Throughfall for Summer 

Thunderstorms in a Juniper 

and Pinyon Woodland 

Cibecue Ridge, Arizona 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 485-B 

Throughfall for Summer 

Thunderstorms in a Juniper 

and Pinyon Woodland 

Cibecue Ridge, Arizona 

By M. R. COLLINGS 

VEGETATION AND HYDROLOGIC PHENOMENA 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 485-B 

The relation between throughfall, precipitation, 

stemjlow, and interception is investigated and 

analyzed 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1966 
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary 

GEOLOGICAL SURVEY 

William T. Pecora, Director 

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington, D.C. 20402 - Price 20 cents (paper cover) 
CONTENTS 

hp p~ 

Abstract __________________________________________ _ B1 Analysis___________________________________________ B3 

Introduction ______________________________________ _ 1 Relation of throughfall, stemflow, interception, and 

Acknowledgments __________________________________ _ 2 precipitation_____________________________________ 12 

Physical aspects of through falL _____________________ _ 2 Conclusions________________________________________ 12 

Experimental procedure ____________________________ _ 2 Selected bibliography________________________________ 13 

Definitions and assumptions _________________________ _ 3 

ILLUSTRATIONS 

Page 

FIGURE 1. Map of Cibecue Ridge area________________________________________________________________________ B1 

2-5. Graphs showing precipitation-throughfall relation for2. Juniper----------------------------------------------------------------------------------- 4 

3. Pinyon------------------------------------------------------------------------------------ 5 

4. Juniper and pinyon_________________________________________________________________________ 6 

5. Oak trees and manzanita bushes __________________________________________ -_-_-_-_----------- 11 

6. Graph showing relation between precipitation and interception_________________________________________ 12 

TABLES 

Page 

TABLE 1. Location and arrangement of rain gages in the Cibecue Ridge area_ _ __________ - _- _------------------------- B2 

2. Covariance analysis, test of the regressions of precipitation versus through fall of juniper and of pinyon trees_---- 7 

3. Precipitation and throughfall data for equal-size storm groups______________________________________________ 8 

4. Three-way analysis of variance ______________________________________________________________________ --- 9 

5. Orthogonal contrasts of significant variables ___________________________________________________________ - 10 

m 

VEGETATION AND HYDROLOGIC PHENOMENA 

THROUGHFALL FOR SUMMER THUNDERSTORMS IN A JUNIPER AND PINYON WOODLAND 

CIBECUE RIDGE, ARIZONA 

By M. R. CoLLINGS 

ABSTRACT 

To determine throughfall for summer thunderstorms in a 

juniper and pinyon woodland and to gain an understanding of 

the factors involved, a stratified random sampling experiment 

was conducted on Cibecue Ridge, Ariz. Forty-eight rain gages 

were used to measure throughfall. The strata, or variables, 

investigated were tree type, tree size, and direction and distance 

of the gage from the tree bole. Equations for curves of precipitation against throughfall were computed for each tree 

type used. Statistical analyses were used to test the variables 

investigated, and it was found that: (1) the throughfall for 

Utah juniper is the same as that for pinyon, (2) the amount of 

rainfall catch that the gage will receive is a function of the 

direction in which the gage is located in relation to the tree bole, 

(3) throughfall is not dependent on tree size (for the sizes tested), 

(4) the throughfall catch is a function of the distance that the 

gage is located from the tree bole in three of the five storm groups 

tested, (5) the combined effect of direction and distance from 

the tree bole causes a significant difference in throughfall catch 

for the storm groups tested, and (6) broad-leaved oaks in the 

study area have less throughfall than juniper and pinyon if 

precipitation is more than 0.08 inch. 

The relation between throughfall (T), precipitation (P), stem .. 

flow (S), and interception (I) may be expressed as 

T=P-S-1. 

From this relation a curve of precipitation against interception 

was drawn. Interception increases in the initial stages of a 

storm, reaches a maximum at 0.50 inch of precipitation, and 

then becomes constant (assuming constant-intensity storms 

and excluding wind and evaporation effects). 

INTRODUCTION 

Cibecue Ridge is on the Fort Apache Indian Reservation in east-central Arizona and is at an altitude of 

5,300 to 5,600 feet above mean sea level (fig. 1). The 

annual precipitation is about 19 inches, of which about 

50 percent falls during the major runoff period July 

through September. In early and middle July, moist 

airmasses from the Gulf of Mexico are moved into 

Arizona by the western part of high-pressure systems , 

moving over the southeastern coast of the United 

States. The moisture in these airmasses is precipitated 

mainly during convective-type thunderstorms. The 

."""'-... ..........._ 

N 

r 

Cibecue Ridge 

study area '• 

FIGURE I.-Location of Cibecue Ridge, Ariz. 

cumulonimbus clouds form above the Mogollon Rim, 

to the north and east of Cibecue Ridge, and then 

propagate over the area where rainfall occurs. Winter 

precipitation is received from polar continental and 

polar Pacific airmasses in the form of frontal-type 

storms. Winter precipitation is not considered in this 

report. 

The most abundant tree types at this altitude on the 

reservation are Utah Juniper Juniperus osteosperma 

(Torr.) Little and pinyon (Pinus edulis Engelm). 

The crowns of these trees cover about 50 percent of 

the Cibecue Ridge site. 

Tw·o small drainage basins, 63 and 42 acres in area, 

were selected on Cibecue Ridge for intensive study of 

the effects of juniper and pinyon removal on runoff. 

In general, the purpose of this investigation was (1) 

Bl 
B2 VEGETATION AND HYDROLOGIC PHENOMENA 

to study throughfall in a juniper and pinyon woodland 

on Cibecue Ridge and (2) to further understanding of 

the factors affecting the physical aspects of throughfall. 

ACKNOWLEDGMENTS 

F. A. Branson provided the basis for choosing tree 

species and tree sizes by his vegetation transect measurements. D. R. Dawdy and N. C. Matalas offered 

many helpful suggestions in their comprehensive 

reviews. Data were collected with the help of R. M. 

Myrick, who also critically reviewed the report. 

PHYSICAL ASPECTS OF THROUGHFALL 

The effect of vegetal cover intercepting and thus 

reducing the amount of precipitation reaching the 

ground (throughfall) is significant on Cibecue Ridge. 

Because interception is satisfied mainly from the first 

part of a rainstorm and because many storms produce 

less than 0.25 inch of precipitation-less precipitation 

than is required to reach the retention capacity of 

the vegetal cover-interception accounts for a substantial amount of the annual rainfall on Cibecue Ridge. 

Interception may be considered a form of storage: 

raindrops from a storm are intercepted and stored on 

the surface of the vegetation until retention capacity is 

reached. When saturation or filling of the leaves has 

taken place, subsequent interception is close to nil. 

Wind and evaporation affect interception. Wind tends 

to keep the vegetation from becoming saturated and 

because of evaporation more rain is required before 

the leaves reach their saturation point. The measurement of evaporation during a storm is extremely 

difficult; however, in this study evaporation was 

considered to be a negligible factor during a storm 

event, and any errors introduced by ignoring evaporation are minor. 

EXPERIMENTAL PROCEDURE 

In the spring of 1963 a sampling experiment was 

devised to measure precipitation throughfall in a 

juniper and pinyon woodland. The experimental 

procedure consisted of stratified random sampling 

(table 1); the strata used were as follows: 

Tree types: 

Utah juniper 

Pinyon 

Others 1 

Tree sizes (diameter of bole, in inches) : 

1-3 

3-10 

>10 

1 Trees other than juniper and pinyon were sampled (table 1) but were not included 

in the main part of the analysis because of their small percentage of areal cover. 

Fraction of tht3 distance of gage from tree bole to 

edge of crown cover: 

7~ (distance A) 

% (distance B) 

% (distance C) 

% (distance G; considered within throughfall 

area because of shadow effect of a tree 

(Penman, 1963, p. 9)) 

Direction of gage in relation to tree bole: 

North 

East 

South 

West 

The do min ant tree type, the do min ant size, and the 

percentage of areal cover occupied by each type were 

determined from 15 vegetation transects by F. A. 

Branson for the 63-acre drainage basin on Cibicue 

Ridge. From the vegetation transects a study was 

TABLE 1.-Location and arrangement of rain gages used to measure throughfall in the Cibecue Ridge area 

[Distance: A, ~~ the distance from the tree bc,le to the edge of the crown cover; B, 

%the distance from the tree bole to the edge of the crown cover; C, at the edge of 

the crown cover; G, %;, or~. beyond the edge of cover. Direction: N, north; S, 

south; E, east; W, west] 

Tree Relation of gage to tree bole 

Gage 1---------------.---·--1-------

Type Size class Direction Distance 

(inches) 

---------------1-----------

1 Juniper___________________________________ >10 E 2 Arizona white oak________________________ 1-3 N 3 Juniper___________________________________ 1-3 E 4 Pinyon___________________________________ 1-3 W 

5 Scrub oak_------------------------------- I Large N 6 Juniper___________________________________ 1-3 N 

7 _____ do __ ---------------------------------- 1-3 N 8 Pinyon___________________________________ 1-3 W 

9 _____ do __ ---------------------------------- 1-3 S 10 Juniper___________________________________ >10 N 11 Pinyon___________________________________ 1-3 S 

12 _____ do_----------------------------------- 1-3, S 13 Scrub oak_------------------------------- I Large N 14 Juniper___________________________________ 3-10 E 

15 _____ do_----------------------------------- 3-10 E 

16 _____ do __ ---------------------------------- <1 E 17 _____ do __ ---------------------------------- 3-10 N 18 Pinyon_---------------------------------- 1-3 E 19 Juniper___________________________________ 1-3 N 

20 _____ do __ ---------------------------------- 3-10 W 21 _____ do____________________________________ 3-10 S 22 Manzanita ________________________________ ---------- W 

23 Pinyon___________________________________ 1-3 E 24 Arizona whit~:; oak________________________ 3-10 S 25 Manzanita ________________________________ ---------- N 

26 _____ do ______________________ ------------- ___ -------- E 

~~ -~~~~~~=================================== g=~8 : 29 _____ do __ ---------------------------------- 1-3 S 

g~ i~flo~~--wlifil;<>~tk'======================== ~~ ~ gi -~~~~oe~=:::::::::::::::::::::::::::::::::: i--~8 ~ 

g~ -=-i~~~~=================================== g=~8 ~ g~ 38 -~~-~~oe~ Arizona = white =========== oak________________________ ======================= 3-10 g=~g ~ W 

!g 41 _:_i~~~~=================================== _____ do __ ---------------------------------- 3:lg 1-3 ~ E 42 _____ do____________________________________ 1-3 N 

43 _____ do __ ---------------------------------- 3-10 E 44 _____ do __ ---------------------------------- >10 W 45 Scrub oak ________________________________ !Medium W 

!? -~~~~;~=================================== 3:lg : 48 Pinyon___________________________________ 3-10 N 

c 

A 

A 

G 

G 

G 

c 

c 

G 

B 

A 

B 

A 

B 

G 

B 

G 

c 

A 

B 

G 

c 

B 

A 

A 

B 

G 

B 

c 

A 

c 

G 

A 

A 

c 

A 

A 

B 

A 

B 

G 

B 

c 

A 

c 

B 

c 

c 

1 A large oak is >6 in. in diameter; a medium oak is 1 to 6 in. in diameter. 
THROUGHFALL IN A JUNIPER AND PINYON WOODLAND, CIBECUE RIDGE, ARIZONA B3 

made of tree height, areal extent of crown cover, and 

tree volume in relation to the bole diameter of given 

types. The findings show that the bole diameters of 

the trees studied have nearly the same percentage 

relation to dominance within a given tree type with 

respect to the magnitude of tree height and volun1e 

and to percentage of areal cover. Therefore, tree 

diameters were used to place rain gages at localities 

where the most abundant size class occurred within a 

type group. On the basis of percentage of areal cover, 

an allotted number of rain gages was assigned each 

tree size within that type (table 1). The trees were 

picked at random within a predetermined 15-acre area 

of the 63-acre drainage basin. 

Wedge-type rain gages were used to measure the 

throughfall. Two 8-inch standard rain gages were 

used to measure the total precipitation in the open, 

and a weighing-type recording gage was used to distinguish between the different storms by giving the 

storm time. Table 1 shows the number and relative 

location of the rain gages used to measure throughfall. 

Storm events were recorded from July through 

September. Many small storm events were not used 

in the study because of inaccuracies introduced in 

measuring very small amounts of precipitation. All 

storms with throughfalls of zero or a trace of precipitation were omitted. Immediately after or very soon 

after a storm, the gages were read and emptied to 

minimize the error caused by evaporation and to insure 

that data were related to individual storm events. 

Olive oil was used in the gages to suppress evaporation. 

Storm intensities were not measured. The storms 

analyzed were all high-intensity summer thunderstorms. 

DEFINITIONS AND ASSUMPTIONS 

In this investigation all the analyses used to study 

throughfall are based on the assumption that the data 

are normally distributed. Common logarithmic transformations were used in parts of the analysis to reduce 

interactions or to more closely approximate the normal 

distribution and to stabilize the variance (Cramer, 

1946, p. 397). The assumption of normality was tested 

by plotting on normal probability paper the cumulative 

probability distributions of the (1) log of juniper 

throughfall, (2) log of pinyon throughfall, and (3) log 

of total precipitation and the throughfall (not transformed) of juniper and pinyon trees combined for one 

storm group. The plotting position used was (M- ~~)/N 

(Hazen formula) where M is the order of magnitude 

and N is the number of events. On normal probability 

paper a normal distribution plots as a straight line. 

The normal distribution fits the data fairly well in the 

cases tested. 

The data for individual storm groups were studied 

(table 3), and each group, when the data were plotted 

on probability distribution paper, approximated a 

normal distribution without the use of transformations. 

To evaluate interaction between variables, storms of 

about equal total precipitation (within measurable 

error) were grouped. Interaction is an estimate of 

variance used to test the differences between means that 

cannot be 81Ccounted for by shifts in, say for example, 

the means of tree size, direction, and distance. Zero 

interaction would be indicative of an additive modelthat is, the effect of any one factor, say tree size, on 

throughfall is not related to magnitude of any other 

factor, say direction. However, additivity was accepted 

only because interaction was ruled out by the appropriate F test, both the F test and the assumption of 

additivity are invalid if significant interaction does 

exist. Thus, if interaction does exist and is not evaluated, it is treated as part of the error (within group) 

component, in which case the mean square ratios of the 

variables do not follow the F distribution used to test 

the variables (Brownlee, 1960, p. 373; Dixon and 

Massey, 1957, p. 166; Scheffe, 1961, p. 124). 

ANALYSIS 

Throughfall was related to storm precipitation for 

both juniper and pinyon, and the results are shown in 

figures 2 and 3. The equations for the curves in figures 

2 and 3 are similar. A regression equation of the relation of juniper throughfall to pinyon throughfall was 

computed as 

Tj=0.99T/·02• 

Neither the slope nor the intercept is significantly 

different from 1.0. Statistical analysis indicates no 

significant difference between juniper and pinyon 

throughfalls (table 2); one curve may best be used to 

describe the precipitation-throughfall relation for both 

tree types. The plot of total precipitation versus the 

throughfall for juniper and pinyon is shown in figure 4. 

The equation of the curve is 

T=0.873P1 •

156• 

The standard error of estimate is + 12.2 percent and 

-11.0 percent (0.049 log units) with a coefficient of 

correlation of 0.994. For a l-inch rainfall, this standard 

error would give a range in throughfall from 0.78 to 

0.98 inch. 

The throughfall data (table 3) for both jtmiper and 

pinyon aTe used in an analysis to determine the effect of: 

(1) the storm event (the storms were grouped into size 

classes, each class having several throughfall events 

with the same total precipitation, as in table 3), (2) direction of gage from tree (table 1), (3) tree type (this 
B4 

(f) 

w 

I 

(.) 

~ 

~ 

......:;. 

~--~ 

__J 

__J 

<( 

1..1.. 

I 

<.!J 

::> 

0 

0::: 

I 

1--

0::: 

w 

a.. 

z 

::J 

' 

VEGETATION AND HYDROLOGIC PHENOMENA 

3.0r---------~------------------------------~--------------~------------+-----~ 

0.5 

Equation: I; = 0.879 P 1.166 

Standard error= 0.0586 log units, + 14.9 percent -13.0 percent 

Correlation coefficient= 0.991 

Standard 

error 

0.1 0.5 

PRECIPITATION ( P), IN INCHES 

FIGURE 2.-Precipitation-throughfall relation for juniper. 

1.0 2.0 3.0 
en 

w 

I 

() 

z 

~ 

....J 

....J 

<( 

LL. 

I 

(.!) 

:::> 

0 

0::: 

I 

1-

z 

0 

>-

z 

a: 

THROUGHFALL IN A JUNIPER AND PINYON WOODLAND, CIBECUE RIDGE, ARIZONA 

3.0r---------~----------------------------~------------+------------4----~~ 

Equation:TP = 0.0867P 1.147 

Standard error =0.0398 log units, + 10.0 percent -9.0 percent 

Correlation coefficient= 0. 996 

error 

0.1 

79·1-599 o-66--2 

• 

0.5 

PRECIPITATION ( P), IN INCHES 

FIGURE 3.-Precipitation-throughfall relation for pinyon. 

1.0 2.0 3.0 

B5 
B6 

....J 

....J 

<( 

u. 

I 

(!) 

::J 

0 

0:::: 

I 

fVEGETATION AND HYDROLOGIC PHENOMENA 

3.or---------~------------------------------~------------~------------~r-------; 

Equation: T = 0.873 P 1.156 

Standard error=0.04861og units, +12.2 percent -11.0 percent 

Correlation coefficient =0.994 

error 

0.1 

x Juniper 

• Pinyon 

• 

0.5 

PRECIPITATION (P), IN INCHES 

FIGURE 4.-Precipitation-throughfall relation for juniper and pinyon. 

1.0 

//;1 

/ 

2.0 3.0 
THROUGHFALL IN A JUNIPER AND PINYON WOODLAND, CIBECUE RIDGE, ARIZONA B7 

TABLE 2.-Covariance analysis, test of the regressions of precipitation versus throughfall of juniper trees and of pinyon trees 

[P, precipitation; T, throughfall] 

Source of variance 

Sum of 

squares 2;T2 about 

regression 

line 

------------1---·1---------

Within each group: Juniper_----------___________________ 2. 44231 Pinyon______________________________ 2. 44231 

2. 84778 3. 37878 

2. 80069 3. 23838 

0.05822 

.02672 

-.00010 

• 08539 Among means ------------------------- 0 

Within -------------------------------- 4. 88462 

0 -.00010 

5. 64847 6. 61716 

TotaL----------------------------- 4. 88462 5. 64847 6. 61706 . 08529 

NOTE.-Tests: 

For difference in means, F= -0.04 (not significant). Whether one regression line can be used for all observations, F= -0.07 (not 

significant). 

is another test to. see if juniper and pinyon throughfall 

are different), (4) tree size (trees with boles 1-3 and 3-10 

in. in diameter were tested), and (5) the distance that 

the rain gage is located from the tree bole (table 1). 

Five groups of events (the 0.76-, 0.60-, 0.42-, 0.28-, 

and 0.12-in. storm groups) with replications were 

analyzed using a three-way analysis of variance (table 

4). The mathematical model underlying the first 

three-way analysis of variance is 

Ttikv=JL+Et+Di+tk+(ED)ti+(Et)tk 

where 

+ (Dt) ~k+ (EDt) tik+Eiikv 

Ttikv=an individual throughfall measurement, 

JL=a fixed value representing the general mean of the throughfall, 

E 1=the random effect associated with 

storm event, 

D1=the fixed effect due to gage direction, 

tk=the fixed effect of tree type, 

(ED) t 11 (Et) tk, 

and (Dt) 1k=two-way interactions of indicated 

variables, 

(EDt)Hk=three-way interaction of indicated 

variables, and 

EtJkv=random component or error term. 

The analyses of the five storm groups are summarized 

.in the upper part of table 4. Because E is a random 

effect and D and t are fixed effects, the F ratio was 

obtained by testing E, ED, Et, and EDt against the 

within-group mean square, D and t against ED and Et 

respectively, and Dt against interaction EDt (Scheffe, 

1961, p. 274). 

E was found to differ for small-storm groups but not 

enough to warrant concern. The errors introduced in 

measuring small storms become rather great percentagewise; for example, the component of variance 

( uE2) was calculated for both the 0.28- and 0.12-inch 

storm events as 0.0009 and 0.0004 inch, respectively. 

Because the analysis indicated that the events do not 

differ within the storm group, it may be assumed that 

the classification of storms into groups provides replication (more than one throughfall measurement for a 

given size storm) which may be used to define the sampling error for testing the other variables. This 

analysis showed further that the tree types did not 

differ more than would be expected by chance, and thus 

further indicated that the throughfall for juniper and 

pinyon trees is the same. 

To investigate other variables and test the direction 

(D) by a more sensitive method, a second three-way 

analysis of variance was made on the five storm groups 

used in the upper part of table 4. The mathematical 

model used was 

Ttikv= JL+ D t+ Sd1k+ (DS) ti+ (Dd) tk 

where 

+ (Sd)ik+ (DSd)tik+EHkv 

Ttikv= an individual throughfall measurement, 

JL=a fixed value representing the 

general mean of the throughfall, 

Dt=a fixed effect due to gage direction, 

S 1=a fixed effect representing throughfall for different tree-bole diameters, 

dk= a fixed effect due to rain-gage 

distance from the tree bole, 

(DS) til (Dd) tk, 

and (Sd) 1k=two-way interaction of variables, 

(DSd) 11k=three-way interaction of the variables, and 

EtJkv=random component or error term. 

The analyses for the 0.76-, 0.60-, 0.42-, 0.28, and 0.12-

inch storm groups-using D, S, and d as variablesare summarized in the lower part of table 4. The 

three variables are fixed values and, therefore, were all 

tested using the error or within-groups mean square. 

Statistical tests showed that (1) the amount of 

throughfall a gage catches is a function of the direction 

of the gage in relation to the tree bole, (2) the size of 

the tree bole (1-3 and 3-10 in. in diameter) was found 

not to affect the amount of throughfall from a given 

size storm, (3) the distance that the gage is located 

from the tree bole did not vary the throughfall catch 

more than would be expected by chance for the 0.76-inch 

storm group but did more strongly affect throughfall 

for the 0.60-, 0.28-, and 0.12-inch storm groups, and 

(4) the combined effect of direction and distance was 
TABLE 3.-Precipitation and throughfall data, in inches, for equal-size storm groups 

Precipitation over Throughfall at gages placed at tree type indicated area 

Juniper Total for 

Group individual 

average storm 

1 3 6 7 10 14 15 16 17 19 20 21 27 28 29 32 33 36 37 46 47 4 

------------------------------------------

0. 76 { 

0. 74 0.43 0.54 0.62 0.60 0.64 0.85 0. 77 0.50 0. 75 0.66 0.40 0. 72 0.45 0.68 0.51 0.50 0.55 0. 73 0. 75 0.57 0.46 0.33 . 77 . 78 . 76 .86 . 70 . 79 . 79 .15 .34 . 76 .66 .56 . 70 .38 .39 .51 1. 35 .62 . 75 .90 .61 .36 .32 . 76 .36 .49 .50 .67 .56 1.18 .60 1. 21 . 78 .40 .25 .69 .38 .59 .85 .28 .32 . 72 .65 .38 .47 .30 

.60 { .56 .39 .37 .48 .59 .50 .47 .60 .55 .63 .49 .47 .60 .40 .52 .62 .60 .42 .55 .61 .46 .44 .35 

.61 .36 .29 .47 .58 .62 .85 .53 .49 .61 .44 .34 .58 .34 .46 .54 .30 .27 .60 .68 .47 .39 .32 

.42 { .41 .38 .32 .38 .42 .40 .48 .37 .30 .42 .37 .20 .38 .28 .20 .24 .37 .25 .41 .58 .36 .18 .20 

.43 .20 .20 .26 .42 .34 . 51 .39 .48 .45 .24 .15 .43 .27 .42 .47 .19 .22 .42 .56 .24 .32 .21 

.28 { .29 .14 .09 .26 .28 .21 .54 .24 .65 .29 .14 .04 .29 .16 .22 .35 .08 .14 .26 .26 .13 .23 .15 

.26 .11 .09 .20 .25 .17 .35 .21 .33 .25 .11 .04 .27 .16 .12 .15 .07 .11 .22 .22 .13 .17 .15 

.12 { 

.13 .07 .05 .14 .12 .08 .15 .08 .16 .15 .03 .03 .14 .05 .08 .09 . 01 .04 .14 .18 .10 .08 .11 

.09 .03 .03 .06 .08 .05 .11 .06 .14 .09 .05 .03 .11 .03 .06 .06 .04 .03 .09 .06 .03 .04 .03 

.14 .03 .05 .07 .12 .07 .11 .10 .08 .13 .05 . 01 .12 .03 .02 .04 .01 . 01 .14 .07 .06 .02 .05 

---------- 2.42 1.98 1. 75 1.85 1. 77 2.05 1.86 2.19 3.06 2.49 3.01 3.35 2.10 2.15 2. 77 3.00 3.44 2. 71 1. 91 3.10 1. 51 2.36 1. 75 

---------- 1. 46 1. 07 .88 1. 25 1.35 1. 43 1.28 1. 37 1.07 1. 52 1.12 1.05 1.47 1.10 1. 22 1. 22 1. 45 .94 1. 46 1. 92 1.16 .97 . 74 

----------- 1.00 .59 .53 .81 . 79 1.02 1. 07 . 76 . 73 .95 . 51 .68 .93 .80 1.06 1.13 .35 .46 .96 1.48 .96 .90 .71 

---------- .80 .60 .52 . 70 .62 .82 1.14 . 73 1. 27 .86 .88 .80 . 75 . 52 .69 . 70 . 74 . 58 .82 1.08 .66 . 70 .42 

---------- .67 .34 .32 .48 .55 .49 .84 .50 .68 . 70 .25 .30 .64 .42 .52 .66 .20 .25 .67 .84 .49 .48 .50 

---------- .56 .39 .28 .38 .36 .40 .56 .54 .62 .54 .58 .66 .58 .44 . 75 . 70 .63 .54 .42 .64 .27 .44 .22 

---------- .20 .06 .08 .14 .18 .11 .22 .16 .16 .22 .07 .04 .22 .09 .12 .18 .04 .02 . 21 .15 .10 .05 .18 

Precipitation over Throughfall at gages placed at tree type indicated area 

Oak 

Total for Pinyon Manzanita bush 

Group individual Arizona white Scrub 

average storm 

23 30 34 35 39 40 41 42 43 44 48 2 24 31 38 5 13 45 22 25 26 

---------------------------------------------

0. 76 { 

0. 74 0. 79 0.52 0.81 0.60 0.37 0.63 0.88 0.61 0. 73 0.32 0. 78 0.42 0.22 • 0. 70 0. 75 0.66 0.46 0.42 0. 70 0.80 0.69 . 77 .98 .37 . 70 .51 .39 .62 1. 27 .82 . 76 .24 .83 .55 .20 .64 .90 .86 .54 .34 . 74 . 72 .47 . 76 .64 .44 .38 .65 .69 .71 .68 .59 . 74 .25 . 72 .46 .22 .65 .66 . 79 .39 . 70 .65 .71 .64 

.60 { .56 .59 .39 .54 .45 .31 .50 .63 .49 .53 .37 .54 .44 .30 . 51 .45 .51 .31 .32 .60 .61 .51 . 61 .57 .45 .40 .62 .55 .61 .62 .54 .64 .21 .64 .58 .21 .54 .60 .60 .44 .44 .54 .57 .50 

.42 { .41 .36 .28 .26 .32 .24 .44 .63 .48 .47 .08 .51 .51 .11 .36 .50 .42 .30 .12 .40 .34 .26 

.43 .39 .29 .39 .40 .32 .43 .39 .26 .38 .16 .35 .20 .26 .45 .32 .38 .22 .35 .22 .42 .45 

.28 { .29 .26 .17 .11 .26 .19 .27 .25 .14 .26 .10 .23 .17 .07 .26 .20 .27 .08 .29 .23 .30 .24 

.26 .20 .16 .13 .24 .21 .16 .20 .11 .13 .10 .16 .13 .08 .28 .17 .22 .12 .18 .30 .30 .26 

.12 { 

.13 .08 .03 .02 .15 .07 .15 .18 .08 .18 .01 .09 .06 .04 .15 .06 .17 .05 .12 .15 .10 .11 

.09 .04 .03 .01 .08 .05 .07 .05 .05 .07 .01 .08 .02 .05 .08 .07 .07 .04 .08 .09 11 .10 

.14 .20 .03 .01 .12 .07 .11 .09 .06 .11 .01 .10 .05 .01 .11 .08 .12 .05 .09 .12 .13 .11 

------------ 2.42 3.44 1.94 3.08 1.65 1.64 1.66 (I} 2.60 2.52 2.11 2.86 2.03 1.09 1. 72 2.00 1.85 1. 74 1. 70 2.07 2.10 2.00 

------------ 1. 46 1.42 1.16 1.32 1.34 1.14 1. 24 1. 50 1.13 1.30 .52 1.34 1.34 .58 1.38 1.18 1. 44 1.06 . 78 1.48 1.71 1.40 

----------- 1.00 .88 . 70 .88 .95 . 75 .93 1. 20 . 73 .97 .54 .71 .82 .39 .94 .83 .93 .64 .86 .97 .90 .86 

------------ .80 1.06 .49 .93 .52 .57 .82 1.06 .86 .90 .40 .95 .60 .47 .59 .93 .82 .50 .66 . 70 . 72 . 73 

------------ .67 .61 .44 .85 . 70 .56 .69 . 72 .41 .68 .38 .50 .32 .28 .69 .50 .68 .38 .60 .66 .65 .64 

------------ .56 . 79 .38 .71 .31 .28 .31 .40 .43 .37 .22 .55 .28 .30 .44 .48 .38 .30 .31 .54 .56 .50 

------------ .20 .11 .07 .04 .18 .12 .21 .13 .13 .18 .04 .14 .07 .06 .19 .12 .21 .08 .20 .20 .21 .20 

-- -- ·- , __ 

1 Gage washed out. 

Pinyon 

8 9 11 12 18 

--------------- 0.55 0. 73 0.39 0.49 0.90 

.60 .68 .35 .44 .78 

.48 . 79 .53 .62 .55 

.57 .59 .45 .43 .59 

.45 .59 .39 .45 . 72 

.38 .40 .26 .23 .38 

.34 .41 .38 .35 .44 

.20 .29 .19 .21 .34 

.16 .23 .16 .17 .27 

.14 .14 .11 .10 .02 

.03 .09 .06 .04 .05 

.03 .15 .04 .08 .04 

2.30 2.11 2.18 2.00 3.26 

1.40 1. 35 .87 1.03 1. 41 1.14 1. 01 . 75 . 72 .93 • 78 .88 .60 .58 .87 

.63 . 70 .48 .62 .56 

.40 .42 .39 .33 . 78 

.10 .21 .15 .16 .09 

Mean of throughfall 

Juniper Pinyon Oak Manzanita 

bush 

---

0.60 0.61 0.52 0. 73 

.65· .63 .55 .64 

.59 .57 .55 .67 .51 .49 .40 .57 

.49 .52 .49 .54 

.35 .35 .33 .33 

.34 .35 .31 .42 

.24 .21 .19 .26 

.18 .17 .17 .27 

.09 .10 .09 .12 

.06 .05 .06 .10 

.06 .08 .07 .12 

2.40 2.32 1. 71 2.06 

1.25 1.19 1.11 1.53 

.83 .85 . 77 .91 . 77 . 75 .65 . 72 

.50 .59 .51 .65 . 51 .43 .35 .53 

.12 .13 .13 .20 

ttl 

00 

;3 

C) 

tz;j 

1-1 

~ 0 

z 

~ '=' 

~ '=' 

~ 

0 

t"4 

0 

C) 

1-1 

c 

'"d 

~ 

~ ~ 
Source of variance 

E.----------------------

D----------------------- t_-- --------------------- E X D------------------

E X L------------------

D EX XL------------------ D X t__ ____________ 

Within (error) __________ 

Sum of square for indicated storm groups 

TABLE 4.-Three-way analysis of variance 

[Asterisk indicates result is significant] 

Degrees of freedom for indicated storm groups Mean square for indicated storm groups 

0.76 in~ I 0.60 in._ I 0.42 in. __ I 0.28 ~· --~.12 I in~ _:6 in~-I o.oo. O.~~Yu. o.~ I __ 0.12 in. o.~~ I o.oom.l o.~m.l o.n I o.tzw. 

Variables: storm event (E), direction of gage (D), and tree type (t) 

0. 04089 0. 00191 0. 00002 0. 03563 o. 03063 2 1 2 0. 02044 0. 00191 0.00002 10.03563 2 0. 01532 . 66184 . 07765 .10002 . 03093 • 00225 3 3 3 • 22061 . 02588 .03334 . 01031 .00075 • 01870 . 00544 . 00620 . 00008 . 00107 1 1 1 . 01870 .00544 . 00620 . 00008 . 00107 .14391 • 02031 .09875 . 00840 . 00300 6 3 6 . 02398 . 00677 . 03292 .00280 . 00050 • 00373 . 01183 . 00069 • 00035 . 00222 2 1 2 • 00186 . 01183 . 00069 . 00035 . 00111 .17245 . 07686 . 02718 . 02458 . 00488 3 3 3 . 05748 . 02562 .00906 . 00819 .00163 .23049 .00519 . 01115 . 00465 .00420 6 3 6 . 03842 • 00173 . 00372 . 00155 • 00070 2. 23585 . 58222 .44272 .31308 .14295 72 48 72 . 03105 • 01213 . 00922 . 00652 . 00198 ------------------------

F ratio for indicated storm groups 

o.76 w.l o.oo in. I o.~ in. I o.zs m.l 0.12 w. 

0.66 0.16 ... o *5.46 *7. 74 *9.20 3.82 1. 01 3.68 1.50 10.05 .46 8.98 .23 .96 • 77 .56 *3.57 .43 .25 .06 .98 .07 .05 .56 1. 50 *14. 81 2.44 5.28 2.33 1.24 .14 .40 .24 .35 

---------- .................. __ ---------- ---------- ----------

TotaL_----------' 3. 50786 . 78141 .68671 . 41770 .19120 95 63 95 '----------'----------'----------'----------'----------' ----------· ----------'----------' -------- __ ,----------

Variables: direction of gage (D), size of tree (S), and distance of gage from tree bole (d) 

D- ---------------------- 0. 76464 0.10742 0.12833 0.03097 0. 00714 3 3 3 s _____ ------------------- . 00735 . 01155 . 01182 . 00360 . 00150 1 1 1 

d D ___ X --------------------- . 03791 .07952 .01560 • 04484 . 01324 3 3 3 s __________________ D X d .13780 • 03212 • 01823 .01193 . 00962 3 3 3 ___________________ . 68044 . 27595 .12946 .16257 . 04841 9 9 9 

S X d------------------- .13563 . 04212 • 02824 .01809 . 00327 3 3 3 D X S X d ______________ .32762 .04346 .16184 .07478 • 02715 9 9 9 Within (error) __________ 1.37967 • 20430 .19715 . 07640 • 08213 64 32 64 

------------------------ TotaL ___ --------- 3.47106 . 79644 .69067 .42318 .19246 95 63 

- - - ---

tAn estimate of the mean square forE component of variance is a2+4·4·2a28, or a28=0.00091 and 0'8=0.0302. 

95 

0.25488 o. 03581 0. 04278 0.02032 0. 00238 *11. 82 • 00735 • 01155 .01182 . 00360 .00150 .34 • 01264 . 02651 . 00520 . 01495 .00441 .59 .04593 .01071 .00608 .00398 .00321 2.13 . 07560 . 03066 . 01438 . 01806 . 00538 *3. 51 .04521 . 01404 . 00941 .00603 . 01109 2.10 .03640 .00483 . 01798 .00831 . 00302 1. 69 . 02156 • 00638 . 00616 . 00239 . 00128 ----------

---------- ---------- ---------- ---------- ---------- ----------

*5.61 *6.94 1. 81 1.92 *4.16 .84 1.68 .99 *4.80 *2.33 2.20 1.53 

. 76 *2.92 

---------- ----------

---------- ----------

*4.32 

1. 51 *6.25 

1.66 

*7.56 

2.52 

*3.48 

----------

----------

1. 

1. 

*3 . 

2. 

*4. 

*2: 

--------

--------

86 

17 

44 

51 

20 

5 

6 

2 An estimate of the mean square forE component of variance is a2+4-4-2a28 or a28=0.00042 and 0'8=0.0205. 

-

~ P::l 

0 

q 

I 

z 

> 

t;l 

~ ~ 

~ I'd 

z 

~ 

0 

z 

~ g 

~ ~t;j 

c 

1-4 

ttl 

t;l 

c 

q 

t;l 

~ 1-4 

t;j 

0 

~t;l 

~ 1-4 

IS 

~ 

td 

~ 

• 
• BlO VEGETATION AND HYDROLOGIC PHENOMENA 

found to cause a significant variation of throughfall in 

the five storm groups tested. 

The effect of direction on throughfall in the Cibecue 

Ridge area may be explained as follows: (1) the 

summer-thunderstorm clouds have a tendency to form 

above the Mogollon Rim, to the north and east of 

Ci.becue Ridge, an<\ to propagate over the area where 

ramfall occurs and (2) the tree foliage may be thicker in 

one direction than in the others. Local areas of 

throughfall concentration were attributed by Horton 

(1919) .to the variation in density of the foliage. 

Ha vmg determined that direction distance and the 

b. ' ' 

com med effect of direction and distance have a 

significant effect on throughfall, the next step is to 

compare and test for the elements of direction and of 

distance that are causing the difference in the catch 

of throughfall gages. This is accomplished by using 

appropriate orthogonal (independent) contrasts and 

statistical tests. All contrasts were tested against the 

error o; the wi~hin-group mean square of the three-way 

analysts of variance used for a particular storm group. 

The coefficients of each set of contrasts define orthogonal 

contrasts because the sum of each contrast is equal to 

zero and the sum of the products of the three contrasts 

is equal to zero. The sum of squares for each contrast 

~.any storm group added together equals the unpartltwned sum of squares for the variable used in the 

three-way analysis of variance (table 4, lower part). 

Thus, the error in mean square for a given storm group 

may be used for the F test . 

. Tin:ee contras~s for each of four storm groups using 

dtrectwn as the significant variable and for each of three 

storm groups using distance as the significant variable 

were considered. (See table 5.) The direction cont~asts (table 5, upper part) indicate that: (1) the north 

stde of the tree does not have more variance in throughfall than the east side, (2) the south side has significantly 

less throughfall than the north and east sides of .the 

tree for the 0.42-inch storm group, but not for the 0. 76-, 

0.60-, and 0.28-inch storm groups, and (3) the west side 

has throughfall significantly different from that of 

the north, east, and south sides. The distance contrasts 

(table 5, lower part) indicate that: (1) the two gages 

nearest the tree bole do not have significantly different 

throughfall, (2) the gage at the edge of the tree receives 

~hroughfall which is significantly different for the 0.60-

I~ch and 0.28-inch storm groups and not significantly 

dt!ferent for the 0.12-inch storm group when compared 

wtth the throughfall received by the two gages nearest 

the tree bole, and (3) the gage at G distance has a 

greater difference in throughfall than would be expected 

fo; the 0.28- and 0.12-inch storm groups when compared 

wtth throughfall at the A, B, and C distances. 

The distance contrasts indicate that the amount of 

TABLE 5.-0rthogonal contrasts of significant variables 

[X indicates significant result] 

Contrasts for Result of Fo.t& test on Situation indicated direction of gage indicated storm group, in inches 

desc~~~d in l---,-----,------:---1---.----..,-----,.--

North East South West o. 76 0. 60 0. 42 0. 28 

----1---1---1---1---------------

L -------------

2_ -------------

3_ -------------

-1 

1 

1 

0 

-2 

1 

0 -------- -------- -------- -------- 0 X X X -------- -3 X X X X 

----1--___;_ _ _..:__: _ _:__ __ 1------------

A 

1 _____________ _ 2 _____________ _ a _____________ _ 

Contrasts for indicated 

distance from tree bole 

B 

-1 

1 

1 

c 

0 

-2 

1 

G 0. 60 0. 28 0. 12 

0 -------- -------- -------- 0 X X 

-3 -------- X X 

throughfall received by a gage at distance C is significantly different from that received by gages at 

distances A and B for the larger storm groups tested. 

It may be that during the 0.12-inch storms a gage at 

distance C received a drip that did not cause a significant variation in throughfall; however, during the 

0.28- and 0.60-inch storms the leaf capacity was filled 

and drip added a significant amount of throughfall. A 

gage at G distance would be sUDJected to greater wind 

currents; if wind currents increase catch, then the 

smaller storms, which would logically occur over a 

shorter time period (assuming that all summer storms 

have fairly uniform intensities), would have more 

chance for significantly different throughfall. 

The same contrasts used to compare the elements of 

direction and distance were used to compare the elements of the two-way interaction, direction times 

distance. The 0.76-inch storm group was investigated 

by partitioning of the sum of squares for the inter-action 

into orthogonal contrasts for the given storm group. 

The orthogonal contrasts of the combined effect of 

direction and distance indicate that the gage nearest to 

the tree bole on the east side and the gage at distance G 

on the north side receive throughfall amounts that are 

significantly different from those received at gages 

located at other combinations of distance and direction. 

The effects of direction and distance on throughfall 

are confirmed by Stout and McMahon (1961) who 

found that there is a significant difference in throughfall with respect to distance and direction from the tree 

bole and by Beall (1934) who noted that throughfall is 

less near the bole than near the edge of the crown cover. 

Woody plants other than Utah juniper and pinyon 

were sampled (table 1) for amount of throughfall received. Curves showing the relation of precipitation 

to throughfall for oak tree and manzanita bush are 

shown in figure 5. The equation for the precipitation 

(P) versus oak-tree throughfall (To) is 

To= 0. 7 44P1 •

072 
en 

w 

I 

() 

z 

~ 

Cl 

z 

<( 

1--0 

....J 

....J 

<( 

LL. 

I 

<..!) 

::> 

0 

0::: 

I 

ITHROUGHFALL IN A JUNIPE.R AND PINYON WOODLAND, CIBECUE RIDGE, ARIZONA 

3.0r-------~------------------------------~------------+-----------_,------~ 

2.0 

Equations: 

To= 0.744Pl.072 

Standard error= 0.0401 log units, + 10.0 percent -9.0 percent 

Tm = 0.917Po.969 

Standard error= 0.03861og units,+ 9.7 percent- 8.9 percent 

0.1 

• Oaks (To) 

x Manzanita ( Tm) 

0.5 

PRECIPITATION (P), IN INCHES 

1.0 

FIGURE 5.-Precipitation-throughfall relation for oak trees and manzanita bushes. 

2.0 3.0 

Bll 
Bl2 VEGETATION AND HYDROLOGIC PHENOMENA 

with a standard error of estimate of + 10.0 percent and 

-9.0 percent (0.0401 log units). The broad-leaved 

oak trees permit less throughfall (0.74 in.) for a l-inch 

storm than the needle-leaf Juniper and pinyon trees 

(0.87 in.). Coffay (1962) found the equation for broadleaved species to be 

T= 0.834P1 •

046 

with a standard error of about + 19 percent and -16 

percent. The equation for the precipitation (P) versus 

manzanita-bush throughfall (Tm) is 

Tm=0.917P0 •

969 

with a standard error of +9.7 percent and -8.9 percent 

(0.0386 log units). The curve for precipitation versus 

manzanita-bush throughfall probably is influenced by 

precipitation ground splash. All the gages used to 

measure manzanita-bush throughfall were 18 inches 

from the ground to enable placement of the gages below 

the leafy part of the bush. 

RELATION OF THROUGHFALL, STEMFLOW, 

INTERCEPTION, AND PRECIPITATION 

The relation between throughfall ( T), stemflow (S), 

interception (/), and precipitation (P) may be shown 

by the equation 

T=P-S-1. 

The amount of throughfall is equal to the amount of 

precipitation minus the quantity of water which 

reaches the ground by running down the stem of the 

tree minus the amount of the precipitation stopped by 

the leaves of the tree. 

Stemflow was measured on nine trees, six Utah 

junipers and three pinyons, ranging in diameter from 

0.30 feet to 1.3 feet. Stemflow increases slightly with 

decreasing tree diameter. The stemflow of a tree ha ving a 4-inch bole diameter is used to show the relation 

between throughfall, stemflow, and interception, as 

follows: 

The relation of precipitation to stemflow was found 

to be 

8=0.09P1·

25• 

The equation for the precipitation-throughfall relation 

was found to be 

T=0.87 pt.16 • 

By substitution, the relation between precipitation 

and interception is 

By rearranging terms, the equation becomes 

I =P-0.09Pt.25 -0.87 PL16• 

Figure 6 graphs th ' preceding equation and shows 

that interception i. cr ,ases rapidly in the first part of a 

storm and reaches a maximum (0.072-in.) after 0.50-

inch of precipitation. The mathematical curve can 

continue until negative interception is indicated. 

However, each constant is subject to error, and is 

defined only over the range of precipitation used. 

Therefore, the derived equation has a mean-square 

deviation of sample points from the estimated regression line at least equal to the sum of the mean-square 

deviations of each of the component equations. None 

of the curves of these equations may be extrapolated, 

for each would result in conclusions such as throughfall 

and stemflow being greater than precipitation or negative interception. Theoretically, after the leaves have 

become filled and precipitation increases, it is not 

unreasonable for the curve to approach a constant 

limiting value of I (Penman, 1963, p. 14); interception 

would be z 3ro for the remainder of the storm. The 

dashed line on figure 6 is an estimate of uniform conditions. The relation would be expected to vary in the 

late stages of a storm because of climatic forces such as 

wind. 

en 

L&.J 

:c 

u 

z 

z 

~ 0.10 

'-" -

z 

0 

i= 0.05 CL 

Li.J 

u 

a:: 

Li.J 

~ 0 

EXPLANATION 

Interception ( 1 )=precipitation ( P)- stemflow -throughfall 

I= P-0.09PI.25 -0.87P 116 for P<-0.5 inches 

r 

v- ~--· ------ ~----- ~------

v -

- I 

0.2 0.4 0.6 0.8 1.0 1.2 

PRECIPITATION ( P), IN INCHES 

FIGURE 6.-Relation between precipitation and interception. 

CONCLUSIONS 

1. The summer-storm throughfall for juniper does not 

vary from that of pinyon on the Cibecue Ridge 

study area. The equation for throughfall in a 

juniper-pinyon woodland is 

T= 0.873P1•

156 

where (T) is throughfall and (P) is precipitation, 

in inches. 

2. The amount of throughfall the gage catches is a 

function of the direction in which the gage is 

located. It was found that throughfall in the 

Cibecue Ridge study area is greater on the north 

and east sides of the tree because (1) the summer 

storms have a greater frequency of moving in 

from the north and east and (2) the foliage may 

be thicker on one side of the tree than on the other. 
THROUGHFALL IN A JUNIPER AND PINYON WOODLAND, CIBECUE RIDGE, ARIZONA B13 

3. The tree sizes tested (1-3 and 3-10 in. in diameter) 

do not vary in throughfall more than would be 

expected by chance. Of the five storm groups 

tested, none show a significantly different throughfall for different tree sizes. 

4. For gages located at four different distances from 

the tree bole, it was found that the throughfall 

differed in three of the five storm groups tested. 

For the storms that showed a variation in throughfall with distance from the tree bole, it was found 

that: (1) the two gages nearest the tree trunk 

have similar throughfall, (2) the gage at the edge 

of crown cover received different throughfall for 

the two largest storms tested but not for the 

smallest storm, and (3) the gage farthest from 

the tree bole has significantly more throughfall 

for the two smallest storms tested but not for the 

largest storm. 

5. The combined effect of direction and distance from 

the tree bole causes a significant difference in 

throughfall catch for all storm groups tested. 

The gages nearest the tree bole on the east side 

and farthest from the tree bole on the north side 

receive throughfall amounts that are significantly 

different from those received at gages located at 

other combinations of distance and direction. 

6. Broad-leaved oaks were sampled for throughfall on 

Cibecue Ridge and were found to have less 

throughfall than juniper and pinyon during large 

storms. 

7. Interception increases in the initial stages of a storm. 

It was assumed that as precipitation increases, 

interception approaches a constant value that will 

vary depending on climatic forces such as wind. 

8. The results of this investigation substantiate the 

findings of Stout and McMahon (1961) and Beall 

(1934): that throughfall under a tree varies with 

direction and distance from the tree bole. 

SELECTED BIBLIOGRAPHY 

Beall, H. W., 1934, The penetration of rainfall through hardwood and soft wood canopy: Ecology, v. 15, p. 412-415. 

Brownlee, K. A., 1960, Statistical theory and methodology in 

science and engineering: New York, John Wiley & Sons, 

Inc., 570 p. 

Cochran, W. G., 1953, Sampling techniques: New York, John 

Wiley & Sons., Inc., p. 87-109 .. 

Coffay, E. W., 1962, Throughfall in a forest: Bull. International 

Association of Scientific Hydrology, v. 7, no. 2, p. 1Q-16. 

Cramer, Harald, 1946, Mathematical methods of statistics: 

Princeton, N.J., Princeton Univ. Press, 575 p. 

Dixon, W. J., and Massey, F. J., Jr., 1957, Introduction to 

statistical analysis: New York, McGraw-Hill Book Co., 

488 p. 

Hoover, M. D., 1953, Interception of rainfall in a young loblolly 

pine plantation: Southeast Forest Exp. Sta. Paper 21. 

Horton, R. E., 1919, Rainfall interception: Monthly Weather 

Rev., v. 47, p. 603-623. 

Huff, F. A., 1955, Comparison between standard and small 

orifice rain gages: Trans. Am. Geophys. Union, v. 36, 

p. 689-694. 

Kittredge, J., 1948, Forest influences: New York, McGraw-Hill 

Book Co., 394 p. 

Mitchell, J. A., 1930, Interception of rainfall by the forest: Jr. 

Forestry, v. 28, p. 101-102. 

Ovington, J.D., 1954, A comparison of rainfall in different woodlands: Forestry, v. 24, p. 41-53. 

Penman, H. L., 1963, Vegetation and hydrology: Technical 

Communication No. 53, Commonwealth Bureau of Soils, 

Harpenden, 111 p. 

Rowe, P. B., and Hendrix, T. M., 1951, Interception of rain and 

snow by second-growth ponderosa pine: Trans. Am. 

Geophys. Union, v. 32, p. 903-908. 

Scheffe, Henry, 1961, The analysis of variance: New York, 

John Wiley & Sons, Inc., 455 p. 

Snedecor, G. W., 1946, Statistical methods: Iowa. City, Iowa 

State College Press, 476 p. 

'Stout, B. B., and McMahon, R. J., 1961, Throughfall variation 

under tree crowns: Jour. Geophysical Research, v. 66, 

no. 6, p. 1839-1843. 

Trimble, G. R., Jr., and Weitzman, S., 1954, Effect of a hardwood 

forest canopy on rainfall intensities: Trans. Am. Geophys. 

Union, v. 35, p. 226-234. 

Voigt, G. K., 1960, Distribution of rainfall under forest stands: 

Forest Science, v. 6, p. 2-10. 

Wood, 0. M., 1937, The interceptjon of precipitation in an 

oak-pine forest: Ecology, v. 18, p. 251-254. 

0