You’ve used Surfer mapping software to grid your data and created a great looking map. You put it in the final report for your presentation. And you think, that was easy and I’m all done now. And then someone asks you, how do you know that map is accurate? You start to wonder. How do I know if it is correct? Is there any way to verify the gridding? If the grid file matches the original data, then I could confidently say the map is correct. But, how do I know if the grid file matches the data?
In the previous blog, we discussed visually inspecting a grid to see if the grid created is a good representation of the original data. To do this, we compared a contour map from the grid to a classed post map from the data.
Visually inspect the original data to the grid by
overlaying a class post map and contour map.
This gave us a first visual look at how well the data was fit by the gridding. So, you know that the grid is a good fit. But, you would still like some kind of number to determine how good of a fit the grid really is. One way to do this is by calculating the residuals for the grid. Once the residuals are calculated, you could perform statistics on the residual values to get an estimate of the goodness of the fit. Or you could grid the residuals and create a residual map to see where the grid is further away from the data. This may indicate areas where more data may be needed.
To calculate the residuals, you need a worksheet with at least three columns: X, Y, and Z for all of the areas that you want to check. For this example, let’s compare the gridded value with the original value.
The worksheet automatically opens. You can scroll over to the residuals column and look at the values. Residuals are the difference between the gridded value and the data value in the worksheet. This can be positive or negative. To see some statistics about the column,
The calculated statistics are displayed in the dialog.
This shows that the gridded Z value furthest away from the actual data point Z value is 409.35 Z units. This may seem like a lot initially, but recall that the grid covers Z=0 to 24000. So, 409.35 is less than a 2% variation. The mean (average value) is 4.91. Because the mean is fairly close to zero, the gridded value is fairly close to the original Z data value, for most of the grid. The standard deviation is 155.29. This shows that the grid shows some variation in how accurate the original data points are represented depending on where the data point is located. You can close this dialog by clicking the Close button.
Another common numerical value that is used to determine the goodness of fit is the R2 value. To calculate this value, you need to make several calculations.
Calculate the R2 value in the worksheet to obtain
a numerical value indicating goodness of fit.
This R2 value can be included in a report to give a numerical indicator of how well the grid fits the original data. The R2 value should be between zero and one using the method outlined above. If the R2 value were exactly equal to 0, then the model would fit none of the data points. If the R2 value were equal to 1.00, then the model would exactly predict the data points. Generally, the higher the R2 value is, the better the fit of the grid.
Finally, you can take the original residual values and create a map. This can show where taking obtaining more data (if possible) may be useful to fitting the grid better. To create this map:
The dialog should look similar to the above, with the Minimum
and Maximum values reflective of the variation in your grid file.
The residual contour map updates.
The residual map is displayed. This map shows the difference
between the original Z value and the gridded Z value.
Areas with higher positive or negative Z contour values are filled red. By evaluating these areas, you can get a better understanding of how well the grid fits the data. These areas may need additional data points to more effectively control the gridding, or you may want to use a different gridding method or use different grid geometry.
Surfer's graphing software has many tools available to answer the question: does this grid fit my data? You don’t have to take our word for it. Calculate the results yourself. Do you have another favorite method that you use to determine if your grid is accurate? Please share it with us!
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