10.3 Double-sampling Methods

Video presentation

Watch this video presentation for an overview and discussion of double sampling methods.

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Learning Guide

Double Sampling and Indirect Methods

Several sampling methods exist that apply a double sampling approach to determine plant biomass. Double sampling is done when the variable of interest is difficult and/or time-consuming to measure, but another variable that is easier to measure is highly correlated with the variable of interest. For biomass measurements, double sampling most often includes frequent estimation and infrequent measurement. This lesson focuses on standard approaches to double sampling, ranking methods (comparative yield and dry weight rank), and indirect methods.  For each of these methods, it is necessary to determine the relationship between the easier, auxiliary variable and actual biomass: usually this relationship is revealed using regression analysis.

Double Sampling

Double sampling combines the accuracy of harvesting with the speed of estimating to assess biomass. Observers estimate the weight of plant material in multiple plots and then harvest the plant materials from a subset of the plots. The clipped weights obtained from harvesting are used to create a correction factor to adjust the estimated values, which tends to improve the accuracy of the estimations.


Advantages of Double Sampling
  • More time efficient than harvesting
  • More accurate than estimation
  • Not as destructive to vegetation as harvesting


Disadvantages of Double Sampling
  • Requires significant training and skill
  • Current year’s growth can be difficult to separate from previous years’ growth.

Steps for Double Sampling Biomass

  1. Select a quadrat appropriate for the type of vegetation being sampled.
  2. Place the quadrat along a transect line or in a location determined by the selected sampling protocol.
  3. Estimate the biomass of each species using weight units determined for that species as described in the previous lesson on estimation methods.
  4. Estimate enough quadrats to capture the variation in biomass across the landscape of interest. The more variation in the vegetation — the more plots that will need to be estimated. We will call these plots the “sample” plots. Temporarily mark the location of the sample plots using pin flags, so they can be relocated if they are selected for harvesting.
  5. After all of the sample plots have been estimated, select a subset of the estimated plots to be harvested. These plots should contain all the major species that were present in the estimated plots. Harvest, weigh, and record the weight of each species in each of the selected plots.  The harvested material should also be dried in order to adjust fresh weights to dry weights. We will call these plots the “harvested” plots as the actual weights and estimates from these plots will be used to create a correction factor to adjust the estimated weight of the sample plots.
  6. A correction factor can be calculated on a plot-by-plot basis by dividing the harvested weights by the estimated weights of each species, and averaging the correction factors for each species individually (National Range and Pasture Handbook, Chapter 4, page 4-5; and Sampling Vegetation Attributes, pages 106-107).  A preferred approach to determining the correction factor is through regression analysis, explained below.

Note: Estimators should not see the actual weight of any plots until all the estimating is completed. Knowing the actual weight of one plot could influence their estimation of the weight of the next plot. This can reduce the accuracy of the regression equation used to correct the estimated plot weights.

How Many Plots to Clip?

The number of quadrats to both estimate and clip depends on the number of sample plots. Research has demonstrated that one quadrat should be clipped for every seven that are estimated. Table 1 provides guidelines for the minimum number of quadrats to be clipped based on the number of sample quadrats estimated.

Table 1. Minimum number of quadrats to clip and weigh based on the number of quadrats estimated when double sampling. From: Sampling Vegetation Attributes, pg 106.

Number Quadrats Estimated Minimum Number Quadrats To Be Clipped
1 – 7 1
8 – 14 2
14 – 21 3
22 – 28 4
29 – 35 5
36 – 42 6

Regression Analysis

The correction factor is determined by conducting a regression analysis using the values from plots that were estimated and clipped. The correction factor is the equation of the simple linear regression line. Regression equations are generally written in the form:

y = mx + b.


  y is the fresh, or harvested weight (dependent variable)

x is the estimated weight (independent variable)

b is the y-axis intercept (a constant that is added to each estimate)

m is the slope of the regression line

The easiest approach to calculating a regression equation is to use a computer spreadsheet program.  The dry weight and the estimated weight values are plotted as a scatter graph, and the software will calculate a regression line from the plotted values.

The procedure for calculating regression equations by hand can also be found in most basis statistics textbooks.  An additional resource for statistical help in calculating a regression line may be found at the following link: Regression Models & Correlation


  1. Use the regression equation to correct all of the estimated values from the sample plots. For each plot, substitute the estimate value for “x” in the regression equation. The resulting value “y” is an adjusted biomass estimate.For example:If the calculated regression line is: y = 1.5x – 20

    And, your estimated value (x) is 30 g/plot in the field

    Then y = (1.5*30) – 20

    y = 25, and the adjusted estimate is 25 g/plot

  2. The adjusted weights should then be converted to a dry weight basis following the procedure described in Lesson 2 on harvesting and estimation.
  3. Once all of the adjusted weights have been converted to a dry weight basis and averaged, the result will be the dry weight biomass per quadrat or plot. You will need to convert these average weights to meaningful units such as kg/ha or lbs/ac.

The Lesson 3 video presentation (found at the beginning of this lesson) includes a short tutorial with a real-time demonstration showing how to use Microsoft Excel to create a scatter graph, generate the regression equation from the plotted points, and use the equation to correct the estimated values from all sample plots to a value that has been adjusted based on the harvested weights.

Ranking Methods

Several methods have been developed in which quadrats are classified based on the amount of biomass relative to a reference quadrat or standard. With these approaches, the objective is to compare the amount of biomass, rather than trying to estimate the absolute amount of biomass to a specific unit of weight (e.g., grams, kilograms, or pounds). Comparative yield is one of the most widely used ranking approaches employed by rangeland professionals, and if provides an estimate of total biomass of all species combined. Comparative yield is commonly conducted simultaneously with the dry weight rank method, which provides information about species composition on a biomass basis (see chapters by Smith and Despain, and Despain and Smith in Ruyle et al. 1991 for an in-depth discussion of these methods).

Comparative Yield

The comparative yield method involves comparing the total biomass of all species in a sample quadrat to a set of five reference quadrats, or standards, that are set up to represent a linear range of biomass values present on the site. Reference quadrat 1 represents a low (but not an absolute minimum) amount of biomass present on the site, and reference quadrat 5 represents a high-yielding location on the site (Figure 1).

Figure 1. Five standards representing the average maximum and minimum biomass for quadrats are used for comparisons by rank.

Ideally, reference quadrat 5 should contain about five times the amount of biomass as reference quadrat 1, with the biomass value of reference quadrat 3 midway between the values of reference quadrats 1 and 5. Reference quadrats 2 and 4 should contain biomass values that are intermediate reference quadrats 1 and 3, and 3 and 5, respectively. It is important that the reference quadrats are ranked in this linear fashion to improve the accuracy of the results. The process of establishing the reference quadrats serves as training for the observers, and if done collectively, greatly improves consistency among multiple observers.


  • Relatively rapid method that does not require as much training as estimation
  • Reference quadrats are positioned on the site for ready access by observers to verify their rankings
  • Does not require identification of individual species


  • Provides information on total biomass only, not biomass by species
  • Requires training to accurately classify quadrats

Steps to Determine Comparative Yield

  1. Instead of estimating weight for each sample quadrat, the observer compares the total biomass of the sample quadrat to that of the reference quadrats and assigns the sample quadrat a rank corresponding to the appropriate reference quadrat. For example, if the observer determines that the biomass of a sample plot is most similar to reference quadrat 3, the sample plot is assigned a rank of 3. If the amount of biomass in a sample quadrat is intermediate to the reference quadrats, a half rank, such as 3.5, can be assigned.
  2. To calibrate the ranks, a set of quadrats need to be clipped. This can be done after all of the sample quadrats have all been assigned ranks, or a subset of the sample quadrats can be clipped after they have been assigned ranks. The reference quadrats are also clipped after the sampling is concluded. Several plots representing each rank should be harvested.
  3. Weigh bags of clipped forage in the field to provide a fresh weight, then dry and weigh them again at the lab to provide a conversion factor from field to dry weight.
  4. The calculation of the total production can be calculated by a ratio method (described by Despain and Smith 1991) or using regression analysis. With both approaches, the average rank of the sample quadrats is corrected by the average biomass per rank of the harvested quadrats.

Dry-Weight Rank for Species Composition

Dry weight rank (DWR) is similar to direct estimation of biomass by species, except that observers simply rank the three highest-yielding species (the species with the most biomass) in each quadrat. The highest yielding species are assigned the ranks 1, 2 or 3, and other species in the quadrat are not ranked.


  • Simpler and faster to assign ranks to 3 species than to assign percentages to each species in the quadrat.
  • Actual weight of each species can be determined when combined with the comparative yield method described above.
  • Requires less training than simple estimation.


  • Observers must be able to identify species
  • Does not work well in areas with large shrubs

DWR Procedure

At each sample quadrat, the observer records the three species that have the highest amount of biomass on a dry-matter basis, with the highest yielding species given a rank of 1, the next highest a rank of 2, and the third highest a rank of 3. If fewer than 3 species are found in a quadrat, multiple ranks are assigned to the existing. For example, a rank of 1 and 3 or 1 and 2 could be assigned to the grass species in Figure 2, and the white flower would be assigned the unassigned rank (2 or 3); the assignment of multiple ranks ensures that species composition is calculated to total 100%.

Figure 2. Dry weight ranks assigned in two diagrams of quadrats: a) green grass 1, purple clover 2, white flower 3; and for b) green grass 1, white flower 2, green grass 3.  Note that in a) four species are present (pink columbine is in the bottom right corner), but only three species can be ranked, and in b) only two species are present, but three ranks must be given so one species receives two ranks.

Calculating Species Composition from DWR

Refer to Table 2 while reading the following steps for calculating percent composition from DWR data:

  1.   For each species, tally the total number of times it is ranked 1, 2, and 3, based on all of the quadrats in the sample.
  2. Ranks of 1, 2, and 3 correspond to 70%, 20% and 10% composition, respectively, (although this is not a consideration during the ranking process). Multiply the tally of ranks 1, 2, and 3 by 7, 2 and 1 respectively.
  3. Sum the three products obtained in Step 2, and record as the Weighting for that species.
  4. Repeat this process for each species and then sum the Weighting values for all the species.
  5. Divide each species’ Weighting Value by the total Weighting Value of all the species to get the percentage composition. Percent composition, by definition, should total 100 percent.

Table 2. Example of calculating species composition using data collected with the dry weight rank method.


Combining DWR with Comparative Yield

The biomass of individual species can be determined when data from Comparative Yield and DRW methods collected simultaneously. Since comparative yield estimates total biomass, and DWR estimates species composition on a biomass basis, the biomass of an individual species can be determined by multiplying the total biomass estimate by the proportion that the species contributes to species composition.

For example, if the Comparative Yield method revealed that the average biomass was 550 lbs/acre, and Species “A” comprised 46% composition as described by DWR, then the biomass of species “A” would equal 550 * 0.46 = 253 lbs/acre

Indirect Methods to Sample Biomass

There are dozens of plant attributes, or parameters that are related to biomass and can be measured instead of directly measuring biomass. For example, the canopy dimensions of a shrub and the height of trees can be related to biomass, because the larger the shrub, or the taller the tree, the greater its mass will be. Quite simply, if some attribute of a plant can be measured and shown to be related to biomass it can be used in an indirect measure of biomass.

Indirect measures are attractive because they are generally much less time consuming than direct harvest. Therefore, they allow for larger quantities of information to be gathered with similar investment of time and resources. The key to all indirect techniques is that biomass can be estimated if there is a way to establish the relationship between the parameter being measured and actual biomass. Thus, a double sampling procedure is needed where several plants are measured and then clipped and weighed.

Crown Area

Crown Area – The crown area of a plant is often highly correlated to current season’s growth and total biomass.

  • The widest dimension of the plant is recorded as dimension 1 (D1).
  • The dimension perpendicular to DI is dimension 2 (D2).
  • Crown area = π*D1*D2
  • A sub-sample of the measured plants are then clipped and weighed.
  • A regression analysis is completed, as described above with crown area as the x-variable and clipped weight as the y-value.

Crown Volume or Dimension Analysis

The crown volume of a plant is also often highly correlated to current season’s growth and biomass. Therefore, the 3-dimensional volume of a plant can be used in a double sampling technique.

The dimensions measured to estimate crown volume depends on the 3-dimensional shape that best describes the plant (e.g., inverted cone, half spheroid, sphere). Most shapes require the measurement of several diameter and height dimensions.

Step 1 – Look at the plant in its natural state

Step 2 – Envision a geometric shape that describes the shape of the plant


Step 3 – Take appropriate measurement of that shape on that plant


Step 4 – Calculate Volume (v) of the plant according to the different equations below.


Step 5 – Clip and weigh biomass from a sub-sample of the measured plants

Step 6 – Calculate the relationship between volume and biomass with regression analysis. Then, predict weight of all measured plants based on volume.

Vegetation Height

A long time ago, people studying grasslands realized that plant height is strongly related to biomass.  This is especially true for dense stands of sod-forming grasses called swards. Consequently, researchers developed multiple devices to consistently estimate the height of swards, including Rising Plate Meters, Falling Plate Meters (Figure 3), and Sward Boards. All these devices operate in basically the same way:


  1. find a way to consistently estimate height
  2. clip a few plots
  3. develop a relationship between height and weight
  4. estimate weight based on height

Figure 3. A falling plate meter used to measure height of dense, uniform grassland. The plate slides on the ruler and is allowed to fall until the vegetation stops its descent. The height of the plate on the ruler is noted and recorded on a datasheet.

Height meters can be very effective in dense, uniform stands of grass. However, they often do not work well in more arid landscapes dominated by a mix of bunchgrasses and shrubs, or where distances between plants can be large.

Remote Sensing Methods

The era of digital technologies and remote sensing has spawned a series of options for measuring spectral attributes of plants and landscapes. The measured spectral attributes are then related to biomass through double sampling.

Normalized Difference Vegetation Index (NDVI)

The most frequently used remotely sensed measure of vegetation known to be related to biomass is a Normalized Difference Vegetation Index or “NDVI.”

NDVI is an index of plant “greenness” or photosynthetic activity, based on the observation that different surfaces reflect different types of light differently. Vegetation that is photosynthetically active (i.e green) absorbs most of the red light while reflecting much of the near infrared light that hits it. In contrast, vegetation that is dead or stressed reflects more red light and less near infrared light, while non-vegetative surfaces absorb red and near-infrared light equally. NDVI is calculated from the normalized difference between the red and near infrared bands in an image. The NDVI is then paired with actual biomass measurements (ground truthing) to develop a double sampling regression.


Limitations of NDVI

While NDVI has the capability of providing massive amounts of biomass information with limited on-the-ground efforts, it can be affected by atmospheric conditions, scale of the imagery, vegetation moisture, soil moisture, overall vegetative cover, differences in soil type, and management. Therefore, it should not be regarded as the panacea for rangeland monitoring, but recognized as another method to obtain useful information within limitations

There are several newer remotely sensed attributes that are currently being examined for relationships with biomass. For example, the Moderate Resolution Imaging Spectroradiometer or MODIS was launched and started offering image products in early 2000. This satellite offers products that approximate leaf area index and thus have been successfully related to biomass.

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