Dear Safwan,

I think you should explain the details for the interpolation of 5 available points containing wind direction data. Do you want to get a direction value in one internal point relatively to the available points? Or do you want to get values for some grid?

The direction can cause some problems during interpolation since it varies from 0 to 360 degrees. You can use other wind characteristics related to the wind direction. When I used wind data, I worked with its components (zonal and meridional wind: u and v). u and v have no limits that can affect their interpolation, they can have different signs ("+" or "-") instead. You can obtain zonal and meridional wind through wind direction and wind speed. Then you can get interpolated values of zonal and meridional wind for some points. After that you will be able to get the wind direction from u and v back.

Wind components are given by the formulae:

u = -speed * sin(dd)

&

v = -speed * cos(dd)

 where dd is the direction of the wind as reported according to the specification of wind direction.

Sincerely,

Oleksandr.

Dear Oleksandr Yeshanu

Thank you for your answer.

Yep I want to get the value of direction.

But if we are giving value according to 360 degree when we interpolate this how it will work.

If the area is plain area It will quite work. My study area  is undulating topography.

Thank you

Dear Safwan,

As I understand, you are not sure about the procedure of interpolation for the wind data retrieved at the places of different topography. I think that you should obtain and check multiple statistical characteristics for the wind data at each point from 5 points. You must consider time series for each point; take a look at their distribution, dispersion, etc. After that you will see if the data from different points can be compared and used together for spatial interpolation. Some data points can be excluded from interpolation procedure due to their inhomogeneity or non-representativeness.

I can advice you to look at the following official document with interpolation mentioned:

- WMO-No. 100 (Guide to Climatological Practices) published in 2011. The PDF file is attached. You should look at its chapter 5.9 "Estimating Data" (pages 82-85). The chapter 5.9.3 “Spatial estimation methods” (pages 83-84) can give you some good advice for your problem of spatial interpolation when undulating topography is present.

Some brief answers about interpolation difficulties are given in my message by the following block of text (copied from the mentioned document WMO-No. 100).

5.9.3 Spatial estimation methods

Spatial interpolation is a procedure for estimating

the value of properties at unsampled sites within

an area covered by existing observations. The

rationale behind interpolation is that observation

sites that are close together in space are more likely

to have similar values than sites that are far apart

(spatial coherency). All spatial interpolation

methods are based on theoretical considerations,

assumptions and conditions that must be fulfilled

in order for a method to be used properly.

Therefore, when selecting a spatial interpolation algorithm, the purpose of the interpolation, the

characteristics of the phenomenon to be

interpolated, and the constraints of the method

have to be considered.

Stochastic methods for spatial interpolation are

often referred to as geostatistical methods. A

feature shared by these methods is that they use a

spatial relationship function to describe the correlation

among values at different sites as a function

of distance. The interpolation itself is closely

related to regression. These methods demand that

certain statistical assumptions be fulfilled, for

example: the process follows a normal distribution,

it is stationary in space, or it is constant in all

directions.

Even though it is not significantly better than

other techniques, kriging is a spatial interpolation

approach that has been used often for interpolating

elements such as air and soil temperature,

precipitation, air pollutants, solar radiation, and

winds. The basis of the technique is the rate at

which the variance between points changes over

space and is expressed in a variogram. A variogram

shows how the average difference between values

at points changes with distance and direction

between points. When developing a variogram, it

is necessary to make some assumptions about the

nature of the observed variation on the surface.

Some of these assumptions concern the constancy

of means over the entire surface, the existence of

underlying trends, and the randomness and independence

of variations. The goal is to relate all

variations to distance. Relationships between a

variogram and physical processes may be accommodated

by choosing an appropriate variogram

model (for example, spherical, exponential,

Gaussian or linear).

Some of the problems with kriging are the computational

intensity for large datasets, the complexity

of estimating a variogram, and the critical assumptions

that must be made about the statistical nature

of the variation. This last problem is most important.

Although many variants of kriging allow

flexibility, the method was developed initially for

applications in which distances between observation

sites are small. In the case of climatological

data, the distances between sites are usually large,

and the assumption of smoothly varying fields

between sites is often not realistic.

Since meteorological or climatological fields such

as precipitation are strongly influenced by topography,

some methods, such as Analysis Using

Relief for HYdrometeorology (AURELHY) and

Parameter-elevation Regressions on Independent

Slopes Model (PRISM), incorporate the topography

into an interpolation of climatic data by

combining principal components analysis, linear

multiple regression and kriging. Depending on the

method used, topography is described by the

elevation, slope and slope direction, generally

averaged over an area. The topographic characteristics

are generally at a finer spatial resolution than

the climate data.

Among the most advanced physically based methods

are those that incorporate a description of the dynamics

of the climate system. Similar models are routinely

used in weather forecasting and climate modelling

(see section 6.7). As the computer power and storage

capacity they require becomes more readily available,

these models are being used more widely in climate

monitoring, and especially to estimate the value of

climate elements in areas remote from actual observations

(see section 5.13 on reanalysis).

Sincerely,

Oleksandr.

You can also have a look at the following discussions related to interpolation:

https://www.researchgate.net/post/When_can_I_use_nearest_neighbor_over_bi-linear_interpolation_for_interpolating_modeled_data

https://www.researchgate.net/post/What_interpolation_technique_is_best_for_AWS_data

https://www.researchgate.net/post/Could_anyone_please_explain_how_and_why_the_Spline_Interpolation_Method_is_the_best_for_heterogeneous_terrains

Dear Oleksandr Yeshanu

Once again my hearty thanks to you.

Let me read mentioned discussion and understand the concepts behind it and  will let you know.

Sincerely

Safwan