Forest Measurement and Modelling.

Nothing in the natural world can be measured without some error. However, this should not be a problem unless the user of the measurements denies or ignores the error.

The universal nature of measurement error means that measurements should not be quoted as an exact value - they should instead indicate a range within which the true value lies. [Standard ways of writing values] allow this range to be implied.

Errors can arise from many sources. Errors may also [interact] with each other - errors in some estimates compounding the magnitude of errors in other estimates. An understanding of the [types or errors] may allow their effects to be considered and their magnitude controlled.

The tolerable amount of error must be considered by person who is in charge of quantifying the forest as well as the person who will use the information. A clear understanding of the acceptable level of error will enable appropriate measurement methods to be selected. Measurement resources can be more efficiently allocated to reducing the dominant sources of error.
Types of error Errors can be classified into four kinds:

  1. Mistakes. These errors are caused by human carelessness, casualness or fallibility. Mistakes can include the incorrect use of an instrument, an error in recording or a calculation error. The magnitude of these errors cannot be determined. Good measurement practice is needed to minimise mistakes.

  2. Compensating (accidental). These errors are due to the nature of the object being measured, inconstant environmental conditions, limitations in instruments and deficiencies in assumptions. A positive error will, on average, be balanced by a negative error.

  3. Systematic (bias). A systematic distortion in a measurement or estimate is defined as a bias. These errors are not compensating. Systematic errors may be caused by faulty equipment or technique and subjectivity of measurers. However some bias may be acceptable - see the discussion on estimating sectional area of a tree bole.

  4. Sampling. Sampling error is the error associated with an estimate purely due to sampling. If samples are selected using a probability-based approach or other objective system, sampling errors tend to be compensating. The magnitude of a sampling error can be estimated from the variance of the population and the size of the sample taken.

A measurement or estimate may be defined as accurate when the total error is small. This is normally a qualitative classification as there is no generally acceptable definition of a small total error. The total error includes the effects of bias and precision.
Activity Use any recent experience in measurement to make a list of possible or actual errors. Classify these errors into their appropriate categories and estimate their likely magnitude. Which would be the easiest error to control? Which would be the hardest error to control?

Error calculations A final parameter estimate (say "A") may be calculated from intermediate measurements or estimates (say "B" and "C"). The magnitude of the error associated with A (denoted as "a") can be calculated if the errors associated with B and C (denoted as "b" and "c") are known:

When A = B + C 
then a = 

When A = B x C 
then a = 
Significant digits It may be misleading to report a measurement as an exact figure because all measurements contain error. This error means that there is a range within which the true value lies. For example, accidental error in a 30 cm wooden ruler (say temperature fluctuations causing the ruler to swell or shrink by 3 mm) mean that you may read the length of an object as 300 mm when it is 297 or 303 mm. The accidental error when using a piece of string may be much higher, and the range within which the true value lies may be plus or minus several cm!

Reporting the range within which the true value lies would avoid misleading readers about the precision of a measurement. So, for example, the object measured above with the rule may be reported as 297 - 303 mm, but if measured with the string, it may be 285 - 315 mm. Calculations based on these ranges would also result in ranges of values within which the true value would be expected. For example, the true area of a square with one side between 297 - 303 mm and another side between 285 - 315 mm would be expected to be between 84 645 and 95 445 mm^2. The magnitude for the range of the resulting calculations is determined by the range of input measurements.

Figures that do not change within the range involved in the error of measurement or calculation may be considered as significant figures. Rules for writing significant figures should be observed to avoid implying a greater or lesser precision than was achieved. These rules may be found in the Code of Forest Mensuration Practice (

It is particularly important that the outcome from a number of calculations performed by a computer (e.g. a spreadshseet package) is reported to the appropriate number of significant digits. Computer packages often print the results of calculations to as many decimal places as computer memory allows. This is often well in excess of the appropriate number of significant places!

[temp.htm] Revision: 6/1999