I'd use Chebyshev's inequality to see if there are serious "outlying" stations. Additionally there are numerous outlier-tests available, where you can control the type-1 error rate of the false-classification rate. Many of them require particular assumptions of the distribution of the values (mostly normal distribution), so you should check if these assumptions are met. In any way, it would be important to get an idey *why* the values from the "outlying" stations are so far away from the average. If there is a considerable amount of "outliers" you should re-think the whole story, the data acquisition, and the appropriateness of your model (you probably should include some station-specific characteristics or other predictors to your model).

The best method is expert judgment. There is really no universally accepted test; any one of them has its qualities and pitfalls. Usually when a value is way out of range it qualifies for an outlier. Box and whisker plots may be useful too.

The second point I want to make is that you have to consider the possible explanation of the outliers. In your case it is simple, it is probably a mistake in the readings/data, or it could be from processing. Here it seems that you may want to take an average for the regions that are close and compare the relevant individual values against them. I am thinking you may want to start with identifying everything that goes above or below three standard deviations of the aforementioned averages. I advise you to review the results before going further.

although the use of Chebyshov (also written as Tchebyscheff, Chebyshev, Čebišëv, ) inequality like Jochen, you can NOT ignore the theory, and make an analysis about the appearance of these values.

However this is good to do the following:

Detect Univariate Outliers

-One way to identify univariate outliers is to convert all of the scores for a variable to standard scores.

-for sample size is 80 or fewer cases, a case is an outlier if its standard score is ±2.5 or beyond.

-for sample size is larger than 80 cases, a case is an outlier if its standard score is ±3.0 or beyond

-This method applies to interval level variables, and to ordinal level variables that are treated as metric. It does not apply to nominal level variables.

Multivariate outliers are cases that have an unusual combination of values for a number of variables. The value for any of the indvidual variables may not be a univariate outlier, but, in combination with other variables, is a case that occurs very rarely. In our analyses, we will be concerned with multivariate outliers for the set of independent variables in our data analysis.

Detect Multivariate Outliers

You can use Mahalobis Distance

-Mahalanobis D2 is a multidimensional version of a z-score. It measures the distance of a case from the centroid (multidimensional mean) of a distribution, given the covariance (multidimensional variance) of the distribution.

-A case is a multivariate outlier if the probability associated with its D2 is 0.001 or less. D2 follows a chi-square distribution with degrees of freedom equal to the number of variables included in the calculation.

-Mahalanobis D2 requires that the variables be metric, i.e. interval level or ordinal level variables that are treated as metric.