Hi Elias, are you generating Thiessen polygons from the 19 stations, and the ground data from the NCDC stations ? If the 19 stations are reliable, that might be adequate, or would you wish for greater spatial representation ?  If so, you could create another Thiessen polygon set from the NCDC stations for the same time period, and compare the two spatial rainfall layers. If you are interested,  I used a MATLAB function to generate Thiessen/Voronoi polygons for rainfall in the pub below:

Article A Hydrological Budget (2002-2008) for a Large Subtropical We...

I don't know that I know the correct answer, but if someone has a range of postcodes but can't include all and they want a sample, wouldn't they just generate a random number list

It depends on the purpose of your analysis, but simply computing the average value of 112 "stations" could be the better way to proceed.

Just what comes to my mind: If your study area is homogenous then you could do a random sample from the 112 stations, or also use - as Luca suggested - some kond of average measure (median, mean) from all stations. if there are gradients that should be included in the model you have to make sure that you sample randomly along that gradient, once you have the data subsetted you can again decide if you use a summary stat for each subset. If your study area can be split in disctinct sub-areas (e.g. depnding on the size an morphology of teh data-set there could be plateau areas and more mountaineous areas tha finally end-up in a delta) I would maybe try to apply a stratified random sample to have stations describing the outcome variables in all sub-areas. Ok, so in my opinion it really depends on what you are aiming to model and in what detail. The stations you model have to be representative on for the processes you want to model. E.g. if you want to derive a model "simply describing" discharge from the entire watershed you could say that you chose the stations at the outlet point and try to produce a model that describes that data. Ok these are just some thought... It feels to me like this is as usual a short question that doesnt not necessarily have a short answer.

A good solution, in my opinion, would be to perform Principal Component Analysis (PCA), on the precipitation series of your stations (temperature is suppossed to be more homogeneus in space, despite elevation gradients, therefore i would focus on precipitation). You perform the PCA and obtain a number (tipically no more than 4-5) of new uncorrelated series called principal components that explain most of the variance contained in your original 112 series; then you look at the loading factors, which indicate the correlation of your 112 series with each obtained principal component, and select the stations that best correlate with each principal component. There you have your stations that are representative of the variability of your data.

I like Christians idea of stratified random sampling. However, typically there are much fewer stations at high elevations or in isolated areas than in low elevation/densly populated areas. You could include all the stations from "exotic" locations and chose randomly from the other locations. kind regards Irene

I agree with Christian, the question is not that simple because in such a large area, as the one you are analyzing I am sure it is not homogeneous so the first analysis is to determine your subareas and then group to characterize. It seems to me that a mean in a non-homogeneous area would not be representative. Just a thought.

my suggestions: group the stations according to

1) elevation and 2) north/south or east/wset orientation in your catchment and chose subsamples for groups with many sites.

good luck!

Dear all,

Thank you very much for the various interesting answers. I later on found a website that has some insitu measurements of rainfall data for the study area dating back from the 50s to the mid 2000 for about 55 rainfall stations. I have screened the data and come out with 19 reliable stations that have continuous  monthly rainfall data of atleast 15 years each between 1979 and 2007. I have recorded the points in the XY direction in excel and transferred it arcgis 10.2. I intend to create thiessen polygons with the spatial data and then add the ground data to thissen polygons. Each ground point  will fall inside a polygon so i will calculate the statistics between that point data rainfall and the spatial point rainfall. If two ground points fall within the same polygon, i will assign one to the closest polygon that has no point data given that the area is relatively very very flat . I do not know if this is the right route to take anymore suggestions? Point of correction i downloaded the spatial data from Climate Forecasting System Reanalysis  website specially prepared for swat modelling application.

Dear Elias,

I have no clue on the GIS-side of your problem (shame on me), but otherwise your plan seems fine to me.

best wishes, Irene

 It is good idea. Thiessen polygons are almost good for analysis local climate conditions.

Good luck

Joanna

Hi Elias,

Using Thiessen polygon to average the rainfall/climate data to the catchment scale is a good idea. Though it is a classic method but many comparative studies against more sophisticated method (i.e. geostatistical) resulted less significant differences. However, subsequent to Thiessen, I suggest you to make an altitude-correction based on the relationship between average annual rainfall and gauges altitude. Your resulted climate data will be much reliable since your altitude correction will offset the Thiessen drawback in averaging values in an area which has high topographic variations.  Good luck.

You can use the clustering  techniques.

Good luck

I would consider the relatively new method of "balanced sampling". Although originally intended as a design-based strategy it also performs very well as a model-based technique. The sample can be balanced with respect to multiple covariates simultaneously, for example rainfall, temperature, altitude, spatial coordinates. 

First its good to learn that your research is not limited in terms of data availability! As regards the way forward I suggest the following:

1. Carry out a homogeneity test using the climatic parameters at your disposal. This will show you the stations that can be clustered based on homogeneity before sampling.

2. Check the available data to establish their lengths and entirety over the periods and consider those that meet the the threshold of at  least 30 years continuous record for climatic studies.

3. Based on the suggestions given, use conventional methods to sample the suitable stations for your research. Good luck!!!

Hi Elias, are you generating Thiessen polygons from the 19 stations, and the ground data from the NCDC stations ? If the 19 stations are reliable, that might be adequate, or would you wish for greater spatial representation ?  If so, you could create another Thiessen polygon set from the NCDC stations for the same time period, and compare the two spatial rainfall layers. If you are interested,  I used a MATLAB function to generate Thiessen/Voronoi polygons for rainfall in the pub below:

Article A Hydrological Budget (2002-2008) for a Large Subtropical We...

Thiessen polygon is the obvious solution. But I read a paper a while back which talked about selecting a few stations which represent the entire watershed, by testing the temporal and spatial stability of the data. You can take a look at that.

http://www.sciencedirect.com/science/article/pii/S0034425704001750

all answers are correct, however, my experience has shown me that to have a real representation of the results of the analysis that you are performing data stations, regardless of the period of observation, data consistency, data reliability etc., ie data from weather monitoring stations used, you should consider your point of location, ie Thiessen polygons are "representative" in areas where there is no large topographical or covered slope similar surface the area to be evaluated, but so, can correlate more than one method as kriging or interpolation and thereby define zones within the area to be assessed by similar characteristics and then choose the data reliability.

Carmen, that's a very interesting point you mention, about topographical heterogeneity in a Thiessen polygon that covers a large area because of a low density of rainfall stations. In my work in Tanzania, I  faced this.. was working on a catchment whose headwaters lay in the Eastern Arcs Mountains (perpetually clouded tops, very high rainfall as compared to the lowlands). However there was not a single meteorological station in the entire catchment. There were some in the larger region, including a couple in the mountains (adjoining catchments). As you mention, different kriging methods yield different isohyets, so its a good suggestion to compare various kriging methods to get at least a coarse regional picture.

the best way for rainfall is to do things backwords. you just need to chose a bridge( section of the bridge) and slope. later if you have appropriate curve number you can correlaeate the flow and curve number. later you will have the best rainfall date.

You can choose a set of stations as a testing data and the rest of stations as validate data. Then you can use ARCGIS Spatial statistics tools and check which of the available methods (IDW, Kriging, GWR) are best fit on your data.

Certainly  Stations which have longer period are more appropriate. It is also necessary stations were selected so that they cover the entire basin. in this way some station will eliminated. then you apply Carmen Julia Navarro answer and others.

Hi Elias, 

If you didn't solve that yet. Data from NCDC is a girded point data, so if you make Thiessen Polygons you are going to end up with rectangular boxes. Actually those boxes will have size approximately 35 km by 40 km, then one pixel is going to cover area of 1400km2 then if you make a rough calculation you will have a minimum of 54 stations inside your watershed. If you use Thiessen polygon the numbers of the stations will go down by a minimum of 70%. 

Most of the polygons in your watershed are going to have the same area and there weight on areal rainfall or temperature will be the same. 

Abeyou Wale 

The most important question is what do you mean by "representative", that is not a statistical term. It may have an intuitive meaning but then the question is how do you propose to use the "representative" data? I.E. what characteristics do you think "representative" data have?