Upkeep - EAEA experimental data
Introduction
Pending a dedicated experiment, the expected area error amplitude (EAEA) formula was applied to parcel coordinates of existing surveys. The variability of point survey measurements was analyzed using data set from the GNSS validation for buffer tolerance.
Test conditions
Coordinates are recovered from GNSS validation test for area measurement made by Finish Services and Paying Agency in January 2010. Key data characteristics:
- The point surveys were made with a GeoXH GNSS receiver using real time Trimble VRS differential corrections, with estimated point accuracy (RMSp) of around 50 cm.
- The data set represents 6 sets of 4 independent repetitions of total for each of the 6 parcels.
- The parcels differ both in shape and size. Their areas range from 0.07 to 1.57 hectares and their perimeter from 190 to 515 meters (see Table 1).
- The set of coordinates per repetition is collected within a time frame that compatible with the dGPS settings and normal field practices.
- All parcels have a B-value of 2.45 except the smallest parcel that has a B-value of 2.96 (fully surrounded by trees)
==Test Results
Parcel ID | S1 | F1 | S2 | S3 | F2 | F3 |
Area (ha) | 0,0663 | 0,2456 | 0,3014 | 0,3164 | 0,5447 | 1,5671 |
Perimeter (m) | 237,5 | 192,2 | 287,4 | 343,4 | 284,6 | 514,4 |
# of vertices | 13 | 12 | 14 | 14 | 10 | 17 |
table 4g.1: area, perimeter and number of vertices of each of the 6 parcels
Figure 4g.1 provides the boxplots with
- In black/red: the observed variation during the test represented with a boxplot:
- the observed 1st and 3rd quartile (black box);
- the observed median (red line);
- the minimum and maximum observations not detected as potential outliers (black lines);
- potential outliers (red crosses).
- An observation is set as potential outlier if it is not in the interval [1st quartile - 1,5 x IQR ; 3rd quartile + 1,5 x IQR] where IQR is 3rd quartile - 1st quartile. This interval theoretically contains approximately 99% of the distribution
- In orange: the 99% interval of the distribution calculated as “perimeter x validated buffer value”
- In blue:
- the estimated 1st and 3rd quartile calculated from the proposed EAEA formula (blue)
- the estimated 99% interval of the distribution calculated by from the proposed EAEA formula (light blue)
Figure 4g.2 provides the comparison between the observed EAEA (i.e. 1.96 x the observed standard deviation; black stars) and the estimated EAEA from the perimeter buffer tolerance rule (orange) and the proposed formula (light blue). The intervals in black represent the uncertainty of the observed EAEA. This interval is based on the chi square distribution with a degree of freedom equal to 23 (i.e. 6 x 4 repetitions - 1).
Discussion
This preliminary test supports the relevance of the expected area error formula:
- All repetitions measured an area that lays well inside the predicted 99% intervals for both methods (see Figure 1).
- All the statistical outliers (but one for the proposed formula) fall inside the predicted 99% intervals (see Figure 1).
- Contrarily to the perimeter buffer tolerance rule, the proposed formula produces predicted EAEA values that all fall in the 95% confidence intervals (Figure 2)
- It also shows that in all cases, for this type of area measurement, the MEA is a closer estimator of the observed variation than the perimeter buffer method (see Figures 1 and 2).
A dedicated test will shortly be set up for a more advanced assessment of the proposed formula that is:
- More precise measurement tools (e.g. RTK system);
- Uncorrelated measurement errors;
- More repetitions for each parcel;
- Parcels with different shapes but sharing the same perimeter
- In such conditions, the perimeter buffer tolerance rule will produce exactly the same area error amplitude for each parcel while the proposed formula will produce specific one for each parcel
The formula should be used before the settings of the field test in order to identify in advance the shapes that will better highlight the differences of predicted area error amplitude.
Further reading
- expected area error amplitude formula
- Fasbender, D., Lucau, C. and Bogaert, P. (2013). A new theoretical framework for the assessment of error propagation on polygonal area measurements, working paper.
- uncertainty of the observed EAEA
- Cochran, W. G. (1934). The distribution of quadratic forms in a normal system, with applications to the analysis of covariance, Mathematical Proceedings of the Cambridge Philosophical Society, 30(2): 178–191. or see wikipedia
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