Accuracy and Error of Hydrological Measurements – Part 2

Click here to read Part 1 – background about measurement accuracy and error, definitions and more

This series of discussions are to first give you a scientific picture of hydrological measurement errors and then open the interesting discussion of how to automatically detect, validate and correct erroneous sensor data given the observations from Data Acquisition System (DAS) and field visit information.

Let’s now have a closer look into the various types and sources of sensor errors.

Figure 1 illustrates different types of errors and the concept of uncertainty. The true value of the parameter is shown as a straight line with no variation over the given time. In this example, systematic error is a constant offset and the distribution of random error is assumed to be Gaussian with standard deviation S.

Offset error could originate from the incorrect determination of the reference point of an instrument called datum, for instance, difference between the staff-gauge zero and the weir-crest levels. It could also be generated by changing operational condition for sensors. For instant, pH transducers are calibrated at certain temperature (e.g 25oC ) from the manufacturers. Figure 2 shows a typical characteristic curve for a pH transducer. Characteristic curve maps a given physical parameter to measurable electrical quantities like voltage or current.

The ideal curve will exist only at one temperature (usually 25°C), while the actual curve will be between the minimum temperature and maximum temperature limits depending on the temperature of the sample and pH electrode. From the graph, it is clear that the deviation from calibrated temperature offsets the observed pH up or down from true value.

As an example, offset error on pH telemetry signal is also shown in figure 3.

The random variation of the observed measurements (figure 1), is generally scattered around the average deviated by systematic error which is offset error in this case.

Figure 1: Explanation of errors

As mentioned above, the uncertainty and confidence level are closely related; the wider the uncertainty, the greater the confidence that the true value is within the stated range. In hydrology, a commonly used confidence level is 95 percent, which, in a Gaussian distribution, relates to two standard deviation (α=2). In this case confidence interval would be four times standard deviation (4S).

As shown in Figure 1, spurious error can also be referenced to the average of observed measurements similar to random error.

I invite your comments and in coming blog posts, I’ll discuss about other types of systematic measurement errors commonly occur in real-time monitoring systems such as drift, non-linearity, hysteresis, instability, communication, etc.

Figure 2: Typical pH sensor characteristic curve showing temperature sensitivity that causes offset error. From [2]

Offset-ErrorFigure 3: Offset error on pH signal


[1]Guide to Hydrological practices, World Methodological Organization – WMO-NO. 168, 2008

[2] J.J. Carr, Sensors and Circuits Prentice Hall, 1993

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