserve the quality of this code, I dare to ask you a final question: once identified each single period in the column foehn1c, this period can be taken into consideration only if within it the mean of max_speed is higher than 8.0 (which is speed in m/s).
Could you please help me in this final step?

Thank you again for all your help
Stefano


         (oo)
--oOO--( )--OOo----------------
Stefano Sofia PhD
Civil Protection - Marche Region
Meteo Section
Snow Section
Via del Colle Ameno 5
60126 Torrette di Ancona, Ancona
Uff: 071 806 7743
E-mail: stefano.sofia at regione.marche.it
---Oo---------oO----------------

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Jim Lemon
    

    

      
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Hi Stefano,
If I understand your request, this may also help, Uses the same data
transformations as my previous email.

png("SS_foehn.png")
plot(mydf$data_POSIX,
 ifelse(mydf$main_dir %in% c("WSW","SW"),mydf$max_speed,NA),
 type="b",main="Wind speed (WSW or SW) by time",
 xlab="Time of day",ylab="Wind speed km/h",
 col=rainbow(16)[as.numeric(mydf$main_dir)])
abline(h=8,col="orange",lwd=2)
source("../rollmean.R")
rmws<-rollmean(mydf$max_speed,4)
lines(mydf$data_POSIX,rmws,col="orange",lwd=2)
legend("topleft","Rolling mean of 4 for wind speed",
 lty=1,lwd=2,col="orange")
dev.off()

Jim

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      Jeff Newmiller
    

    

      
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While I can understand that such techniques might not seem obvious at first, they are building blocks that you should be able to use to solve similar problems in the future. Don't give up because it surprised you this time, and do play with modifying it to better understand this time.

Replace code starting with calculation of foehn1d:

# calculate mean values by candidate group
mydf$foehn1c2 <- ave( mydf$max_speed
                   , mydf$foehn1b
                   , FUN=mean
                   )
# find starts of foehns
mydf$foehn1d <- with( mydf
                    , 0 < diff( c( 0, foehn1c & 8<foehn1c2 ) )
                    )
# identify foehns distinctly (multiple days)
mydf$foehn1e <- with( mydf
                    , ifelse( foehn1c
                            , cumsum( foehn1d )
                            , 0
                            )
                    )
mydf[ , c( "data_POSIX" , "main_dir", "max_speed" , "foehn1e" ) ]

        
On May 18, 2020 3:14:06 AM PDT, Stefano Sofia <stefano.sofia at regione.marche.it> wrote:

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Jeff Newmiller
    

    

      
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? source("../rollmean.R") ?

        
On May 18, 2020 4:11:52 AM PDT, Jim Lemon <drjimlemon at gmail.com> wrote:

            

      
      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Jim Lemon
    

    

      
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Sorry, I should know better:

rollmean<-function(x,width=2) {
 lenx<-length(x)
 result<-rep(NA,lenx)
 for(i in 1:lenx) {
  chunk<-i:(i+width-1)
  if(i<width) chunk<-c(rep(1,width-i),1:i)
  if(i>(lenx-width)) chunk<-c(i:lenx,rep(lenx,i-(width-1)))
  result[i]<-mean(x[chunk])
 }
 return(result)
}

I forgot to replace this with:

library(zoo)
rollmean...

Jim

        
On Tue, May 19, 2020 at 1:26 AM Jeff Newmiller <jdnewmil at dcn.davis.ca.us> wrote:

            

      
      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Abby Spurdle
    

    

      
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I was impressed by Jim's effort.
So, I thought I'd try to produce an exploratory plot.

I've adapted some of his code.
The following script produces a heatmap for a cylindrical density estimate.
Bright areas are (mathematical) regions of high density.
However, the interpretation is complicated by the fact that the data
uses max wind speed rather than wind speed, per se.

I note your subject line, "Classification of wind events".
I'm not sure what sort of classification is possible.

Could there be some sort of lagged effect...?
(i.e. Could wind direction or speed at time t, be related to wind
direction or speed at time t-1, t-2, etc ...?).

------------------------------------------------------
library (barsurf)
library (probhat)
set.bs.theme ("blue")

g <- c ("WSW", "WSW", "SW", "SW", "W", "WSW", "WSW", "WSW", "W", "W",
    "SW", "WSW", "SSW", "S", "SW", "SW", "WSW", "WNW", "W", "WSW",
    "WSW", "SE", "SE", "SE", "NW", "NNE", "ENE", "SE", "NNW", "NW",
    "NW", "NW", "NW", "NW", "NW", "NE", "NW", "NW", "NW", "NW", "NW",
    "N", "WNW", "NW", "NNW", "NNW", "NW", "NW", "NW", "WNW", "ESE",
    "W", "WSW", "SW", "SW", "SW", "WSW", "SW", "S", "S", "SSW", "SW",
    "WSW", "WSW", "WSW", "WSW", "WSW", "WSW", "WSW", "SW", "WSW",
    "WSW", "WSW", "WSW", "SW", "SW", "WSW", "WSW", "WSW", "WSW",
    "WSW", "SW", "SW", "SW", "SW", "SW", "SW", "SW", "SW", "SW",
    "WSW", "WSW", "WSW", "WSW", "SW", "SW", "SW", "SW", "WSW", "SW",
    "SW", "SW", "SW", "SW", "WSW", "SW", "SW", "W", "WSW", "WSW",
    "SSW", "S", "WNW", "SW", "W", "WSW", "WSW", "SE", "SE", "SE",
    "NW", "NNE", "ENE", "SE", "NNW", "NW", "NW", "NW", "NW", "NW",
    "NW", "NE", "NW", "NW", "NW", "NW", "NW", "N", "WNW", "NW", "NNW",
    "NNW", "NW", "NW", "NW")
levels <- c("E", "ENE", "NE", "NNE", "N", "NNW", "NW", "WNW",
    "W", "WSW", "SW", "SSW", "S", "SSE", "SE", "ESE")
g <- factor (g, levels=levels)

r <- seq (0, 337.5, by=22.5)
x <- r [as.integer (g)]

y <- c (4.6, 4.6, 3.4, 3.1, 4.8, 4.2, 4.1, 4.5, 4.7, 4.3, 2.4, 2.3,
    2.2, 2.1, 2.9, 2.8, 1.8, 2.7, 4.3, 3.3, 2.3, 2.3, 3.2, 3.2, 2.9,
    2.3, 1.5, 1.8, 2.9, 2.4, 1.8, 2.4, 2.3, 2.6, 1.8, 2.3, 1.9, 2.2,
    2.8, 2.4, 1, 1.1, 1.6, 2.3, 2.5, 3.3, 3.4, 3.2, 4.5, 3.9, 3.1,
    2.4, 6, 7.8, 6.3, 7.8, 8.1, 6.1, 7.4, 9.5, 8.9, 9.1, 10.1, 10.5,
    11.1, 10.1, 10.9, 11.3, 13.4, 13.5, 12.8, 11.5, 13.1, 13.5, 11.1,
    10.5, 8.5, 10.1, 10.7, 13.6, 11.9, 14.9, 10.9, 10.9, 12.8, 12.1,
    9.1, 8.3, 8.8, 7.4, 8.4, 10.3, 10, 7, 8.5, 8.4, 8.6, 6.7, 7.3,
    6.2, 5.9, 5.9, 5.1, 5.8, 5.6, 6.5, 6.6, 11.7, 11.3, 8.7, 7.1,
    6.9, 4.3, 3.8, 4.3, 3.3, 2.3, 2.3, 3.2, 3.2, 2.9, 2.3, 1.5, 1.8,
    2.9, 2.4, 1.8, 2.4, 2.3, 2.6, 1.8, 2.3, 1.9, 2.2, 2.8, 2.4, 1,
    1.1, 1.6, 2.3, 2.5, 3.3, 3.4, 3.2, 4.5)

data.frame (g, x, y)

x2 <- c (x - 360, x, x + 360)
y2 <- rep (y, times=3)

fh <- pdfmv.cks (cbind (x2, y2), bw = c (240, 9.5) )

N <- 64
u <- seq (270, -90, length.out=N)
v <- seq (0, 15, length.out=N)
fv <- outer (u, v, function (x, y) fh (cbind (x, y) ) )

#not necessary for exploratory purposes
Fh <- cdfmv.cks (cbind (x2, y2), bw = c (240, 9.5) )
scaling.factor <- probmv (Fh, c (0, 0), c (360, max (y) ) )
fv <- fv / scaling.factor

#currently problems with descending x/y coords
#(to fix in near future)
#so set x-axis to [0, 1]
u2 <- seq (0, 1, length.out=N)

plot_cfield (u2, v, fv,
    axes = c (FALSE, TRUE),
    main="Wind Speed\n(Cylindrical Density Estimate)",
    xlab="direction", ylab="max wind speed",
    hcv=TRUE)
axis (1, c (0.05, 0.275, 0.5, 0.725, 0.95), c ("South", "West",
"North", "East", "South"), FALSE)
abline (v=0.5, lty=2, col="white")

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