A procedure to identify different groups of hydraulic-conductivity and moisture-retention curves for soil horizons

Journal of Hydrology, 86 (1986) 133-145

133

Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands

[5]

A PROCEDURE TO IDENTIFY D I F F E R E N T GROUPS OF HYDRAULIC-CONDUCTIVITY A N D MOISTURE-RETENTION CURVES FOR SOIL HORIZONS

J.H.M. WOSTEN, M.H. BANNINK, J.J. DE GRUIJTER* and J. BOUMA

Netherlands Soil Survey Institute, Wageningen (The Netherlands) *TNO Institute of Applied Computer Science, Wageningen (The Netherlands) (Received J a n u a r y 29, 1986; revised and accepted March 24, 1986)

ABSTRACT WSsten, J.H.M., Bannink, M.H., De Gruijter, J.J. and Bouma, J., 1986. A procedure to identify different groups of hydraulic-conductivity and moisture-retention curves for soil horizons. J. Hydrol., 86: 133-145. Saturated and unsaturated hydraulic-conductivity and moisture-retention data were measured in 25 C horizons with a sand texture and in 23 C horizons with a clay loam and silty clay loam texture. Measurements were made on large, undisturbed soil columns. The identification of the two types of C horizons was based on calculated functional properties rather than on physical characteristics themselves. Three functional properties were distinguished: (1) travel times from soil surface to water table, (2) water-table depth allowing a defined upward-flux density, and (3) downward-flux densities at a defined air content. The two types of horizons considered here were identified as two distinct groups by analysing the standard errors of prediction of the three functional properties. Graphs are presented t h a t allow an estimate of the desired accuracy (expressed in terms of a prediction interval) as a function of sample size and measurement costs. The procedure which is illustrated here for two textural classes will in future be applied to all textures.

INTRODUCTION

Saturated and unsaturated hydraulic-conductivity and moisture-retention data are important soil-physical characteristics for models which simulate the water movement in the unsaturated zone. A major problem in applying simulation models is lack of data. Therefore, simple and reliable methods are needed allowing multiple measurements at many locations in a relatively short period of time (e.g. Bouma, 1983). In addition, soil maps are used to define pedological soil horizons according to soil-physical criteria forming groups of different pedological horizons with similar soil-physical properties. Identification of these groups allows reliable extrapolation of data and, therefore, fewer measurements (WSsten et al., 1985). Groups of horizons can be identified on the basis of a statistical analysis of physical data of the individual horizons (e.g. Baker and Bouma, 1976). How0022-1694/86/$03.50

© 1986 Elsevier Science Publishers B.V.

134 ever, it is more attractive to identify these groups on the basis of functional properties related directly to practical applications. Then, the identifications will be governed by accuracy of prediction and not by statistical significance of differences between groups. This approach requires calculations using both hydraulic-conductivity and moisture-retention data. In this study, three functional properties are introduced: (1) calculated travel times of water from the soil surface to a defined water table; (2) calculated water tables which allow a defined upward-flux density to a defined level; (3) calculated downward-flux densities that correspond with a defined air content in the soil. In order to calculate these functional properties, certain assumptions have to be made and resulting values are, therefore, not necessarily associated with real field conditions. The relation between the sample size (n) and the standard error of prediction (SEP) of the functional properties can be used to minimize the number of measurements needed to obtain a defined accuracy of prediction. Considering the above, the purpose of this study is to: (1) identify two groups of soil horizons, as derived from Dutch soil survey criteria, using the three functional properties defined above; (2) define the minimal number of measured individual soil horizons that are needed to obtain a desired accuracy of prediction.

MATERIALS AND METHODS Soi/s In this study, two groups of C horizons were used: one with a sand texture and one with a clay loam and silty clay loam texture, as distinguished in the Dutch soil survey. Twenty-five C horizons with a fine sand texture (Soil Survey Staff, 1975) originated from pleistocene cover-sand sediments with an organicmatter content less than 1~/o and a silt content ranging from 0 to 8%. The clay content varied between 0 and 3%. Average and standard deviation of the bulk density were 1620 kg m- 3 and 30 kg m- 3. The horizons were structureless (single grain). The 25 soil profiles containing these horizons were classified according to Soil Survey Staff (1975), yielding 18 sandy, siliceous, mesic, Typic Haplaquods; 5 sandy, siliceous, mesic, Plaggepts and 2 sandy, siliceous, mesic, Typic Humaquepts. This classification indicates that similar subsoil horizons may occur in different soil types (see also WSsten et al., 1985). Twenty-three clay loam and silty clay loam C horizons had developed in holocene fluviatile or marine deposits with an organic-matter content less than 1% and a clay content ranging from 25 to 35%. Average and standard deviation of the bulk density were 1420kgm -3 and 4 0 k g m -a. The horizons had moderately developed prisms, parting to a weak, fine, subangular blocky structure.

135 H o r i z o n s were b o t h c a l c a r e o u s and non-calcareous. T h e 23 soil profiles cont a i n i n g these h o r i z o n s were classified a c c o r d i n g to Soil S u r v e y Staff (1975), yielding 19 fine silty, mixed, mesic, T y p i c F l u v a q u e n t s and 4 fine silty, mixed, mesic, F l u v e n t i c E u t r o c h r e p t s .

Physical methods R e l a t i v e l y simple and rapid l a b o r a t o r y t e c h n i q u e s (e.g. Bouma, 1983) were used to m e a s u r e the w a t e r r e t e n t i o n (0 - h) and the h y d r a u l i c c o n d u c t i v i t y (k - h). H y d r a u l i c c o n d u c t i v i t i e s of soil above the w a t e r table were m e a s u r e d by: (1) the c o l u m n m e t h o d for v e r t i c a l ksa t (e.g. Bouma, 1982); (2) the crust-test for k .... t down to a p p r o x i m a t e l y h = - 50cm (latest version of the m e t h o d r e p o r t e d by B o u m a et al., 1983); (3) the s o r p t i v i t y m e t h o d for lower v a l u e s of k .... t in sand (Dirksen, 1979); and (4) the hot-air m e t h o d for lower values of k . . . . t in clay loam and silty clay loam (Arya et al., 1975). M o i s t u r e - r e t e n t i o n curves were o b t a i n e d by slow e v a p o r a t i o n of wet, undist u r b e d samples in the l a b o r a t o r y , as r e p o r t e d by B o u m a et al. (1983). In these samples, pressure heads were periodically m e a s u r e d with transducert e n s i o m e t e r s and at the same time subsamples were t a k e n to d e t e r m i n e moist u r e contents. Thus, points r e l a t i n g h and 0 were obtained. M o i s t u r e c o n t e n t s c o r r e s p o n d i n g w i t h pressure heads lower t h a n - 800cm were o b t a i n e d by c o n v e n t i o n a l m e t h o d s using air pressure (Richards, 1965). In the clay loam and silty clay loam soils a s t a i n i n g t e c h n i q u e was applied to r e c o r d the effects of h o r i z o n t a l c r a c k s on the u p w a r d flux of w a t e r from the w a t e r table to the r o o t z o n e (k ..... ; Bouma, 1984).

Calculation of travel times from soil surface to a defined water table T h e t r a v e l time (T), as m e n t i o n e d in the i n t r o d u c t i o n , is the time t h a t it t a k e s w a t e r to t r a v e l from the soil surface to the w a t e r table. Assuming t h a t all the w a t e r in the u n s a t u r a t e d zone is mobile and t h a t piston-flow occurs, T is c a l c u l a t e d as follows: T -

D.O N

(1)

w h e r e T = t r a v e l time of w a t e r from the soil surface to the w a t e r table (day), D = t h i c k n e s s of the u n s a t u r a t e d zone (m), 0 = a v e r a g e m o i s t u r e c o n t e n t of the u n s a t u r a t e d zone (m 3m-3), and N = a v e r a g e y e a r l y p r e c i p i t a t i o n surplus expressed as a daily r a t e for a w i n t e r period of 6 m o n t h s (for T h e N e t h e r l a n d s N = 1.4 × 10 3m day 1). T h e t h i c k n e s s of the u n s a t u r a t e d zone is assumed to be l m . T h e a v e r a g e m o i s t u r e c o n t e n t is c a l c u l a t e d using as i n p u t data: (1) h y d r a u l i c c o n d u c t i v i t y and m o i s t u r e r e t e n t i o n data;

136 (2) the s t e a d y d o w n w a r d flux of 1.4 × 1 0 - 3 m d a y 1. T h e steady flux is t r a n s f o r m e d into a c o r r e s p o n d i n g pressure head, using the k - h c u r v e for the C h o r i z o n a s s u m i n g u n i t - g r a d i e n t flow in a semi-infinite p o r o u s medium. The c a l c u l a t e d h v a l u e is t r a n s f o r m e d into m o i s t u r e c o n t e n t (0) using the c o r r e s p o n d i n g 0 - h curve, yielding an a v e r a g e m o i s t u r e c o n t e n t for the u n s a t u r a t e d zone. This v a l u e of 0 is used in eqn. (1), assuming D = 1 m. Calculation of water table allowing a defined upward-flux density

C a l c u l a t i o n of the w a t e r table, as m e n t i o n e d in the i n t r o d u c t i o n , is based on the D a r c y e q u a t i o n for steady, upward, v e r t i c a l flow: v =

- k

1 + ~zz

(2)

w h e r e d h / d z = g r a d i e n t of the pressure h e a d ( m m 1), k = h y d r a u l i c conduct i v i t y ( t o d a y - i ) , and v = flux density ( m d a y 1). I n t e g r a t i o n (Gardner, 1958) yields: hn

zn =

-

f 1 +dhv/k

(3)

0

w h e r e z. = d e p t h (m) below a r e f e r e n c e layer, such as the lower b o u n d a r y of the r o o t z o n e at w h i c h b o u n d a r y a pressure h e a d of - hn (m) is experienced. By c h o o s i n g a s t e a d y upward-flux density (v) and by r e a d i n g a p p r o p r i a t e h y d r a u l i c - c o n d u c t i v i t y v a l u e s from the k - h r e l a t i o n at a specific h, a complete g r a p h of z v e r s u s v m a y be plotted. C a l c u l a t i o n s are m a d e by a c o m p u t e r (e.g. De Laat, 1980). F o r this test, v is assumed to be 0 . 0 0 2 m d a y -1 and h = - 500 cm. Calculation of d o w n w a r d - f l u x densities at a defined air content

In o r d e r to allow r o o t a c t i v i t y and p l a n t growth, the a e r a t i o n status of the soil profile should be such t h a t the profile c o n t a i n s at least 5% air by volume. This v a l u e has been proposed as a general c r i t e r i u m (FAO, 1985). T h e critical, steady, d o w n w a r d flux allowing 5°//0 air by v o l u m e in the soil profile is calculated using the m e a s u r e d soil-physical c h a r a c t e r i s t i c s . The critical p r e s s u r e h e a d h at w h i c h the w a t e r c o n t e n t is 5~o lower t h a n the w a t e r c o n t e n t at s a t u r a t i o n (h = 0 cm) is derived from the m o i s t u r e - r e t e n t i o n curve. This p r e s s u r e h e a d h is t r a n s f o r m e d into a flux density using the h y d r a u l i c - c o n d u c t i v i t y curve, a s s u m i n g u n i t - g r a d i e n t flow w h e r e the flux density is equal to the h y d r a u l i c c o n d u c t i v i t y . Thus, one v a l u e for the flux density is obtained, as discussed in the i n t r o d u c t i o n .

137

Statistical analysis The mean hydraulic conductivity and the mean moisture-retention curves for sand and for clay loam and silty clay loam were calculated by using data measured for the individual horizons. The 25 values of k and 0 for sand were averaged at 13 selected values of h. The same procedure was followed for the 23 values for clay loam and silty clay loam. Mean values for travel time, water table and downward-flux density were calculated by averaging the 25 values calculated for the individual sand horizons and the 23 values calculated for the individual clay loam and silty clay loam horizons. The standard errors of prediction (SEP) of travel time, water table and downward-flux density were calculated from the standard deviations (S) of these properties and the sample size (n), according to: SEP

= S v / 1 + 1In

(4)

With increasing sample size, the standard error of prediction approaches the standard deviation. This minimal value of the standard error of prediction reflects the variability of the population with respect to the functional property, plus the error in measuring this property. Approximate 90% confidence intervals for the means and half widths of 90% prediction intervals for the functional properties; (1) travel times from soil surface to water table, and (2) water-table depth allowing a defined upward-flux density were calculated, assuming that both data sets were random samples from normally distributed populations. For the functional property; (3) downward-flux densities at a defined air content, both data sets were transformed because they showed a log-normal distribution. In fact, the samples were purposive instead of random and the actual frequency distribution will deviate from normality and log-normality. The results may therefore be considered as rough approximations only, but they fulfil the primary purpose of illustrating the approach.

RESULTS

Basic physical data The hydraulic-conductivity curves for sand and for clay loam and silty clay loam are shown in Figs. 1 and 2. The latter expresses the effect of horizontal cracks. Corresponding moisture-retention curves are presented in Figs. 3 and 4. The figures show mean relations and their upper and lower 90% confidence limits. In the following sections, comparisons between the curves will be based on the three functional properties discussed earlier.

138 k(crn d -1) 10 3

1 0 2 ~ . ,

10-7 100

101

102

10 3

104

105 Ihl (cm)

Fig. 1. Mean k h relation and its 90% confidencelimits for sand.

Travel times from soil surface to a water table depth of I m The mean of the travel times for sand is 135 days, the 90% confidence limits of the mean are 118 and 152 days, and the half width of the 90% prediction interval is 89 days. The mean of the travel times for clay loam and silty clay loam is 298 days, the 90% confidence limits of the mean are 285 and 311 days and the h alf width of the 90% prediction interval is 64 days. The higher mean values for the clay loam and silty clay loam are primarily due to the higher average moisture cont ent of the u n s a t u r a t e d zone in clay loam and silty clay loam. The h alf width of the 90°/0 prediction interval of the travel time as a function of the sample size (n) is presented in Fig. 5. The smaller the prediction interval the higher the accuracy.

139

k ( c m d -1) 10 3 '

10'1

\\ \\ \\ \\ \\ \ \ \ \ \\ \~\

10"

10 C

10 ¸ '\x 10 .2

\\\\ 10 3

10 4

'C~i,'

10-5 10 0

101

10 2

10 3

10 4

10 5

Ihl (cm)

Fig. 2. Mean k h relation and its 90% confidence limits for clay loam and silty clay loam with horizontal cracks.

Ihl (cm)

10 5.

[

10 4

10 3

\x 10 2

101

10 0 0

10

20

30

40

e (cm 3 cm -31

Fig. 3. Mean 0 h relation and its 90% confidence limits for sand.

140 JhJ (cm) 105

104

"\ \.\\ \ \\ "\ x \ \. \

\ \

103

102

\\\\.

~i\!~.

10 ~

!/',

10 °

20

1'0

0

30

40 50 (9 (cm 3 crn -3)

Fig. 4. Mean O-h relation and its 90#/0 confidence limits for clay loam and silty clay loam with horizontal cracks.

half width ofthe 90%prediction interval(d)

170

150

130

110

sand

90

70

loam and silty clay loam

5O •

4

8000

,

6

.

,

8

.

.

.

10

20000

.

.

.

12 14

.

.

16

30000

.

.

18

.

.

20

40000

.

22

.

,

24 26 28 30 sample size (n) 50000

60000 costs (Dfl)

Fig. 5. Half width of the 90~o prediction interval of the travel time from soil surface to a water-table depth of 1 m as a function of the sample size (n).

141 S a m p l i n g effort c a n also be expressed in t e r m s of c o s t s i n v o l v e d . M e a s u r e m e n t o f 0 - h and k - h r e l a t i o n s of o n e soil h o r i z o n c o s t s a p p r o x i m a t e l y Dfl. 2000.-($700.-). F i g u r e 5 e n a b l e s t h e user to d e t e r m i n e t h e s a m p l e size t h a t is for i n s t a n c e n e e d e d to c a l c u l a t e travel t i m e s in c l a s s e s o f h a l f a y e a r for a soil map at a s c a l e o f 1:50,000 ( B r e e u w s m a et al., 1986). Water tables allowing an upward-flux density of O.O02mday -1 towards a reference layer with h = - 5 0 0 c m T h e m e a n of t h e w a t e r tables for sand is 94 cm, t h e 90% c o n f i d e n c e limits of t h e m e a n are 87 and 101 cm, and t h e h a l f w i d t h o f the 90% p r e d i c t i o n i n t e r v a l is 37 cm. T h e m e a n of t h e w a t e r tables for clay l o a m and silty clay l o a m is 64 cm, the 90% c o n f i d e n c e limits of the m e a n are 55 and 73 cm, and t h e h a l f w i d t h of the 90% p r e d i c t i o n i n t e r v a l is 46 cm. T h e deeper w a t e r tables for sand are due to t h e h i g h e r k-values for s a n d d o w n to a pressure h e a d of h = - 500 cm. T h e h a l f w i d t h of t h e 90% p r e d i c t i o n i n t e r v a l of t h e w a t e r table as a f u n c t i o n of t h e sample size (n) is p r e s e n t e d in Fig. 6. This figure e n a b l e s the user to c h o o s e t h e desired degree o f a c c u r a c y of t h e c a l c u l a t e d w a t e r table, a g a i n also considering the costs involved.

half width of the 9 0 % prediction interval (cm) 90

80

70

60

50

a y l o a m and silty clay loam .

40

sand 30 A

v4

6

8 t'o 1'2 1'4 1'6 1'8 2'0 ~2 242'6 2'83'0 sample size (n)

8000

20000

30000

40000

60000

60000

costs (Dfl)

Fig. 6. Half width of the 90% prediction interval of the water table allowing an upward-flux density of 0.002 m day-1 as a function of the sample size (n).

142

Natural fluctuations of the water tables in The Netherlands are determined according to Dutch soil survey procedures (Van der Sluijs and De Gruijter, 1985) defining water table classes (Gt-values). The best accuracy for a water table t h a t can be obtained, when using Gt-values, is a 90°//0 prediction interval of approximately 80 cm. Figure 6 enables the user to determine the sample size if this accuracy is considered to be sufficient.

Downward-flux densities at an air content of 5% and with unit-gradient flow The data are transformed logarithmically and the results of the statistical analysis are transformed back to the original scale. The geometric mean of the downward fluxes for sand is 198mmday ~, the 90% confidence limits of the mean are 122 and 323mmday 1, and the half width of the 90% prediction interval is 1185 mm day 1. The geometric mean of the downward fluxes for clay loam and silty clay loam is 0.6 mm day- 1, the 90% confidence limits of the mean are 0.4 and 0.9 mm day 1, and the half width of the 90% prediction interval is 2.4 mm day 1. The higher values for sand are due to the higher critical pressure head and corresponding higher flux density in sand. The half width of the 90% prediction interval of the flux density as a function of the sample size (n) is presented in Figs. 7 and 8 for sand and for clay loam and silty clay loam respectively. This figure enables the user to choose the desired degree of accuracy of the calculated downward-flux density, again also considering the costs involved.

half width,of the 90 % prediction i n t e r v a l ( m m d -1) 1100(

900q

7000

5000

\

3000

sand

1000

4

, . , . , 6 8 10

. . . . . 12 14 16

. . . . . 18 2 0 22

.

. 24

. 26

28

, 30

samplesize(n) 8000

20000

30000

40000

50000

60000 COSTS (Dfl)

Fig. 7. Half width of the 90~o prediction interval of the downward-flux density for sand at an air content of 5% and with unit-gradient flow as a function of the sample size (n).

143

h a l f w i d t h of t h e 90 % prediction i n t e r v a l ( m m d -1) 15

13

clay loam a n d s i l t y c l a y l o a m

~'~. 4

. 6

, • . . . 8 10 12

8000

20000

. . . . . . . 14 16 18 2 0

30000

40000

. . . . . , 22 24 26 28 30 s a m p l e size (n) 50000

60000 COSTS (Dfl)

Fig. 8. Half width of the 90% prediction interval of the downward-flux density for clay loam and silty clay loam at an air content of 5% and with unit-gradient flow as a function of the sample size (n). W i t h s p r i n k l e r irrigation, this downward-flux density c a n be m a n i p u l a t e d in s u c h a w a y t h a t a n a d e q u a t e a e r a t i o n s t a t u s is created. H o w e v e r , n a t u r a l rainfall c a n n o t be m a n i p u l a t e d and it is t h e r e f o r e likely t h a t u n d e r D u t c h w e a t h e r c o n d i t i o n s the a e r a t i o n s t a t u s of clay loam and silty clay loam is often insufficient w h e r e a s sand n o r m a l l y has no problems in this respect.

DISCUSSION M e a s u r e m e n t s of k - h and 0 - h r e l a t i o n s in pedological h o r i z o n s h a v e i n d i c a t e d t h a t different soil h o r i z o n s are n o t always associated with signific a n t l y different physical c h a r a c t e r i s t i c s (e.g. W S s t e n et al., 1985). H o w e v e r , the q u e s t i o n s h o u l d be raised w h i c h p r o p e r t i e s are to be used to judge differences in soil-physical c h a r a c t e r i s t i c s b e t w e e n soil horizons. In this paper, a p r o c e d u r e is p r e s e n t e d to i d e n t i f y soil h o r i z o n s by m e a n s of t h r e e p r a c t i c a l soil-physical i n t e r p r e t a t i o n s t h a t yield c h a r a c t e r i s t i c numbers, r a t h e r t h a n by c o m p a r i n g t h e c o n d u c t i v i t y and r e t e n t i o n f u n c t i o n s as such. T h e p r o c e d u r e has been d e m o n s t r a t e d for h o r i z o n s in two c o n t r a s t i n g soil-texture classes, as used

144

in the Dutch soil survey at a scale of 1:50,000. The procedure will now also be applied to horizons that belong to other texture classes. The connection with the texture classes is important, because data obtained will have to be used for calculations of land areas as delineated on soil maps. The connection also implies that the different groups of horizons cannot be chosen freely, as they correspond with the existing soil-texture classification as used in soil-map legends. The principles presented in this paper will be used to examine whether different existing texture classes can be combined or not. If the standard error of prediction for the combined texture class is markedly larger than that for the separate classes, the classes will not be joined; if this is not the case, classes may be combined. The critical value of the standard error of prediction, determining whether or not classes are combined, depends on the desired accuracy of prediction. Once a group of soil horizons has been identified, the question arises as to how many individual samples should be taken to'arrive at a required accuracy of prediction. This level of accuracy is a function of the intended use of the data, which may vary, and of funds available. A graph is therefore presented that allows an estimate of the accuracy as a function of the number of samples and the associated costs. The desired accuracy should not exceed the limited degree of detail that is often adequate for specific interpretations. This aspect deserves special attention as to avoid over-accuracy.

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