PUBLICATIONS

A111D4 5mm3

NBSIR 79-1604

A COMPARISON OF CENTRIFUGE AND FREEZING CALORIMETER

METHODS FOR MEASURING FREE WATER IN SNOW

R. N. Jones

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

NBSIR 79-1604

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A COMPARISON OF CENTRIFUGE AND FREEZING CALORIMETER

METHODS FOR MEASURING FREE WATER IN SNOW

R. N. Jones

Electromagnetic Fields Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

May 1979

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

^1\^NATI0NAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS iv

ABSTRACT I

INTRODUCTION 2

BACKGROUND 2

CENTRIFUGE METHOD 5

FREEZING CALORIMETER METHOD—. 8

THE TWO METHODS COMPARED 12

CENTRIFUGE EXPERIMENTS WITH SAND 28

CONCLUSIONS 30

APPENDIX I 31

APPENDIX II 35

ACKNOWLEDGMENT 38

REFERENCES 39

iii
1

2

3

4

5

6

7

8

9 10

11

12

13

14

age

3

4

9

13

18

19

20

21

22

23

24

25

26

27

LIST OF ILLUSTRATIONS

The hand-driven centrifuge system

Snow sampling tubes and retainer screen The freezing calorimeter system

A comparison of percent free water in snow

as determined simultaneously by freezing calorimeter

and 35 ml centrifuge

Percent free water in snow. Hideaway Park, CO 2/23/78

Percent free water in snow, Hideaway Park, CO 2/28/78

Percent free water in snow. Hideaway Park, CO 3/01/78 —

Percent free water in snow. Hideaway Park, CO 3/02/78 —

Percent free water in snow. Hideaway Park, CO 3/07/ 78 —

Percent free water in snow. Hideaway Park, CO 3/09/78 —

Percent free water in snow. Hideaway Park, CO 3/21/78 —

Percent free water in snow. Hideaway Park, CO 3/22/78 —

Percent free water in snow. Hideaway Park, CO 3/23/78

Percent free water in snow. Steamboat Springs, CO 3/28/78

IV
A Comparison of Centrifuge and Freezing Calorimeter

Methods for Measuring Free Water in Snow

R. N. Jones

National Bureau of Standards

Boulder, Colorado 80303

In using microwave measurements in hydrological studies of

snowpack or avalanche prediction, the presence of free water in

the snow has a strong influence on observed data because it

affects the dielectric characteristics. Although several methods

are in use for determining the percent of free water in snow,

there is very little information in the literature as to how well

the various methods agree. This paper reports on a comparison of

two popular methods; namely, the centrifuge and the freezing

calorimeter. Results from measurements over a two-month period

in the Colorado mountains in the winter of 1978 indicate serious

disagreement between these two methods. Some reasons for the

disagreement are presented and verified. This raises some important questions pertaining not only to what the two methods

actually measure, but also which methods may be appropriate for

particular applications.

Key Words: Centrifuge; comparison of measurement methods;

free water; freezing calorimeter; hydrology forecasting;

microwave remote sensing; snow.
INTRODUCTION

During February and March 1978, measurements of the presence of

free water in snow were made at three sites in the Colorado mountains.

Most of the measurements were of snow samples collected at the surface,

and two different measurement methods were used: the freezing calorimeter and the 35 ml hand-driven centrifuge. Data from these two methods

resulted in wide disagreement in many instances. Presented here are

descriptions of the two systems, techniques employed, resulting data,

and some specially devised experiments to verify the differences which

appear to exist. In general, the percent of free water levels determined by the freezing calorimeter method are significantly higher than

those determined with the hand-driven centrifuge method. Reasons for

the disagreement between the two methods are given together with supporting

experimental evidence.

BACKGROUND

Electromagnetic techniques for gathering hydrological data are

being investigated extensively by the National Aeronautics and Space

Administration (NASA) for possible use in large area and world-wide

hydrological studies using both active and passive microwave equipment.*

The presence of free water in snow is one parameter believed to have a

*Passive systems utilize natural microwave radiation from the earth,

whereas active systems transmit a signal and measure the change in

intensity and/or phase of the return (reflected) signal.

2
Figure 1. The hand-driven centrifuge system.

f

3
4
significant effect upon data obtained by these microwave systems [1,2],

The work described here was done in conjunction with a series of radiometer experiments carried out by the National Bureau of Standards (NBS)

Electromagnetic Fields Division under contract from NASA. Although the

work described utilized only two methods for determining snow quality

(or free water content), several other methods are available. These are

described briefly in a paper by Langham [3]. Bergman [4] worked extensively

with the freezing calorimeter method to determine its precision and limitations

relative to snow types and temperature; however, a literature search failed to

locate any previous efforts to compare the results obtained by different methods.

CENTRIFUGE METHOD

The centrifuge method has been described by LaChapelle [5] and

later with improvements by Langham [6], who refined the method to reduce

errors from air friction melting. Extensive use of the method was also

reported by Carroll [7]. Figures 1 and 2 show the equipment used in

obtaining the data in this report. The hand-driven centrifuge shown in

figure 1 holds two polyeurethane test tubes having a snow-sample capacity

of approximately 35 ml in the upper section. Figure 2 shows the test

tubes used, together with the wire mesh gratings used to retain snow in

the upper section of the tube during centrifuging. The free water is

collected in the lower section and its volume read on the graduated

scale. Snow retainer screens had openings of approximately 0.16 x 0.16 mm

(100 mesh), this being large enough to allow the water to pass through

but small enough to prevent the smallest snow particles from reaching

5
the lower section. Other mesh sizes up to approximately 0.7 x 0.7 mm

were tried without noticeable difference or apparent particle migration

during the centrifuge procedure. Such a small mesh size did have one

slight disadvantage which was an inconvenience: after the snow above

the screen had melted, the tubes required additional centrifuging to

overcome surface tension and to force the water into the lower portion

where the final total water volume could be determined. To obtain the

centrifuged liquid water volumes, two precautions were observed in an

effort to minimize error. The first was to use the repeated centrifuge

procedure described by Langham [6] and Carroll [7] to eliminate error

due to air friction melt. The second precaution was to bring the test

tubes to ambient snow temperature by embedding them in the wall of the

snow pit well before use.

The most serious shortcoming associated with this method was the

inability to determine small centrifuged water volumes accurately. The

minimum graduation on the test tube was 0.5 ml so that water volumes

could be approximated to only ±0.1 ml. Assuming a typical final melted

volume of 15 ml, this places a ± 0.7 percent uncertainty upon the measurement.

For final melted volumes smaller than 15 ml, the percentage uncertainty

due to this error source, of course, becomes greater.

The centrifuge has a gear ratio of approximately fifteen to one,

and five turns of the handle over a period of 3 to 5 seconds were used.

This procedure subjects the snow samples in the test tubes to a force of

more than two hundred and fifty times the force of gravity for a period

6
of 2 to 4 seconds. This procedure was adopted after some experimentation which showed that sustaining the centrifuging for longer periods

did not cause additional water to collect in the tubes. Also, longer

periods of centrifuging can cause melting due to air friction with

resulting errors in determining the true amount of free water.

During the period of these experiments, concern arose that the

centrifuge process did not remove all of the free water from the sample,

especially since the centrifuge values were generally lower than those of

the calorimeter. As one means of testing this possibility, an experiment was conducted wherein centrifuged snow samples were quickly recentrifuged, but in an inverted position. Several repetitions of the

procedure did not produce additional free water.

At this point, some additional discussion is appropriate pertaining

to the snow sample collection techniques used with the centrifuge method.

Early in the experiment period, the practice for surface snow sampling

was to move the two tubes (fig. 2) through the snow surface in the same

direction and side by side. While this did allow the two samples to be

as nearly identical as possible, it was difficult to collect a large

enough sample, especially when attempting to detect small amounts of

free water. Later, we began to use a slightly different method which

facilitated packing more snow into the tubes. This technique involved

taking one tube in each hand and moving them in opposite directions and

toward one another. When the tubes came close together, this opposing

7
motion forced additional snow into the tubes producing a larger sample.

As a result, however, it appears from the data that there was larger

disagreement between the results of the two samples. Notice that the

centrifuge pairs appear to be in closer agreement for the early (February)

weeks of observation than for the later (March) weeks when the second

method came into use (see figs. 5-14). It is believed that the second

method verifies the fact that there is considerable local variation in

the amount of free water and that such variation occurs within distances

of the order of 50 cm.

FREEZING CALORIMETER METHOD

Pictured in figure 3 is the apparatus for the freezing calorimeter

method including three beam balance, stainless steel calorimeter (vacuum

bottle), digital thermometer and temperature probe, stop watch, and

calorimeter fluid. For these experiments, the fluid was a type of

silicon, SF-96-5, produced by the General Electric Company,* which has a

specific heat of approximately 0.44 cal/gram in the region of -10°C.

This method was first described by Radok [8] and has also been mentioned

in some detail by Leaf [9]. The calorimeter heat balance equation describing

the heat exchange between the silicon fluid and the snow sample is given by

W.C.(t„-tJ - SC (t„-t ) = LF (1)

1 x 2 1 s 2 s

*Mention of a specific commercial material is for the purpose of specifying the

ingredients used in an experimental procedure and such identification does not

imply endorsement or recommendation by the National Bureau of Standards, nor does it imply that the material is necessarily the best available for the purpos
9

Figure

3.

The

freezing

calorimeter

system.
where:

= weight of silicon fluid in the calorimeter in grams

= specific heat of silicon, at mean of temperature before and after

adding snow sample, in cal/°C

t 2 = temperature of silicon fluid in °C before adding snow sample

t^ = temperature of silicon fluid in °C after adding snow sample

L = latent heat of fusion of water, 79.71 cal/gram

F = Weight of free water in the snow sample

S = weight of snow sample added to the calorimeter in grams

= specific heat of ice at a temperature midway between t

2 and t^

tg = snow sample temperature (in °C) before insertion into calorimeter

Here it can be seen that if there were no free water present in the snow (F=0)

all the heat exchange would occur between the silicon and the dry snow crystals.

When free water is present the equality is destroyed and a portion of the heat

exchange is consumed by the conversion of the free water to ice.

To arrive at a percentage figure for the amount of free water present by

weight we define a quality factor:

Upon substituting for F in the above equation, we arrive at the expression:

( 2 )

or F = S(l-Q^)

10
1 ( 3 ) W C (t -t ) SC (t -t ) 0 = 1 - —= — + —2

^

'f LS L

and the percentage of free water by weight is than given by;

% H^O = (1-Qj) 100 (4)

A sample data sheet, of the type used, and a discussion of the accuracy

of the method are given in Appendices I and II. Perhaps the main shortcoming of the freezing calorimeter method is the rather lengthy period

(20 minutes) required to measure each sample. This time requirement

makes it difficult for a single experimenter to monitor closely the rapidly

changing snow surface conditions or to follow the progress of melt water

through a snow pack on a warm day.

Because snow conditions apparently change quite rapidly with both time and

location, it is not unusual to observe wide variations in results, especially

when taken twenty minutes apart. In an attempt to verify the repeatability

of the calorimeter results, two operators simultaneously analyzed snow

samples taken as closely as possible from the same location on the surface

of the snow. The following results were obtained:

Time of Day Calorimeter // "R" Calorimeter //"S"

1300 2.2 3.5

1415 4.3 5.6

1540 17.9 14.8

11
Thus, the repeatability bewteen the two systems "R* and "S" appears

reasonably consistent with the accuracy estimates derived in Appendix

II. It is also interesting to note that the centrifuge results, taken

at the same time as the simultaneous calorimeter experiments, were

considerably lower. (See fig. 6.)

THE TWO METHODS COMPARED

Figure 4 is a summary of the results of centrifuge and calorimeter

data accumulated over a period of two months. Each point on the graph

is a simultaneous or nearly simultaneous (within 10 minutes) measurement

of percent of free water content with the ordinate being the centrifuge

results and the abscissa being the calorimeter result. Where a vertical

line appears, it means that the two values of that particular centrifuge

test did not agree, and they are connected to show that they were

derived from the same centrifuge test. In some instances, only one

experimenter was available to operate both methods so that centrifuge

observations had to be either immediately before or immediately after

the calorimeter test. In these cases, there was a lapse of 5 to 10

minutes between collection of the samples. They were, however, collected

at the same location. Data from these corresponding but nonsimultaneous

experiments appear as a single dot where the two centrifuge samples were

in agreement and as two dots connected by a vertical line when they were

different. When two experimenters were available, simultaneous sampling

from the same location was done, permitting the best comparison of the

two methods. These data are identified by triangles surrounding the

dots. Triangles surrounding each dot at the end of a vertical line

12
(N)-

NUMBER

OF

OCCURANCES

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13
indicate the same calorimeter experiment and the two results from one

calorimeter test where there was disagreement between the pair of

centrifuge readings.

In some instances, the calorimeter results when computed produced a

negative value for percent of free water, and these are shown in figure 4.

For best accuracy, the weight of the snow sample should be about 100 grams.

This amount of snow when it is dry, light, and cold fills the calorimeter

very full so that it is difficult to get good mixing of the snow with

the freezing fluid. This produces erratic, nonlinear behavior in the

temperature rise within the calorimeter resulting in reduced accuracy in

determining the temperature increment - t^, in equation (1), with the

occasional occurrence of a negative value for free water. In these

situations, it is probably safe to assume that the percent of free water

present is zero and is considered so in the subsequent data analysis and

observations.

If the two methods were in agreement for all the testing done, then

each coordinate in figure 4 would have fallen on the diagonal straight

line with slope + 1 shown in dotted form. It is obvious that the two

methods disagree by large amounts in many instances and that the calorimeter usually gives larger values. There are approximately 165 observations

including the two results from each centrifuge test and the calorimeter

tests. If the negative calorimeter results are interpreted as zero,

then only 54 of the 165 comparisons fall with the ± 33 percent limits of

tolerance shown on either side of the dotted line Indicating exact

agreement

.

14
Because the freezing calorimeter method can be described mathematically and its uncertainties analyzed with little conjecture, it

appears to be in a better state of experimental control than the centrifuge method and is therefore deemed to be more accurate.

For field use, however, the centrifuge method has several advantages over the freezing calorimeter method in that much less paraphernalia

is required and less time is required to carry out the test procedure.

Thus, it would be beneficial if the differences in the results

obtained by the two methods could be accounted for in a predictable way

so as to permit the use of centrifuge methods in the field with the

freezing calorimeter method serving as a backup reference standard.

As seen from comparing the data from the two methods, the results

from the freezing calorimeter method tend to show a higher free water

content than those from the centrifuge method in most instances. One

possible reason for this is that the snow does not give up all of the

liquid water it contains when subjected to the forces of the centrifuge

action. A simple experiment with the centrifuge using sand Instead of

snow verifies this hypothesis and also indicates that the amount of free

water retained is a function of the total surface area of the particles

in the sample.

15
Previous accuracy estimates of 0.25 percent for the centrifuge

method [7] and 1 percent for the calorimeter method [9] have been given

in the literature. The error analysis in Appendix II does not disagree

radically with the 1 percent for the calorimeter method; and, for the

centrifuge method, a 1 percent uncertainty would appear plausible,

especially in light of possible local variations in free water.

Assuming the foregoing accuracy estimates to be valid, then it is

logical to conclude that the two methods do not measure the same phenomena,

or that water may be present in another form in varying amounts that are

detectable with the freezing calorimeter but not with the centrifuge.

To investigate this possibility, an experiment was conducted whereby the

snow sample was centrifuged before being put into the calorimeter. This

was done in such a way as to assure that no melt occurred between the

time the snow sample was centrifuged and the short period of one or two

minutes later when it was put into the calorimeter. The following

results were obtained:

Table 1

Date Time

Free Water Measured

by Centrifuge

Percent

Additional Water

Measured by

Calorimeter

Percent

3/8/78 14:25 1.6 4.5

3/22/78 14:31 12.4, 12.8 7.5

3/22/78 15:26 6.7, 7.1 8.9

16
It is unfortunate that a second calorimeter system was not available to determine if the total free water might have equaled the sum of

these centrifuge and calorimeter results as shown plotted in figure 12.

Figures 5 through 14 show the data summaries for 10 days of observation where measurements of free water were made frequently by both the

centrifuge and the calorimeter methods. Also plotted are the air and

snow surface temperatures a’t the sampling location.

At the Hideaway Park site, the snowpack achieved isothermal conditions by March 20 following several days when air temperatures reached

+ 5°C or higher for most of the daylight hours and probably remained

above freezing at night. It is interesting to note that in figure 11

for March 21 and all subsequent days of observation, the free water at

the surface measured by the centrifuge method seems to follow the air

temperature fluctuations. Also, after the isothermal condition was

achieved, there appeared to be somewhat better correlation between the

results of the two methods with incidents of very large disagreement

being less frequent. From examining figures 5 through 14, it also seems

apparent that the incidents of greatest departure between the results of

the two methods seemed to occur later during the day after approximately

1400. In several cases, this appeared to occur at the end of the day

when there had been significant amounts of free water at the surface.

In these cases, the centrifuge indicated far less free water present

than did the calorimeter. Situations of this type account for some of

the very large disagreements between the two methods shown plotted in

figure 4.

17
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roc\Ji— o 1— c\Joo<;:tLn txir^co

+ + + llllllll o

Q

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CM

18

Figure

5.

Percent

free

water

in

snow.

Hideaway

Park,

CO

2/23/78.
Do 3ynivy3dW3i

>-

-cC Q

OC\J

19

Figure

6.

Percent

free

water

in

snow.

Hideaway

Park,

CO

2/28/78.
3o 3ynivy3dW3i

cQ

OC\J

20

Figure

7.

Percent

free

water

in

snow,

Hideaway

Park,

CO

3/01/78.
3o 3yni\/y3dW3i >^00001— o I— c\iro<^

+ + + + I I I I

ooLU

DC

cc

q;

oC\J

21

Figure

8.

Percent

free

water

in

snow.

Hideaway

Park,

CO

3/

02/

IQ.
Do 3ynivy3dW3i

^cooji— Oi— CMro

>-

<cQ

OCM

22

Figure

9.

Percent

free

water

in

snow,

Hideaway

Park,

CO

3/07/78.
3o 3ynivy3dW3i

<Q

OC\J 7n

23

Figure

10.

Percent

free

water

in

snow,

Hideaway

Park,

CO

3/09/78.
Do 3ynivy3dW3i

oCM

1

24

Figure

11.

Percent

free

water

in

snow.

Hideaway

Park,

CO

3/21/78.
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00 r^<x)un';d-oocvjr— Oi— coco

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Figure

12.

Percent

free

water

in

snow.

Hideaway

Park,

CO

3/22/78.
Do BynivyDdi^Oi

26

Figure

13.

Percent

free

water

in

snow,

Hideway

Park,

CO

3/23/78.
3o 3ynivy3dW3i

27

Figure

14.

Percent

free

water

in

snow,

Steamboat

Springs,

CO

3/28/78.
CENTRIFUGE EXPERIMENTS WITH SAND

Three sand samples were prepared, each having a total volume of

approximately 20 ml. The samples were screened to have only particles

in a specific size range. The sizes are shown in Table 2. A centrifuge

tube like those shown in figure 2 was used except that the bottom tip of

the tube was cut off to allow the centrifuged free water to escape. The

sand samples were dried and weighed. After weighing, they were thoroughly

moistened by pouring water through the open ended tube. Then, after

centrifuging, the sample was reweighed to give the amount of water still

remaining in the sand. These results are also shown in Table 2 as

percent of water retained by weight. Taking the density of an average

snow sample to be 0.25 g/cc and multiplying the percent of water weight

retained by the sand by the ratio of the density of sand to that of

snow, we arrive at percentage of water by weight retained by snow.

These are 26 percent, 10.6 percent, and 5.6 percent for samples 1, 2,

and 3, respectively. These values appear to be typical of the differences observed between calorimeter and centrifuge results. It shows

that for large particle sizes, the correction for retained water by

centrifuge is much smaller than in instances where the particle size is

small. This suggests that centrifuge results can be corrected to agree

with freezing calorimeter data simply by adding an empirical correction

based on snow density and particle size and that sand can be used as the

medium for determining these empirical corrections.

28
Table 2 Water Retained by Sand after Centrifuging

Percent Equivalent

Retained H

2 O

Sample Particle Size (mm) Retained H

2 O Sand Dry Density for Snow

No. Min. Max (% by weight) g/cc of Density 1

1 0 1 4.8 1.38 22

2 1 5 1.9 1.40 8.9

3 5 10 1.0 1.46 4.9

This approach appears to have some potential except in instances

where the centrifuge method Indicates no free water. Assuming similar

behavior between snow and sand, then there is the possibility that

appreciable, undetected free water may be present especially where grain

structure is very fine or the snow crystals have large surface areas.

In these instances, the centrifuge results cannot be corrected to agree

with the calorimeter results.

The foregoing discussion is not to be interpreted as a condemnation

of the centrifuge method because it is certainly possible that the free

water presence indicated thereby is the most relevant to a particular

situation, say avalanche conditions for example. Also, calorimeter

measurements may provide the best information for yet a different aspect

29
of snow studies. It does appear obvious, however, that whatever the

ultimate purpose for free water determinations, little agreement between

the two methods can be expected.

CONCLUSIONS

1. From the measurement data reported. It is concluded that the centrifuge

and freezing calorimeter method results do not measure the same phenomena

and that water may be present in snowpack in a form which is detectable by

the freezing calorimeter method but not by the centrifuge method.

2. Because of the many instances where the two centrifuge results of a

single operation varied by significant amounts, it is concluded

that the amount of free water present may vary by several percent

over distances of 50 cm or less.

3. Because of the disagreement in free water content as determined by

these two methods and other methods as well, it is apparent that

work is needed to determine which method gives results which

correlate best with microwave phenomena. For data taken by various

experimenters at different times and locations to have a common

basis for comparison, it is evident that a uniform method should be

adopted

.

30
APPENDIX I

The following two pages show the type of data sheet used in carrying out the freezing calorimeter experiments and a typical time vs.

temperature plot of the calorimeter temperature before and after adding the

snow sample. From the time vs. temperature plot, it can be seen how the

before and after sample addition temperature plots are extrapolated to provide

the temperature increment due to the snow sample. This information, together

with the other information shown on the data sheet, is used to compute the

percent of free water in the snow sample.

31
MEASUREMENT OF SNOW QUALITY

(Freezing Calorimetric Technique)

Time Temp°C

0 -46.0

-i--3S,4

J^-37.4

25 -3J.O

3 -3^.6

3-5 -3^.3

A.5 -35.

5.5

6-5 -^^

J—-MZ

-33.9

8 -^3.6

8.5

9.5

10

11

11.5 -/g.^

12 -/2.2

12.5 -/g./

13

13-5 -//.^

-//•/?

15.5 -//

5

18-5 ~//3

17 -//.Z

17-5 -//./

18 -//.<9

Station Observer /p.McJinneS

Date ^/fM ^Hour /<^/^2

Location and description of sampling point S^/iy^ J^njrn

Data

Sample thermos No. Air Temperature_

Height of sample from ground surface

(1) Tare weight of calorimeter

cm.

( 2 ) (3)

(4)

(5)

( 6 ) (7)

gr.

Weight of calorimeter and silicone fluid / gr

Weight of calorimeter + silicone fluid + snow gr

Calorimeter constant (E) _gr,

ti

= -3Z.85 tj = -/2.JS at = Za./"'C

(2) - (1) =

(3) - (2) -

t =

s

-

Heat Balance

WiCi (t„ -t,)-t„C S=LF I i z s where

Wi = (2) - (1) + E, gr. C = specific heat of ice

Ci = specific heat of silicone

C S

L

to = snow temp °C F

tj^ = initial temp. ‘

t^ = final temp. °C

(3) - (2), gr.

latent heat of melting

weight of free water, gr.

I3 = "2 - 's

Snow Quality

Q^

= 1 - [Wi Ci (t2 - tp / LS] - [Cg t^/L]

= /-ysS./S ^4SSox2c>.//7f.7/></9i.2^.4n^-/Z^/n7f}

/-a.25^-7- 0.0^

= 0.825 <3r /y.S Z

32
Do 3ynivy3dW3i

33

TIME

(MINUTES)

APPENDIX II

Beginning with the equation for free water content

Qf

= - [W^C^At/LS] - [Cgt^/L] ( 1 )

where At = t

2 - t^, the extrapolated calorimeter temperatures before and

after adding the snow sample,, and ^3 ~ ^2 ”

^s’ error analysis of the

procedure can be carried out mathematically. This is done by taking the

partial derivative of with respect to each variable in equation (1). Since

there are seven variables, namely L, S, W^, C^, At, Cg, and t^, seven expressions

result which can be evaluated numerically to give an estimated error

contribution from each one. Then, because these give both positive and

negative errors, which may or may not be compensating in a particular

situation, they are combined as the square root of the sum of the

squares to give an uncertainty estimate. The seven error expressions

are the following:

LS - [LS - W.C.At - SC^t„]S

^ X 1 S 3

2 2 L S dL ( 2 )

3Qf LS[L - C t^] - [LS - W.C.At - SC^t„]L ^ s 3 X 1 S 3 dS (3)

35
( 4 )

9Q. LS[-C.At]

f 1 L-S

0 o dw.

2„2 1

9Q LS[-W.At]

(5)

9Q^ LS[-W.C.]

f 11

d(At) ( 6 )

9Q LS[-St ] (7)

9Q^ LS[-CgS]

( 8 )

The total differential, dQ^, which is the uncertainty is:

9Q 9Q 9Q 9Q 9Q 9Q 9Q

9t7

Taking the example of Appendix I and using the following set of values

for the parameters and the corresponding uncertainty estimates:

36
L = 79.7

S = 196.25

W. = 255.15

X

C. = 0.435

1

At = 20.1

Cg = 0.492

tg = 12.75

dL = 0.3

dS = 4

dW. = 12 **

1

dC. = 0.01

X d(At) = 0.01

dCg = 0.01

dtg = 0.2

an uncertainty of ± 1.2 percent is obtained for the free water content.

In two other examples that were similarly analyzed, values of 25.2 percent

(± 2.4 percent) and 4.1 percent (± 1.0 percent) were obtained. Thus,

the estimated uncertainty of 1 to 2 percent for the method appears

reasonable

.

The quantity dW, = 12 includes an allowance of 8 grams for the un- certainty for the thermal mass of the calorimeter. This was the standard

deviation among twelve experiments which were performed in calibrating

the calorimeter.

37
ACKNOWLEDGMENT

The work described was done under the sponsorship of the National

Aeronautics and Space Administration (NASA) Goddard Space Flight Center

of Greenbelt, Maryland, U.S.A. Mr. James C. Shiue was the project

coordinator. Much valuable assistance in the use of the freezing

calorimeter method was received from Messers Steve Howell and Dave Frick

of Resource Consultants, Inc., of Fort Collins, Colorado. The very able

assistance and support of these people is very much appreciated. Also,

Doyle Ellerbruch and Ron Whitman of NBS supplied much needed help with

the measurement procedures. To all of you, my sincere thanks.

38
REFERENCES

[1] Chang, T. C., and Gloersen, Microwave Emission from Dry and Wet

Snow, Operational Applications of Satellite Snowcover Observations,

NASA SP-391, Washington, D.C., pp. 399-407, 1975.

[2] Hall, D. K., A. Chang, J. L. Foster, A. Rango, T. Schmugge, Passive

Microwave Studies of Snowpack Properties, NASA Technical Memorandum 78089,

Goddard Space Flight Center, Greenbelt, MD, April 1978 (Presented

at the Western Snow Conference, 1974), pp. 60-71.

[3] Langham, E. J., Problems of Measuring Meltwater in the Snowpack, Proc.

Eastern Snow Conference, 1974, pp. 60-71.

[4] Bergman, J . A. , A Method for the Determination of Liquid Phase Water in

a Snowpack Using Toluene Freezing Calorimetry, Masters Thesis, Dept, of

Forestry, Univ. of Nevada, Reno, May 1978.

[5] LaChapelle, E. R., The Centrifugal Separation of Free Water from

Melting Snow, J. of Glaciology 2, pp. 769-771, 1956.

[6] Langham, E. J., Measurement of Liquid Water Content of Snow by

Repeated Centrifugal Extraction, Tech. Report Glaciology Division,

Inland Waters Directorate, Water Resources Branch, Dept, of Fisheries and

Environment, Ottawa, Canada, 1978.

[7] Carroll, T., Estimation and Prediction of the Liquid Water Distribution

in a High Altitude Spring Snowpack, Avalanche Workshop sponsored

by NRC, British Columbia Highway Dept., Parks Canada, and the

University of Calgary in Banff, Alberta, Nov. 1-4, 1976.

[8] Radok, U., S. K. Stephens, and U. R. Sutherland, On the Calorimetric

Determination of Snow Quality, U.G.G.I. Assembly, Commission of

Snow and Ice, Helsinki, 1960, I.A.S.H. No. 54, pp. 132-135.

[9] Leaf, Charles F., Free Water Content of Snowpack in Subalplne

Areas, Proceedings of the 34th Annual Western Snow Conference,

Seattle, Washington, April 19-21, 1966.

39
NBS-114A (REV. 9-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

79-1604

a.Gov't

4. TITLE AND SUBTITLE

A Comparison of Centrifuge and Freezing Calorimeter

Methods for Measuring Free Water in Snow

Z, Accession No<

5. Publication Date May 1979

7. AUTHOR(S)

R. N. Jones

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS rsrreer. City, state, ZIP)

National Aeronautics and Space Administration (NASA)

Goddard Space Flight Center

Greenbelt, Maryland

13. Type of Report & Period Covered

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200~word or less factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) In using microwave measurements in hydrological studies of

snowpack or avalanche prediction, the presence of free water in

the snow has a strong influence on observed data because it

affects the dielectric characteristics. Although several methods

are in use for determining the percent of free water in snow,

there is very little information in the literature as to how well

the various methods agree. This paper reports on a comparison of

two popular methods;, namely, the centrifuge and the freezing

calorimeter. Results from measurements over a two-month period

in the Colorado mountains in the winter of 1978 indicate serious

disagreement between these two methods. Some reasons for the

disagreement are presented and verified. This raises some important questions pertaining not only to what the two methods

actually measure, but also which methods may be appropriate for

particular applications.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Centrifuge; comparison of measurement methods;

free water; freezing calorimeter; hydrology forecasting;

microwave remote sensing; snow.

18. AVAILABILITY Unlimited

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I I Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

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