The water quality parameter included right from temperature, hardness, pH etc to anions, cations and other trace elements for this case. Some papers suggest krigging (ordinal or universal) and some papers suggest IDW for the basic parameters. But all method are giving me entirely different results...
A few key things to consider when comparing methods:
To really understand if your methods differ (aside from looking different) on the map you need to know if differences are outside the prediction error itself. Usually competing methods differ by less than the uncertainty in the predicted values for any of the methods. Most reasonable methods will fall within the uncertainty of bounds of prediction at un-sampled locations.
An easy way to get started is to look at two questions...1) are mesurements uncertain at a given location. In other words, do duplicate measurements at the same location and time provide the same of different values. You need some field duplicates to anlayze this issue.
2) Another key question, is regarding the uncertainty in predictions at un-sampled locations. A simple way to investigate this questions is to drop an observation and try to predict it with the remaining data--this is called cross validation.
Without seeing your data, it is hard to guess, but I would expect the uncertainty in cross validation (i.e. true - predicted) to exceed the differences among methods which would indicate that gaining an understanding of the prediction error is much more interesting than puzzling over differences among methods.
But that will lead you to the geostatistical methods because they provide the tools for formal uncertainty analysis. Some work learning geostatistics and it's variants seems to be in your future.
Im not an expert but kriging is used for data that may have a directional component (you would be looking for a directional component)
I recommend you the geostatistical interpolation techniques (e.g. kriging). The variogram analysis will provide additional information about your data (regional variability). You can use secondary variables in order to improve your estimation, and all the results will have a interpolation error estimation. Also, I recommend you the use of conditional geostatistical simulation methods, that preserve the original variablity of your data.
I don't know what data you want to interpolate exactly. But if the data are normally distributed, every method 's result will be not very different. If they are, please check the method program, is there any problem? If they aren't, maybe the OI will be a good choice. But it is a little difficult to define the error function and error correlation function.
An easy method would be the inverse distance , if you would like to use kriging it is better to know somethings first about how the variogram works.(Theory)
In which waters do you want to interploate the parameters? In rivers none of the mentioned methods will give you a satisfying answer, because they are all made for interpolation of areas.
for Groundwater I also would suggest Kriging, but the Interpretation of a semivariogramm is not trivial and needs expirience. regards, André
thank you all for your suggestions. But I am working on a Lake where I want to interpolate the water quality parameters.
IF your measures are precise in their locations and IF they are approximately Gaussian, MAYBE you can be successful in using kriging withouth further complications. But, as André stated, even when every regularity condition is met, interpolating (i.e. kriging) from a variogram model isn't really a trivial task. I'd reccommend you go see the nearest geostatistician :)
Cheers,
Not certain what you mean by interpolation. Whether it's spatial, environmental, or geochemical. You may find a nice discussion in M. Galindo de Obarrio's thesis, though.
http://www.itc.nl/library/papers_2005/msc/wrem/galindo.pdf
A few key things to consider when comparing methods:
To really understand if your methods differ (aside from looking different) on the map you need to know if differences are outside the prediction error itself. Usually competing methods differ by less than the uncertainty in the predicted values for any of the methods. Most reasonable methods will fall within the uncertainty of bounds of prediction at un-sampled locations.
An easy way to get started is to look at two questions...1) are mesurements uncertain at a given location. In other words, do duplicate measurements at the same location and time provide the same of different values. You need some field duplicates to anlayze this issue.
2) Another key question, is regarding the uncertainty in predictions at un-sampled locations. A simple way to investigate this questions is to drop an observation and try to predict it with the remaining data--this is called cross validation.
Without seeing your data, it is hard to guess, but I would expect the uncertainty in cross validation (i.e. true - predicted) to exceed the differences among methods which would indicate that gaining an understanding of the prediction error is much more interesting than puzzling over differences among methods.
But that will lead you to the geostatistical methods because they provide the tools for formal uncertainty analysis. Some work learning geostatistics and it's variants seems to be in your future.
@ John ,
Your advice is quite valid and commendable. However, problem of uncertainty cannot be resolved, it is why scholarly contributions have overwhelmingly suggested probabilistic Kriging instead of deterministic IDW method. In the case of DEM or interpolation of elevation or other values for which precise values of un-sampled locations are already available or can be obtained at low cost in a short time, accuracy of interpolation may be ascertained using a number of methods.
However, in situation where it is not possible or cost is high and time required is long, will it not be advisable to use significance of spatial auto-correlation beforehand to determine the extent of probability of the prediction for un-sampled location to deviate from the reality? Rest may be taken care by variogram etc.
Hello Chitrini Mozumder:
The answer of your question is not unique, because it might differ for each different parameter of interest. To make things worse, the "best" answer for your present data might be different for other region.
If you are extremely worried about the accuracy of the interpolation method, you should choose the "best" among the ones you have available, a choice which is not straightforward in general. My suggestion is the following:
a) select a subset of your data, to be designated as "control data"
b) interpolate with the i-th method the rest of the available data over the location of the control data, which is unknown to the method
c) once you did it for all the available methods, sort them according to any suitable metric (like the RMSE).
d) repeat many times from a) to c) selecting at random different control data sets. Keep the record of the sorted methods!
e) Now you have many cases where the available methods are ordered. It will be unlikely that one method is always the winner, so you should apply some statistical algorithm to decide which is the "statistically significant" winner, with a given confidence level. Use the Friedman Test for that; the procedure is explained at http://www.thedigitalmap.com/~carlos/papers/rep12_4/OnTheInterpolationAlgorithmRanking.pdf
Of course, you have to repeat the whole procedure for each parameter of interest; there is no reason why to expect that the same method will be the winner for all of them.
I strongly agree with Mr. Kern regarding considering also the uncetainty in the measurements; if it is high, almost surely any interpolation method will be equivalent. Uncertainty might be due to repeatibility (i.e. precision) or accuracy (i.e. bias). Ordinary Kriging and other geostatistical methods might be the best, but only provided the variogram is accurate (i.e. the parameter of interest behaves as kriging expects). Otherwise it is just another option, with the advantage that it estimates also uncertainty, but no more.
Hope this helps.
Carlos
Kriging is a very good method if applied after a accurate geostatistical analysis.
The term “interpolation” is understood as the determination of the value of an unknown function within the given interval. In order to make an interpolation the unknown function is approximated with an appropriate analytical function, the value needed being determined afterwards. The polynomial approach is most frequently used.
Smoothing spline interpolation could be used, so also Lagrange interpolation could also be used.
Cokriging which is the multivariate equivalent of kriging is also suggested.
Interpolation is a good method to produce colourful displays for presentation. But in most cases, particularly for ground water, interpolation can give a lot of overoptimistic / overpessimistic deductions.
If we are confident to have a uniform aquifer all through out - interpolation is the best method and for that if the data distribution is irregular - go for kriging. Otherwise its best to plot point data by classifying them into meaningful sub classes using symbols of varying shapes, sizes and or colours(particularly for anions, cations, trace elements) . This is because a lot of factors control the water quality parameters. For parameters like EC, TDS, pH etc, kriging is quite effective, If you want quick results for a synoptic evaluation you may also adopt natural neighbour interpolation using appropriate grid cell size.
Although deductions may be subjective, the onus lies on the scientist to give predictions within the limits of empirical certainty not emotional projections.
From my perspective, since water is a dynamic field , if you want to interpolate a static field, supposing a lake, all these methods can be taken.But if this is a river, some more complex dynamic model must be taken into account.
For contaminants in sediment in rivers, we have been very successful by transforming geographic coordinates into long- and cross-flow coordinates followed by standard geostatistical analyses in the transformed space.
Usually the variogram exhibits strong long-flow anisotropy, and also the cross flow semivariogram is frequently quadratic (concave down) in shape with the sill achieved at half-channel width.
To Mr. Xu Zhang · Wuhan University: You'd better pose your question as a new thread. I'll be glad to give my opinion.
IDW you can go through my papers Environmental Impact Assessment of Air and Heavy MetalConcentration in Groundwater of Maheshwaram Watershed, Ranga Reddy District, Andhra Pradesh, JGSI and Deciphering heavy metal contamination zones in soilsof a granitic terrain of southern India using factor
analysis and GIS,JESS
You could take a look at the following paper:
Article Pollution Models and Inverse Distance Weighting: Some Critical Remarks
For Geo-statistical analysis and stochastic interpolation of water quality parameters such temperature, EC, pH, salinity, turbidity, Chl-a etc, it is quiet appropriate to use kriging, inverse distance weighting and the universal kriging method or NNI. This will help as well as estimating interpolation errors/uncertainties.
I have the same question and I would appreciate any feedback.
I am working with groundwater and I interpolated the fraction (%) of a specific water source. My data has 57 values. I used Topo to raster and Geostatistical analysis, but Kiriging and IDW gave me a RMSE of 32. Topo to raster gave a better interpolation. However, I do not know how to validate the method. thank you in advance
It is probably unreasonably to use a ranking among methods obtained for other regions and datasets instead of trying to test the behavior with your own data. I have recently proposed a protocol regarding comparison procedures for interpolation (http://www.tandfonline.com/doi/abs/10.1080/01431161.2016.1219461) which might be of interest.
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