United States

Department of

Agriculture

Forest Service

Southern

Research Station

Research Paper

SRS-27

Sampling Throughfall and

Stemflow in Young Loblolly

Pine Plantations

S.J. Zarnoch, D.A. Abrahamson, and P.M. Dougherty
The Authors

S. J. Zarnoch, Mathematical Statistician, USDA Forest Service, Southern

Research Station, Asheville, NC; D.A. Abrahamson, Hydrologist, USDA

Agricultural Research Service, J. Phil Campbell Sr. Natural Resource

Conservation Center, Watkinsville, GA; and P.M. Dougherty, Plantation

Productivity Project Leader, Westvaco, Summerville, SC, respectively.

February 2002

Southern Research Station

P.O. Box 2680

Asheville, NC 28802
1

Sampling Throughfall and Stemflow

in Young Loblolly Pine Plantations

S.J. Zarnoch, D.A. Abrahamson, and P.M. Dougherty

Abstract

Throughfall and stemflow estimates were obtained on a rain-event

basis for small (0.09-hectare) plots established in a young loblolly

pine (Pinus taeda L.) plantation in North Carolina. The plots were

exposed to specific fertilization and irrigation treatments, which

resulted in a wide range of basal areas and leaf area indices.

Coefficients of variation were also determined, which revealed a

negative exponential relationship with rain-event magnitude.

Throughfall was substantially less variable than stemflow.

Recommended sample-size curves were developed for throughfall and

stemflow to achieve 5 percent accuracy at the 0.80, 0.90, and 0.95

probability levels.

Keywords: Accuracy, hydrology, sample size, sampling design,

variability.

Introduction

Investigations of global climate change effects on forest

ecosystems require an intensive, multidisciplinary research

approach. One of the most important components that must

be understood in order to predict ecosystem response to

global change is the site water balance. Annual and seasonal

water balances are some of the major estimators of expected

productivity. To obtain good calculations of the hydrologic

process, both moisture inputs and losses must be measured

or estimated using one or more components such as rainfall.

Although numerous experimental techniques have been

used for throughfall collection, sampling intensity has been

the main source of disparity (Peterson and Rolfe 1979). The

desire for statistical precision by using large sample sizes

has often been tempered by the reality of economic and

sampling time restrictions (Miller and Miller 1976). Loustau

and others (1992) found that validation of models used to

simulate throughfall and stemflow inputs to the forest floor,

which compare predicted to observed values, fail to

incorporate the sampling error of measured data such as

gross rainfall, throughfall, and stemflow. This paper examines

the sampling requirements for throughfall and stemflow in

order to accurately characterize rainfall inputs to the forest

floor via throughfall and stemflow in loblolly pine (Pinus

taeda L.) plantations.

Estimation and prediction of hydrological process variables

are fundamentally two distinct problems. Estimation requires

sampling methodologies to arrive at an estimate of the

parameter for a particular location and rain event.

Observations on the hydrological variable are taken on each

sampling unit during the rain event and the appropriate

parameter estimator is computed along with measures of

variability. Prediction requires a regression equation that

relates the hydrological variable to one or more predictor

variables. The regression equation is developed from data

obtained from previous sampling of the hydrological

variable, along with predictor variables that include total

rainfall and may include stand characteristics such as leaf

area index (LAI), basal area (BA), and tree height

(Abrahamson and others 1998). Once such a regression is

formed, the hydrological variable is merely predicted with the

equation for any subsequent rain event, and no sampling of

the hydrological variable is required.

Our objective was to evaluate the sampling properties of

throughfall and stemflow estimates for young loblolly pine

plantations. A simple random sampling design was used for

small [0.09-hectare (ha)] research-sized plots. Variability was

evaluated and used to develop recommendations on

sampling intensity to meet specific precision objectives.

Methodology

Study Site

This study was derived from a larger study designed to

determine the effects of irrigation and nutrition on loblolly

pine growth and stand development in the sandhills of North

Carolina (see Abrahamson and others 1998 for more

information). The larger study included four treatments—

control, irrigated, fertilized, and irrigated plus fertilized—each

installed on 0.09-ha plots [30 by 30 meters (m)] and replicated

four times in a randomized complete block design on a 4-ha

study site. Basal area had been standardized across the

treatments but, over time, effects of the treatments yielded a

wide range of plot BA and LAI. This was ideal for our study

of throughfall and stemfow sampling variability under such a

diversity of stand characteristics. It increased the scope of

inference by widening the range of applicability for sampling

recommendations generated by this research.
2

Note that the latter differs from the traditional variance of the

mean from an infinite population by the factor ,

which is the finite population correction. If the sampling

fraction is low, e.g., < 5 percent, the correction is often

ignored for simplicity. An approximate 100 (1–  ) percent

confidence interval on the population mean is

 (5)

where is the upper α/2 percentage point of the

Student’s t distribution. If the sample size n is at least 50, the

normal distribution is usually used instead. The coefficient

of variation of the estimator is defined as

 (6)

In designing sampling plans, efficiency can be maximized by

determining the required sample size to be within a specified

D percent of the true population mean with a specified

probability 1–α. This requires that the half width of the

confidence interval for the mean be equal to D percent of the

mean, which when stated mathematically becomes

 (7)

The researcher chooses D and α based on perceived

accuracy needs—CV(y) is approximated using a value from

previous sampling efforts. Given these three values, the

required sample size can be computed from

 (8)

or

 (9)

if the finite population correction can be ignored for

simplicity. Note that this must be solved by iteration because

n is on both sides of the equation.

Study Design

Simple random sampling methodology was used to estimate

the mean and variance for throughfall and stemflow for each

plot-rain event (the target population of interest). The four

throughfall and stemflow collectors in each plot comprised

Rainfall was measured with a tipping bucket rain gauge

placed 2 m above the soil surface at a weather station

located in a 60- by 60-m clearing adjacent to the study area.

Throughfall is rain that reaches the forest floor through

spaces in the forest canopy and as drip from the canopy. We

sampled it with four randomly located troughs [150

centimeters (cm) by 10 cm] positioned 0.75 m above the

ground in each plot. Stemflow is rain that is captured on the

canopy and runs down the bole of the trees. We sampled it

from four randomly selected loblolly pine trees per plot.

Plastic tubing was completely wrapped around the

circumference at the base of selected trees and connected to

a collecting container. We performed throughfall and

stemflow sampling on a rain-event basis from 1992 through

1993. Occasionally, when a plot did not have all four

stemflow samples taken, we deleted it from our analysis to

maintain equal sampling intensity throughout the study.

Sampling Methodology

We used a simple random sampling design to gather study

data (see Cochran 1977). Simple random sampling consists of

selecting n units out of the population of N units such that

every sample of size n has the same probability

( ) 1/

N nN n

n N

  −   =

 

! !

!

of being chosen. Let

N = the total number of possible units in the population,

n = number of units taken, and

yi = observation on unit i.

An estimate of the mean is

 , (1)

an estimate of the variance of an observation is

 , (2)

an estimate of the coefficient of variation of an individual

observation is

 , (3)

and an estimate of the variance of the estimated mean is

 (4)

1

n

i

i

y yn =

= ∑ /

tα /2 1 ( ) n−

1 n

N

    −  

( )

2

2 1 s n

s y n N

  = −    

( )

2

2 1

1

n

i

i

y y

s

n

=

−

= −

∑

( ) 100 s CV y

y =

y t sy ± α /2 1 ( ) n− ( )

( ) ( ) ( ) 1/2

1/2

100

1

s y CV y n CV y

y n N

  == −    

( ) ( ) ( ) ( ) /2 1 /2 1

1/2

1/2

100

1 n n t sy t CV y n D

y n N

α α − −   == −    

/2 1 ( ) ( ) 2

Nn t CV y n

Nn D

  α −

=   −  

/2 1 ( ) ( ) 2

t CV y n

n

D

  α −

=    

α
3

sampling units. The finite population correction was ignored

for throughfall because the number of sample units was

small relative to the total number that could be used, i.e., n/N

was <0.05. However for stemflow, the number of trees per

plot was 100 plus or minus 5, and the calculated required

sample size n for a specified precision level could often

result in n/N >0.05. Thus, the finite population correction

was used.

Because our objective was to obtain recommended sample

sizes to meet specific precision requirements, we needed an

estimate of variability. So we calculated the coefficient of

variation on an observation basis CV(y) for each plot-rain

event. Using equations (9) and (8) we could then determine

the sample size necessary for throughfall and stemflow,

respectively, in future sampling efforts in order to achieve 5

percent accuracy at the 0.80, 0.90, and 0.95 probability levels

over the observed range of rain events. However to achieve

this, the CV(y) must be approximated for a given rain event.

Helvey and Patric (1966) show that CV(y) is related to rainevent magnitude in a negative exponential manner, i.e., CV(y)

decreases with increasing rain for a given event. Hence,

CV(y) for throughfall and stemflow were related to rainfall by

fitting the negative exponential model

 (10)

where

a, b, and c (c <0) are estimated parameters and e is the

exponential constant equal to 2.7183.

Note that as rain decreases, CV(y) approaches a + b while as

rain increases CV approaches a. This is the trend reported by

Helvey and Patric (1966). Our objective was not to develop a

precise prediction model for CV(y), but to obtain an estimate

over a range of rainfall by smoothing out the trend observed

in CV(y) from the study. With such an estimate of CV(y) for a

given anticipated rainfall, the sample size could be calculated

from the methods previously discussed.

Results

Descriptive statistics on variables used in our throughfall

and stemflow analyses are given in tables 1 and 2,

respectively. Rainfall averaged around 22 millimeters (mm)

per rain event with the maximum being 65 mm. Stand

conditions over the course of our study are characterized by

an average LAI of approximately 0.80 m2

 per square meter

(0.14 m2 per square meter to 2.26 m2 per square meter) and a

BA approximately 2.92 m2 per hectare (0.25 m2 per hectare to

7.24 m2 per hectare). Rain, throughfall, and stemflow were

quite consistent over treatments despite higher LAI and BA

for treatments 3 and 4. However, the CV(y) for throughfall

generally increased with increasing LAI and BA, the overall

average being 14.6 percent. Figure 1 illustrates the variation

in throughfall CV(y) with the magnitude of the rain event

over all treatments. It indicates large variation with small rain

events (< 25 mm) but a constant, smaller CV(y) with larger

events. The negative exponential model (10) was fit to the

data on an individual treatment basis and then pooled for all

treatments. Although the fits had rather low correlation

coefficients (r), the models did represent the monotonically

decreasing asymptotic relationship of CV(y) to rain and is

very similar to that reported by Helvey and Patric (1966).

Although individual parameter estimates varied by treatment

(table 3), the pooled model was used to represent the general

CV(y) expected over the complete range of plot conditions

(LAI and BA) observed in all four treatments, which renders

the conclusions more broadly applicable. Using the samplesize equation (9), the number of collectors needed to sample

throughfall at 5 percent accuracy at various probability

levels was calculated (fig. 2). Because CV(y) is large when

rain is 25 mm or less, a prohibitive number of collectors are

required. However, with rain events over 25 mm, a more

reasonable number of collectors is needed. For example, if

one wishes to estimate throughfall to within 5 percent

accuracy 90 percent of the time, then about 15 collectors are

required for an anticipated 25-mm rain event. This is similar

to that reported by Helvey and Patric (1966), who suggest 20

for this level of precision.

Variability for stemflow was substantially greater than for

throughfall; CV(y) averaged 39 percent (table 2) with no

apparent trend in LAI and BA. With small rain events, CV(y)

was large but, unlike throughfall, it diminished only slightly

with increasing rain (fig. 3). The negative exponential model

had very low correlation coefficients (r) but still represented

the monotonically decreasing, asymptotic relationship.

Using the pooled model CV(y), we calculated the required

sample size using the finite population correction assuming

100 trees per plot [equation (8)]. The number of collectors

needed to sample stemflow at 5 percent accuracy at various

probability levels is shown in figure 4. For example, 47

stemflow collectors are needed to be within 5 percent

accuracy 80 percent of the time for an anticipated 25-mm rain

event. Because the plot contained 100 trees, almost half the

trees must have stemflow collectors. This illustrates the

increased level of variability present with stemflow sampling

as compared with throughfall.

c ( ) RAIN CV y a be = +
4

Table 2—Descriptive statistics for the stemflow analysis for

small (0.09-hectare) research plots

Treatmenta

Variable and

statistic 1 2 3 4 Pooled

Rain (mm)

Min 2 2 2 2 2

Max 65 6 5 65 60 65

Mean 22.8 21.9 22.3 22.7 22.4

Stemflow (mm2/ha)

Min .015 .016 .013 .013 .013

Max 2.980 2.853 3.102 4.761 4.761

Mean .698 .718 .785 .727 .732

LAIb (m2/m2)

Min .33 .30 .31 .14 .14

Max 1.34 1.32 2.01 2.13 2.13

Mean .67 .63 1.01 .89 .80

BAc (m2/ha)

Min .25 .29 .40 .29 .25

Max 3.68 4.03 6.51 7.24 7.24

Mean 2.15 2.24 3.64 3.70 2.93

CV(y)d

 (%)

Min 9.5 5.8 9.5 5.3 5.3

Max 84.0 97.6 84.1 116.3 116.3

Mean 35.5 38.9 36.8 47.2 39.0

a Treatment 1 (n = 185), treatment 2 (n = 143), treatment 3 (n = 166),

treatment 4 (n = 124), pooled (n = 618).

b Leaf area index.

c Basal area.

d Coefficient of variation.

Table 1—Descriptive statistics for the throughfall

analysis for small (0.09-hectare) research plots

Treatmenta

Variable and

statistic 1 2 3 4 Pooled

Rain (mm)

Min 0 0 0 0 0

Max 65 65 65 65 65

Mean 22.7 22.6 22.5 22.6 22.6

Throughfall (mm)

Min 0 0 0 0 0

Max 62 64 66 65 66

Mean 19.9 20.0 19.6 20.2 19.9

LAIb (m2/m2)

Min .29 .29 .26 .14 .14

Max 1.34 1.32 2.01 2.26 2.26

Mean .66 .63 .94 .89 .78

BAc (m2/ha)

Min .25 .29 .25 .29 .25

Max 3.68 4.03 6.51 7.24 7.24

Mean 2.15 2.24 3.54 3.70 2.91

CV(y)d

 (%)

Min 0 1.6 0 .8 0

Max 70.1 140.4 127.8 83.2 140.4

Mean 12.7 12.8 16.0 17.0 14.6

a Treatment 1 (n = 245), treatment 2 (n = 202), treatment 3 (n = 240),

treatment 4 (n = 199), pooled (n = 886).

b Leaf area index.

c Basal area.

d Coefficient of variation.

Figure 1—The relationship of the coefficient of variation CV(y) for

throughfall to rain on an event basis for individual small research

plots (0.09 hectare).

Figure 2—The number of throughfall collectors (n) needed on an

event basis to sample throughfall on small research plots (0.09

hectare) at 5 percent accuracy and selected probability levels ignoring

the finite population correction.

10 20 30 40 50 60 70

20

40

60

80

100

120

Rain (mm)

120

100

80

60

40

20

Number of throughfall collectors (n)

0.95 probability

0.90 probability – – – –

0.80 probability . . . . . .

0 10 20 30 40 50 60 70

0

10

20

30

40

50

60

70

80

90

120

130

140

150

Coefficient of variation (y)

Rain (mm)

150

140

130

120

90

80

70

60

50

40

30

20

10

0
5

Table 3—Parameter estimates and fit statistics for the

negative exponential model of CV’s in throughfall and

stemflow to rain for small research plots (0.09 hectare)

 Parameter estimates

Treatment a b c M.S.E.a rb

Throughfall

1 8.89 25.0 -0.175 64.2 0.55

2 8.87 20.4 - .155 134.0 .38

3 14.1 48.7 - .547 123.5 .50

4 11.0 17.9 - .081 120.1 .41

Pooled 10.6 22.7 - .163 114.5 .43

Stemflow

1 33.7 21.6 - .245 259.6 .18

2 36.5 85.3 - .467 254.0 .36

3 34.6 10.0 - .105 199.0 .15

4 42.6 31.0 - .155 620.1 .22

Pooled 36.4 25.1 - .208 332.5 ..20

a Mean square error.

b Correlation coefficient

Conclusions

It is apparent that throughfall has an acceptable CV, which is

constant with rain events over 25 mm. Thus, the sample-size

curves presented should be useful in designing throughfall

sampling studies in loblolly pine plantations with similar BA

and LAI. However with small rain events, throughfall

variability increases substantially, resulting in a doubling or

tripling of the required sample size for a 25-mm rain event.

Stemflow variability was much greater than throughfall and

showed little relation with rainfall. Thus, the sample-size

curves indicated that at least 50 percent of all trees should

be sampled for any rain event, a recommendation that

probably will not be feasible in most environmental studies.

Our recommended sample sizes are applicable to loblolly

pine plantations with BA and LAI similar to those of the

plots used in this study, with rainfall up to 65 mm. In

addition, trough sizes and stemflow samplers should be

similar to those we used. Extrapolation outside of these

limits may be risky. In addition, the calculated CV(y)’s from

the negative exponential models are predicted values which

are subject to considerable variability, reflecting an

additional level of uncertainty. Thus, because the CV(y)’s

are not known without error, our sample-size

recommendations should be interpreted only as guidelines

Figure 3—The relationship of the coefficient of variation CV(y) for

stemflow to rain on an event basis for individual small research plots

(0.09 hectares).

Figure 4—The number of stemflow collectors (n) needed on an event

basis to sample stemflow on small research plots (0.09 hectare) at 5

percent accuracy and selected probability levels using the finite

population correction where it is assumed that there are 100 tree

stems on a plot. Number of stemflow collectors (n)

0 10 20 30 40 50 60 70

0

20

40

60

80

100

120

Rain (mm)

Coefficient of variation (y)

120

100

80

60

40

20

0

10 20 30 40 50 60 70

20

40

60

80

100

120

Rain (mm)

120

100

80

60

40

20

0.95 probability

0.90 probability – – – –

0.80 probability . . . . . .
6

for future studies. However, they are very similar to those of

Helvey and Patric (1966), which we find reassuring. If a

conservative approach is to be taken for a given study, the

researcher should use his or her own judgment and increase

the recommended sample size, if possible. The methodology

and CV(y)’s presented could easily be used to determine

recommended sample sizes for accuracy (D) and probability

(α) levels not presented in this paper. Our study emphasizes

the importance of sample size, stand conditions, and careful

sampling techniques for measuring the hydrological

components of throughfall and stemflow to be used in

subsequent calculations of soil-water balance.

Acknowledgments

We thank Andy Laviner, Michelle Canick, Karen Sarsony,

and David Josepheus for their excellent and reliable field and

lab work; and Dr. Lee Allen and Tim Albaugh for use of their

leaf area index and basal area data. We also appreciate the

technical reviews provided by Dr. Daniel A. Marion and Dr.

Ge Sun, which helped to improve the manuscript. The USDA

Forest Service, Southern Global Climate Change Program,

funded this project.

Literature Cited

Abrahamson, D.A.; Dougherty, P.M.; Zarnoch, S.J. 1998.

Hydrological components of a young loblolly pine plantation on a

sandy soil with estimates of water use and loss. Water Resources

Research. 34(12): 3503–3513.

Cochran, W.G. 1977. Sampling techniques. 3rd ed. New York: John

Wiley. 428 p.

Helvey, J.D.; Patric, J.H. 1966. Design criteria for interception

studies. International Association of Science Hydrology Bulletin.

67: 131–137.

Loustau, D.; Berbigier, P.; Granier, A.; El Hadj Moussa, F.

1992. Interception loss, throughfall and stemflow in a maritime

pine stand. I. Variability of throughfall and stemflow beneath the

pine canopy. Journal of Hydrology. 138(1992): 449–467.

Miller, J.D.; Miller, H.G. 1976. Apparatus for collecting rainwater

in three Minnesota forests. Oikos. 23: 14–22.

Peterson, D.L.; Rolfe, G.L. 1979. Determining sample size in

throughfall studies. Forest Science. 25(4): 582–584.
Zarnoch, S.J.; Abrahamson, D.A.; Dougherty, P.M. 2002. Sampling throughfall and

stemflow in young loblolly pine plantations. Res. Pap. SRS-27. Asheville, NC: U.S.

Department of Agriculture, Forest Service, Southern Research Station. 6 p.

Throughfall and stemflow estimates were obtained on a rain-event basis for small

(0.09-hectare) plots established in a young loblolly pine (Pinus taeda L.) plantation

in North Carolina. The plots were exposed to specific fertilization and irrigation

treatments, which resulted in a wide range of basal areas and leaf area indices.

Coefficients of variation were also determined, which revealed a negative exponential

relationship with rain-event magnitude. Throughfall was substantially less variable

than stemflow. Recommended sample-size curves were developed for throughfall and

stemflow to achieve 5 percent accuracy at the 0.80, 0.90, and 0.95 probability levels.

Keywords: Accuracy, hydrology, sample size, sampling design, variability.
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