http://dusk2.geo.orst.edu/gis/geostat_analyst.pdf

http://jssm.umt.edu.my/wp-content/uploads/sites/51/2015/02/1.pdf

Dear Gianmarco,

you have a couple of options to interpolate the wind direction mesurments using Arcmap. As far as I understand you want to determine the wind direction in each location of the studied area using punctual measurements. I am not sure whether you have to absolutely follow the methodology applied in the mentioned publication, but I would suggest this process below.

First you have to decide whether you want only the map of the spatial distribution of the 1) prevailing wind direction or 2) the maps of the distribution of the wind directions in which the wind rose is divided.

Both processes ca be applied for:

- a long-term analysis -> processing of the full dataset for estimate of long term averages 

- temporal analyses of the spatial distribution of the wind direction by week, month, season -> split of the datasets with wind measurments in corresponding subsets 

case 1: assuming you have the data of the wind direction of weather stations, you should process them in order to find the mean value and then to apply an interpolation method you find in Arcmap. Spatial Analyst toolbar > Interpolation, then you can apply one of the available methods: IDW (Inverse Distance Weighted), Kriging, Natural Neighbor, Spline.

case 2:  assuming you have the data of the wind direction of weather stations, you should process them in order to find the frequency of occurency of each sector in which you divide the wind roe (12, 16, 20, 36 sectors). Obviously for double check, the sum of the frequencies in percentage of each sector has to give 1. Once you have these data stored in the tabel of content of the weather stations, you can use on the methods mentioned in the case 1 and to get a number of surfaces equal to the number of sectors.

If you want to store everything in one single file, you could try to store everthing somehow in a netCDF file which is supported by Arcmap, but I am not sure it is something you envisage.

I hope it helps. In case let me know if you need clarifications.

Best,

Stefano

Dear @Stefano, thank you for your reply. I have edited my question to provide a little bit more context. Indeed, my situation matches your case 1. Yes, I am familiar with the interpolation facilities implemented in ArcMAP. The main problem is that I have read here and there that it is not recomended to directly interpolate wind direction since the latter is a circular statistic (like, for instance, the slope aspect), which need a special "treatment". That's why I was asking for that specific procedure.

Should you have any further comment or suggestion, please feel free to reply.

Thank you.

Gm

Dear Gianmarco,

Sorry for my late reply but I have been on trip. Wind direction is for sure a special parameter to interpolate. We did the map of the wind direction using a machinle learning technique but It might be quite complicated. I try to answer your question in a simple way.

if in your shaefile points you have the wind direction in degrees, you multiply by cosine and sine to get the components yur H=1. H can be any arbitrary vaue such as (also) the wind speed vector. The wind speed is in physic a vector, thus characterized by 2 components: its absolute value (i.e. without sign + or -) and its direction in a reference sstem (e.g. carteisian axes). So in the pic, you use the direction to calculate the components of the wind speed in a 2D space (i.e. X and Y). The wind direction is an angle that can be broken up in its X and Y components just using sine and cosine with H=1 for simplicity.

Point c of the pic: it is a pure geometrical convention: you imagine to set a reference system centered in each of your points of the shapefile with the wind direction. As a function of the value of the wind direction, the vector of the wind direction lies in one of the 4 quads. So, if the value of the wind direction is between 0° and 90°, the wind direction lies in the first quad (above-right), if between 90°-180° in the second, etc...

For doing this you should use Python language with some libraries for interpolating the points.

I hope to have replied you

Best,

Stefano

Hello @Stefano,

thanks for your detailed reply, which clarifies a lot the procedure.

I have dug into the issue in the meanwhile, and I seem to have finally grasped the matter. So, as you have described, wind direction has to be split into two components, using the sine and cosine of the wind direction (multiplied by the wind speed). As far as GIS is concerned, one the two components are obtained and stored in the weather stations attribute table, one can interpolate them separately. Then, via raster algebra one has to use the interpolated componenets rasters to get the direction back. Now, as for this latter point, I have found a perhaps easier solution. Instead of creating the conditional statements you were referring to in the last part of your reply, it should be possible to use arctan function to simplify things:

(ATan2(v, u) / (2*3.14159265) + 0.5) * 360

where v corresponds to Y, and u to X of the image that I have attached in my initial thread.

This should "convert" the two components back to the right direction angle.

It should also be noted what stressed here (http://mmc2.geofisica.unam.mx/cursos/geoest/Articulos/Geostatistics/Non-Linear%20Surface%20Interpolations.htm). Due to a difference between mathematical and GIS conventions, while in mathematical convention Y should be equal to the sine of the direction (times the speed) and X to the cosine of the direction (times the speed), in GIS convention that should be actually reversed (using cosine for Y, sine for X). This has been noted for ArcView, and I am wondering if this still holds true for ArcMAP. Do you have any idea on how can I check that?

If you have further insights, especially on the last crucial point, feel free to reply.

Best

Gm

Could you please give me more details of the functions you use?

Personally, I would use python librares or arcpy for this issue. So as you asked, it is a bit unclear what sort of conventions you are talking about. Probably there is an easier way to fix this problem.

@Stefano, thanks for replying back. I will try to describe my issue as clearly as possible. I am currently in a conundrum, and it seems I cannot find a solution.

In GIS (ArcMAP) I have some points representing locations at which the wind speed and direction are measured. Let's focus on wind direction. I need to interpolate wind direction since I need (for the sake of further processings) a continous surface. Therefore, I need:

1) to calculate wind's components u and v

2) interplotate them

3) use the interpolated u and v (i.e., the rasters representing the interpolated u and v) to get back the direction value (in meteorological convention, degrees from North, the latter being 0).

My problems are with step 1 and 3.

As for step 1:

On the one hand, ArcGIS help (http://desktop.arcgis.com/en/arcmap/10.3/manage-data/raster-and-images/resample-function.htm#GUID-E98FE40E-2B75-492E-A258-5FF3D5171E0D) seems to suggest that:

u = m * cos (pi *d / 180)

v = m * sin (pi * d /180)

where m is the magniture (i.e., wind speed) and d is the direction.

On the other hand, a techincal note by S. Grange here on RG (https://www.researchgate.net/profile/Stuart_Grange2/publication/262766424_Technical_note_Averaging_wind_speeds_and_directions/links/54f6184f0cf27d8ed71d5bd4/Technical-note-Averaging-wind-speeds-and-directions.pdf) suggests:

u = -m * sin (2*pi*d/360)

v = -m * cos (2*pi*d/360)

As for the above, my doubts:

1) Is the inversion between sin and cos across the two sources due to the fact the the second is negating m?

2) Negating m (and, ultimately, the sign of the u and v componenets) is justified by the second source "because the wind direction, by metereological convention, is defined from where the wind is blowing, while the vectors fefine the direction where the flow is heading to". I am wondering: is the approach proposed by the second source preferable? Should I follow that one?

As for step 3:

Once I got the u and v components, how can I calculate the direction in degrees?

Different sources propose the use of the atan2 function. For instance,the ArcGIS help documentation (http://desktop.arcgis.com/en/arcmap/10.3/manage-data/raster-and-images/resample-function.htm#GUID-E98FE40E-2B75-492E-A258-5FF3D5171E0D) suggest:

d = atan2 (v / u) * 180 / pi

which only returns values between -180 and 180.

To correct that (my guess), a different formula is suggested in this forum (https://gis.stackexchange.com/questions/110136/generating-wind-direction-raster-using-its-u-and-v-components-in-arcgis-desktop):

(ATan2(v, u) / (2*3.14159265) + 0.5) * 360

My question: is the second formula above the right one to be used? Can the second one be used even if the Grange's approach (the one which was negating the components) is used? If the Grange's method is used, must the v and u within the atan2 formula be swapped?

Thank you.

Best

Gm

Technical Report Technical note: Averaging wind speeds and directions

Hello.

I seem to have finally found a proper solution to the problem. I followed the method described by S. K. Grange (https://www.researchgate.net/profile/Stuart_Grange2), who was framing the method in terms of R coding. Anyway, I got some results that made sense. I checked, for instance, the interpolated direction values between two sampling points: the values in between made sense, while in my previous attempts there was not meaningful relashionship among them.

So, the u and v components were obtained:

u= -SPEED * Sin(2 * 3.141592 * DIRECTION / 360)

v= -SPEED * Cos(2 * 3.141592 * DIRECTION / 360)

In doing that, I followed Grange's advise to negate the wind speed (for the reasons that I referenced to in my previous reply).

After having interpolated the u and v values, the two obtained rasters were processed throught Raster Calculator to eventually arrive to a  wind direction raster, whose values in degrees were meaningfully expressed, without the need of extra calculation or conditional statements. The following is the formula used in Raster Calculator:

(ATan2(u, v) * 360/2/3.141592) + 180

As for the latter formula, it must the noted that (unlike other sources found on the web), u and v must be fed as first and second argument respectively into ATan2, NOT the opposite (as requested by other softwares).

Of course, this is valid for ArcMAP as far as I can tell.

Hope this will prove correct and, hopefully, useful to others.

Any further comment/suggestion is welcome.

Best

Gm

A better link with all Figures.

http://proceedings.esri.com/library/userconf/proc99/proceed/papers/pap122/p122.htm

-in step (1) above, shall I take the sine and cosine of the wind direction only, or these must be multiplied by H (see the upper-left part of the attached image)?

Yes, these must be multiplied by H

-the last step of the procedure, the one that is indicated at point c of the attached image, is rather obscure to me.

See attached Figure to understand four identical vectors.