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Trend surface analysis applied to soil reaction values from Kent, England
Geoderma - Elsevier Publishing Company, Amsterdam Printed in The Netherlands
T R E N D S U R F A C E ANALYSIS A P P L I E D T O SOIL R E A C T I O N V A L U E S F R O M KENT, E N G L A N D
B.E. DAVIES and S.A. GAMM Department of Geography, University College of Wales, Aberystwyth, Cardiganshire (Great Britain) (Received July 24, 1969) SUMMARY Soil pH data were obtained for a 2 km 2 area, containing a c h a r a c t e r istic pattern of calcareous and n o n - c a l c a r e o u s soils, by sampling on a r e g u l a r grid. The data were investigated by trend s u r f a c e analysis and real cubic surfaces were produced for two soil depths. These s u r f a c e s accorded with predictions based on the nature and distribution of the soils and the patterns of residuals were explained satisfactorily by local pedogenetic factors. INTRODUCTION Continuously variable geographic data a r e n e c e s s a r i l y sampled at points and the nature of the a r e a l variation must be inferred f r o m the sample values, often by subjective isoplething. Trend s u r f a c e analysis is a statistical method of analysing such data. The technique has been d e s c r i b e d by several authors, e.g., Whitten (1963) and Harbaugh (1964). Briefly, it r e s e m b l e s the widely used linear r e g r e s s i o n analysis but three dimensions a r e involved r a t h e r than two. Best fit surfaces, of increasing complexity starting with a plane, a r e fitted to the data using polynomials of successively higher o r d e r according to the least s q u a r e s criterion. The positions of the points a r e defined by r e f e r e n c e to a rectangular grid. The applications of trend surface analysis to geographical r e s e a r c h have been discussed by Chorley and Haggett (1965) and the technique has been applied to soil data for geomorphological purposes by Chorley (1964) and by Nackowski et al. (1967) for mineral prospecting. This p a p e r r e p o r t s the application of the method to soil reaction (pH) data obtained during a study of soils in Kent, England (Gamm, 1968). Shiue and Chin (1957) have shown that pH values, although logarithmic, should not be converted to hydrogen ion concentrations before analysis by p a r a m e t r i c tests. pH values reflect the base status of the soil, i.e., the p e r c e n t saturation of the exchange complex~ and, in Britain this often depends on the nature of the parent m a t e r i a l allowing for modification by leaching: neutrality is achieved when all the exchange sites a r e occupied by metallic cations and alkaline values when calcium carbonate o c c u r s f r e e in the soil. In southern England there is a repetitive distributior~ of c a l c a r e o u s (chiefly Geoderma, 3 (1969/1970)
223
t h e Chalk and n o n - c a l c a r e o u s p a r e n t m a t e r i a l s as exemplified in the study a r e a , described below. It was p r e d i c t e d that in this study a r e a pH values would r e a c h an alkaline m a x i m u m o v e r outcropping Chalk while to the north and south of the outcrop, o v e r n o n - c a l c a r e o u s deposits, they would change p r o g r e s s i v e l y to m o d e r a t e l y acid values. Such a p r o g r e s s i v e change was deemed suitable for examination by t r e n d s u r f a c e a n a l y s i s in o r d e r to test the application of the technique to soil data; f u r t h e r m o r e , statistically significant surfaces together with the distribution of r e s i d u a l s ( r e s i d u a l s being the numerical d i f f e r e n c e s between o b s e r v e d and predicted values) might help reveal something of the n a t u r e of the control of pH by environmental factors. AREAL DESCRIPTION The study a r e a , 2 k m × 1 k m , is defined by National Grid coordinates 544155, 544157, 545157 and 545155 (all s q u a r e TQ) and lies a p p r o x i m a t e l y 1 km north of W e s t e r h a m , Kent, a s t r i d e a p a r t of the North Downs cuesta. Fig. 1 is a location map with a sketch m a p of the geology of the study a r e a with s u p e r i m p o s e d contour lines r e p r e s e n t i n g 25 ft. intervals. Annual r a i n fall is approximately 850 m m , annual e v a p o t r a n s p i r a t i o n a p p r o x i m a t e l y 550 m m and a v e r a g e annual t e m p e r a t u r e a p p r o x i m a t e l y 10°C. The soils of the a r e a a r e brown e a r t h s (sols l e s s i v ~ s ! on the plateau deposits and decalcified head, rendzinas on the Chalk, c a l c i m o r p h i c brown soils o r c a l c a r e o u s gleys on c a l c a r e o u s head and brown e a r t h s (sols lessiv~s) with gleyingon the Gault Clay. S i m i l a r s o i l s on s i m i l a r parent m a t e r i a l s have been described by A v e r y (1964) and J a r v t s (1968). METHODS The soils w e r e s a m p l e d at 231 locations on a r e g u l a r grid: s a m p l e No.1 was at (TQ) 544157 and No. 231 at (TQ) 545155. At each sampling point the profile was inspected using a s c r e w auger. Small s a m p l e s w e r e retained f o r analysis f r o m the s u r f a c e (0 cm) and f r o m 20 cm s u c c e s s i v e depths t h e r e a f t e r . At 54 locations the soil profile was d e s c r i b e d and genetic horizons sampled. Following drying at r o o m t e m p e r a t u r e and gentle grinding, soil reaction was d e t e r m i n e d e l e c t r o m e t r i c a l l y a f t e r equilibration f o r 30 minutes with 0.01M CaC12 solution (1:2.5; soil:solution). B e s t - f i t trend s u r f a c e s f o r d e g r e e s 1 - 3 w e r e computed using a p r o g r a m m e written in FORTRAN IV, b a s e d on that of Whitten (1963), and an Elliott 4130 computer. The nature of this p r o g r a m m e r e q u i r e s that e v e r y dependent variable in the computation be m e a s u r e d at e v e r y location. Consequently only values at 0 cm and 20 cm w e r e examined since p r o f i l e s developed on the Chalk w e r e often shallow and a high proportion of pH values for depths ~ 20 cm w e r e missing; also only 213 out of the possible 231 s a m p l e locations w e r e a n a l y s e d b e c a u s e of gaps in the data.
224
Geoderma, 3 (1969/1970)
3
.,3
¢D
~D
O
204.01 6.66 197.35 76.90 120.44 14.46 106.00
D u e to l i n e a r c o m p o n e n t Deviations from linear
D u e to q u a d r a t i c c o m p o n e n t Deviations from quadratic
D u e to c u b i c c o m p o n e n t D e v i a t i o n s frorr, c u b i c
0 cm
12.45 107.07
65.83 119.52
6.33 185.36
191.68
20 c m
S u m of s q u a r e s
T o t a l , 213 d a t a p o i n t s
Source
A n a l y s i s of v a r i a n c e of t r e n d s u r f a c e d a t a
TABLE I
4 203
3 207
2 210
212
D e g r e e s of freedom
3.13 0.88 21.94 0.58 3.11 0.53
3.33 0.94 25.63 0.58 3.62 0.52
6.96
44.19
3.54
F
5.87
37.83
3.56
20 c m
0 cm
0 cm
20 c m
Snedecor's
Mean square
99.9+
99.9+
95.0+
D
(%)
99.9+
99.9+
95.0+
m
(~)
20 c m
Confidence level 0 cm
$44,1~7
LEGEND
~700--
Contours in ft.O.D, a t 25ft. intervals
I]1 . . . .
Quarry
Clay- w i t h - f l i n t s
[]
Chalk
[]
Upper Greensand
[]
Gault
LOCATION MAP
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F i g . 1 . Sketch m a p of the s t u d y a r e a with a l o c a t i o n m a p . RESULTS F o l l o w i n g A l l e n a n d K r u m b e i n (1962) and H a r b a u g h (1964) a n a l y s i s of v a r i a n c e w a s u s e d to t e s t the s i g n i f i c a n c e of e a c h c o m p u t e d s u r f a c e and T a b l e I l i s t s the r e s u l t s : b o t h t h e q u a d r a t i c a n d c u b i c s u r f a c e s w e r e a s s o c i a t e d with c o n f i d e n c e l e v e l s > 9 9 . 9 % and it i s c o n c l u d e d t h e y a r e r e a l surfaces. The p e r c e n t r e d u c t i o n of t h e t o t a l s u m of s q u a r e s f o r e a c h s u r f a c e i s a m e a s u r e of how c l o s e l y that s u r f a c e f i t s t h e o b s e r v e d data. F r o m T a b l e II it is s e e n that t h e c u b i c s u r f a c e s a c c o u n t f o r the g r e a t e s t p r o p o r t i o n of the o b s e r v e d v a r i a n c e in t h e d a t a ; o n l y the c u b i c s u r f a c e s a r e d i s c u s s e d h e r e a f t e r 226
Geoderma, 3 (1969/1970)
and their computed regressions coordinates):
were (when U and V are the geographic
0 c m : pH t r e n d = 0 . 5 0 7 + 0 . 5 6 8 U + 0 . 4 8 4 V - 0 . 4 5 3 U 2 + 0 . 5 3 1 U V + 0 . 4 9 0 V 2 + 0.703U 3 + 0.141U2V - 0.322UV 2 + 0.506V 3 20 c m : pH t r e n d = 0 . 5 1 7 + 0 . 5 0 7 U + 0 . 7 6 7 V - 0 . 3 5 2 U 2 - 0 . 9 0 4 U V + 0 . 1 5 4 V 2 + 0.347U 3 + 0.180U2V - 0.250UV 2 + 0.332V 3 TABLE II % of total sum of s q u a r e s accounted for by s u r f a c e s Soil depth
Linear (%)
Quadratic (~)
Cubic (%)
0 cm 20 c m
3.27 3.30
40.97 37.65
48.05 44.14
6.4
F i g . 2 . C u b i c t r e n d s u r f a c e of s o i l pH, a t t w o d e p t h s , f o r t h e a r e a d e p i c t e d in F i g . 1 . G e o d e r m a , 3 (1969/1970)
227
In addition to the above data, the computer provided predicted and residual values at each location for the two depths. These computed values were entered at the appropriate grid intersection on the map and isopleths drawn and interpretations made according to the following c r i t e r i a . White (1961), using a s i m i l a r sampling technique on s i m i l a r soils 25 k~ east of this study a r e a , concluded that the standard e r r o r for a single positio] (sum of 3 cores) was +0.21 pH unit for surface s a m p l e s ( 0 - 1 5 cm) and +0.20 for the subsoil (15-75 cm). Hence a difference of > 0.6 (1~ ~ 0.05) between two positions indicated a change in soil reaction. It is convenient to r e g a r d residual values -> 1.0 pH unit as anomalous. F u r t h e r m o r e , discussion is r e s t r i c t e d to areas g r e a t e r than one sampling location o c c u r r i n g at both depths so as to minimise spurious results following localised contamination of the soil. The trend s u r f a c e s and the maps of r e s i d u a l s w e r e c o n s t r u c t e d with an isopleth interval of 0.5 pH unit, and for the trend s u r f a c e s the datum was neutrality = pH 6.4 (Davies, 1969). The cubic s u r f a c e s a r e displayed in Fig.2
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Fig.3. Map of r e s i d u a l s of cubic trend s u r f a c e of soil pH, at two depths, for the a r e a depicted in Fig.1. 228
Geoderma, 3 (1969/1970)
and the patterns of residuals in Fig.3 where positive or alkaline (observed predicted) and negative or acid (observed ~ predicted) a r e differentiated by shading. Acid a r e a s to be considered below are labelled with upper case letters and, similarly, alkaline a r e a s with lower case letters.
DISCUSSION Both surfaces (Fig.2) a r e closely s i m i l a r and a c c o r d with the prediction made in the introduction, t h e r e being an alkaline maximum zone over the Chalk, while to the north and south the trend is to acid values. The s i m i l a r i t y between the two surfaces is consistent with the general absence of strongly leached soils. In the north the isopleths -- pH 6.4 are s u b - p a r a l l e l and trend WSW-ENE matching the general strike of the Chalk outcrop and the isopleth 6.4 c o r r e s p o n d s with the top of the dip-slope adjacent to the s c a r p edge. Field mapping showed the soils on the dip-slope were developed in noncalcareous superficial deposits which thinned towards the s c a r p allowing the subjacent Chalk increasingly to influence pedogenesis. Alkaline values over the s c a r p c o r r e s p o n d with the o c c u r r e n c e of rendzinas. To the south the isopleths are lobate with a long axis trending slightly east of south contiguous with the generalised direction of a small dry valley. Chalky head mantled the lower slopes of the s c a r p and extended out over the Gault Clay and its distribution was possibly governed by funnelling down the valley. In the southwest c o r n e r values trend rapidly f r o m neutrality to moderate acidity where the soils were developed in the mildly acid Gault Clay. Although they exhibit minor differences the patterns of residuals at 0 and 20 cm a r e broadly similar. Explanations of these localised d e p a r t u r e s from the regional trend w e r e sought in t e r m s of generally accepted pedogenetic f a c t o r s utilising the information gained from the 54 profile descriptions. There are five acid a r e a s (one of which (D) is continuous at 0 cm but discontinuous at 20 cm) and a common explanation is adduced for a11 save a r e a C. Field mapping indicated that the soils in a r e a C were developed in an isolated a r e a of n o n - c a l c a r e o u s head, a dark yellowish brown (10 YR 4/6) neutral silty clay. A r e a s A and B c o m p r i s e soils f o r m e d on plateau deposits, chiefly clay-with-flints, and identified with the Winchester s e r i e s mapped elsewhere. These two anomalous a r e a s c o r r e s p o n d with woodland, w h e r e a s the same soils under cultivation conformed with the regional trend. These soils have been d e s c r i b e d by Avery (1964), Hodgson (1967) and J a r v i s (1968) as m o d e r a t e l y or strongly acid under woodland but near neutral under cultivation because of additions of chalk or lime. In a r e a s D and E the soils were developed in head o r in Gault Clay incorporating head. Again, the softs of these a r e a s were under woodland except for one profile under old permanent pasture; profiles on s i m i l a r parent m a t e r i a l s whose pH values conformed with the regional trend were nearly all cultivated, the exception was a gley under woodland. Soils under old pasture a r e often relatively acid whereas ground w a t e r gleys may be relatively alkaline. Thus, acidification under woodland, and ploughing and liming have differentiated otherwise s i m i l a r soils on s i m i l a r parent m a t e r i a l s . Only a relatively s m a l l part of the a r e a Geoderma, 3 (1969/1970)
229
w a s w o o d e d s o the r e a c t i o n s of t h e n o n - w o o d e d s o i l s g o v e r n e d t h e r e g i o n a l trend. T h r e e a r e a s of p o s i t i v e r e s i d u a l s w e r e i n v e s t i g a t e d . In t h e s m a l l e s t a r e a a no p r o f i l e s had b e e n d e s c r i b e d s o a f i r m e x p l a n a t i o n of t h i s a n o m a l y cannot b e p r o p o s e d . In a r e a b t h e s o i l s w e r e f r e e l y d r a i n e d and d e v e l o p e d in c h a l k y m a r l , c a l c a r e o u s h e a d o r c a l c a r e o u s c l a y e y h e a d o v e r G a u l t C l a y and n e a r l y a l l w e r e u n d e r b a r l e y o r wheat; an e x c e p t i o n w a s a c a l c a r e o u s g l e y u n d e r woodland. S i m i l a r s o i l s c o n f o r m i n g with t h e r e g i o n a l t r e n d w e r e a l l u n d e r p a s t u r e . In a r e a c the s o i l s w e r e c a l c a r e o u s g l e y s o r c a l c i m o r p h i c b r o w n s o i l s with s u b s o i l g l e y i n g and in a t o p o g r a p h i c p o s i t i o n w h e r e the g r o u n d w a t e r i s s u p p l e m e n t e d by l i m e - r i c h s p r i n g w a t e r a r i s i n g at t h e j u n c t i o n of the Chalk and U p p e r G r e e n s a n d .
CONCLUS~NS In c o n c l u s i o n , t h e a p p l i c a t i o n of t r e n d s u r f a c e a n a l y s i s in t h i s t r i a l a r e a was deemed successful since statistically significant surfaces were generated which a c c o r d e d with p r e d i c t i o n s b a s e d on t h e k n o w n p r o p e r t i e s of s o i l s f o r m e d on p a r e n t m a t e r i a l s s i m i l a r to t h o s e of t h e s t u d y a r e a . F u r t h e r m o r e , the residual values were generally explicable by commonly accepted i n f l u e n c e s on s o i l r e a c t i o n , n a m e l y l a n d u s e a n d g l e y i n g . T h e s e r e s u l t s s u g g e s t that the t e c h n i q u e m e r i t s f u r t h e r i n v e s t i g a t i o n a s an a i d in p e d o l o g i c a l r e s e a r c h . R e g i o n a l s o i l d e s c r i p t i o n s a r e o f t e n b a s e d on l a r g e s c a l e m a p p i n g and a n a l y t i c a l r e s u l t s f r o m a s m a l l n u m b e r of p r o f i l e s s e l e c t e d b y the s u r v e y o r a s r e p r e s e n t a t i v e of t h e m a p p i n g u n i t s . S a m p l i n g on a r e g u l a r g r i d f o l l o w e d b y t h e i n v e s t i g a t i o n of l a b o r a t o r y a n a l y t i c a l r e s u l t s u s i n g s t a t i s t i c a l t e c h n i q u e s s u c h a s t r e n d s u r f a c e a n a l y s i s m i g h t i m p r o v e the r e l i a b i l i t y of t h e i n t e r p r e t a t i o n s of the s u r v e y and t h e o b j e c t i v i t y of t h e r e g i o n a l d e s c r i p t i o n .
ACKNOWLEDGEMENT We a r e i n d e b t e d to o u r c o l l e a g u e M r . D.J. Unwin f o r t h e u s e of his deck of c o m p u t e r c a r d s c o n t a i n i n g the p r o g r a m m e . REFERENCES Allen, P. and Krtnnbein, W.C., 1962. Secondary trend components in the top Ashdown Pebble bed: a case history. J. Geol., 70: 507-538. Avery, B.W., 1964. The soils and land use of the d i s t r i c t around Aylesbury and Hemel Hampstead. Mem. Soil Surv. G. Brit., H.M.S.O., London, 216 pp. Chorley, R.J., 1964. An analysis of the aereal distribution of soil size facies on the Lower Greensand rocks of east central England by the use of trend surface analysis. Geol. Mag., 101: 314-321. Chorley, R.J. and Haggett, P., 1965. Trend surface mapping in geographical research. Trans. Inst. Brit. Geographers, 37:47-67. Davies, B.E., 1969. Tl~e interpretation of soil pH measured in 0.01M CaC12 solution. (unpublished). Gamin, S.A., 1968 Soils in relation to the physique and plant associations of an area in west Kent. unpublished B.Sc. Thesis, Geogr. Dept., Univ. Coll. Wales, Aberystwyth, 95 pp. 2"30
Geoderma, 3 (1969/1970)
Harbaugh, J.W., 1964. A c o m p u t e r m e t h o d f o r f o u r - v a r i a b l e t r e n d a n a l y s i s i l l u s t r a t e d by a study of o i l - g r a v i t y v a r i a t i o n s in s o u t h - e a s t e r n K a n s a s . State Geol. Surv. K a n s a s , Bull. 171, 58 pp. Hodgson, J.M., 1967. T h e s o i l s of the w e s t S u s s e x c o a s t a l plain. Bull. Soil Surv. Gt. B r i t . , 148 pp. J a r v i s , R.A., 1968. Soils of the R e a d i n g D i s t r i c t . M e m . Soil Surv. Gt. B r i t . , 150 pp. Nackowski, M . P . , M a r d i r o s i a n , C.A. and Botbol, J . M . , 1967. T r e n d s u r f a c e a n a l y s i s of t r a c e c h e m i c a l data. P a r k City D i s t r i c t , Utah. Econ. Geol., 62: 1072-1087. Shiue, C.J. and Chin, N.L., 1957. D i r e c t u s e of pH v a l u e s in s t a t i s t i c a l a n a l y s i s of soil r e a c t i o n s . Soil Sci., 84: 2 1 9 - 2 2 4 . White, G.C., 1961. A s u r v e y of the pH of s o i l s of E a s t M a l l i n g r e s e a r c h station. Ann. Rept. E a s t Malling R e s . Stat., 1960: 7 7 - 8 0 . Whitten, E.H.T., 1963. A s u r f a c e fitting p r o g r a m f o r t e s t i n g geological models which involve a r e a l l y d i s t r i b u t e d data. Office Naval R e s . , G e o g r a p h . B r a n c h , Tech. Rept., 2: 3 8 9 - 4 3 5 .
G e o d e r m a , 3 (1969/1970)
231
T R E N D S U R F A C E ANALYSIS A P P L I E D T O SOIL R E A C T I O N V A L U E S F R O M KENT, E N G L A N D
B.E. DAVIES and S.A. GAMM Department of Geography, University College of Wales, Aberystwyth, Cardiganshire (Great Britain) (Received July 24, 1969) SUMMARY Soil pH data were obtained for a 2 km 2 area, containing a c h a r a c t e r istic pattern of calcareous and n o n - c a l c a r e o u s soils, by sampling on a r e g u l a r grid. The data were investigated by trend s u r f a c e analysis and real cubic surfaces were produced for two soil depths. These s u r f a c e s accorded with predictions based on the nature and distribution of the soils and the patterns of residuals were explained satisfactorily by local pedogenetic factors. INTRODUCTION Continuously variable geographic data a r e n e c e s s a r i l y sampled at points and the nature of the a r e a l variation must be inferred f r o m the sample values, often by subjective isoplething. Trend s u r f a c e analysis is a statistical method of analysing such data. The technique has been d e s c r i b e d by several authors, e.g., Whitten (1963) and Harbaugh (1964). Briefly, it r e s e m b l e s the widely used linear r e g r e s s i o n analysis but three dimensions a r e involved r a t h e r than two. Best fit surfaces, of increasing complexity starting with a plane, a r e fitted to the data using polynomials of successively higher o r d e r according to the least s q u a r e s criterion. The positions of the points a r e defined by r e f e r e n c e to a rectangular grid. The applications of trend surface analysis to geographical r e s e a r c h have been discussed by Chorley and Haggett (1965) and the technique has been applied to soil data for geomorphological purposes by Chorley (1964) and by Nackowski et al. (1967) for mineral prospecting. This p a p e r r e p o r t s the application of the method to soil reaction (pH) data obtained during a study of soils in Kent, England (Gamm, 1968). Shiue and Chin (1957) have shown that pH values, although logarithmic, should not be converted to hydrogen ion concentrations before analysis by p a r a m e t r i c tests. pH values reflect the base status of the soil, i.e., the p e r c e n t saturation of the exchange complex~ and, in Britain this often depends on the nature of the parent m a t e r i a l allowing for modification by leaching: neutrality is achieved when all the exchange sites a r e occupied by metallic cations and alkaline values when calcium carbonate o c c u r s f r e e in the soil. In southern England there is a repetitive distributior~ of c a l c a r e o u s (chiefly Geoderma, 3 (1969/1970)
223
t h e Chalk and n o n - c a l c a r e o u s p a r e n t m a t e r i a l s as exemplified in the study a r e a , described below. It was p r e d i c t e d that in this study a r e a pH values would r e a c h an alkaline m a x i m u m o v e r outcropping Chalk while to the north and south of the outcrop, o v e r n o n - c a l c a r e o u s deposits, they would change p r o g r e s s i v e l y to m o d e r a t e l y acid values. Such a p r o g r e s s i v e change was deemed suitable for examination by t r e n d s u r f a c e a n a l y s i s in o r d e r to test the application of the technique to soil data; f u r t h e r m o r e , statistically significant surfaces together with the distribution of r e s i d u a l s ( r e s i d u a l s being the numerical d i f f e r e n c e s between o b s e r v e d and predicted values) might help reveal something of the n a t u r e of the control of pH by environmental factors. AREAL DESCRIPTION The study a r e a , 2 k m × 1 k m , is defined by National Grid coordinates 544155, 544157, 545157 and 545155 (all s q u a r e TQ) and lies a p p r o x i m a t e l y 1 km north of W e s t e r h a m , Kent, a s t r i d e a p a r t of the North Downs cuesta. Fig. 1 is a location map with a sketch m a p of the geology of the study a r e a with s u p e r i m p o s e d contour lines r e p r e s e n t i n g 25 ft. intervals. Annual r a i n fall is approximately 850 m m , annual e v a p o t r a n s p i r a t i o n a p p r o x i m a t e l y 550 m m and a v e r a g e annual t e m p e r a t u r e a p p r o x i m a t e l y 10°C. The soils of the a r e a a r e brown e a r t h s (sols l e s s i v ~ s ! on the plateau deposits and decalcified head, rendzinas on the Chalk, c a l c i m o r p h i c brown soils o r c a l c a r e o u s gleys on c a l c a r e o u s head and brown e a r t h s (sols lessiv~s) with gleyingon the Gault Clay. S i m i l a r s o i l s on s i m i l a r parent m a t e r i a l s have been described by A v e r y (1964) and J a r v t s (1968). METHODS The soils w e r e s a m p l e d at 231 locations on a r e g u l a r grid: s a m p l e No.1 was at (TQ) 544157 and No. 231 at (TQ) 545155. At each sampling point the profile was inspected using a s c r e w auger. Small s a m p l e s w e r e retained f o r analysis f r o m the s u r f a c e (0 cm) and f r o m 20 cm s u c c e s s i v e depths t h e r e a f t e r . At 54 locations the soil profile was d e s c r i b e d and genetic horizons sampled. Following drying at r o o m t e m p e r a t u r e and gentle grinding, soil reaction was d e t e r m i n e d e l e c t r o m e t r i c a l l y a f t e r equilibration f o r 30 minutes with 0.01M CaC12 solution (1:2.5; soil:solution). B e s t - f i t trend s u r f a c e s f o r d e g r e e s 1 - 3 w e r e computed using a p r o g r a m m e written in FORTRAN IV, b a s e d on that of Whitten (1963), and an Elliott 4130 computer. The nature of this p r o g r a m m e r e q u i r e s that e v e r y dependent variable in the computation be m e a s u r e d at e v e r y location. Consequently only values at 0 cm and 20 cm w e r e examined since p r o f i l e s developed on the Chalk w e r e often shallow and a high proportion of pH values for depths ~ 20 cm w e r e missing; also only 213 out of the possible 231 s a m p l e locations w e r e a n a l y s e d b e c a u s e of gaps in the data.
224
Geoderma, 3 (1969/1970)
3
.,3
¢D
~D
O
204.01 6.66 197.35 76.90 120.44 14.46 106.00
D u e to l i n e a r c o m p o n e n t Deviations from linear
D u e to q u a d r a t i c c o m p o n e n t Deviations from quadratic
D u e to c u b i c c o m p o n e n t D e v i a t i o n s frorr, c u b i c
0 cm
12.45 107.07
65.83 119.52
6.33 185.36
191.68
20 c m
S u m of s q u a r e s
T o t a l , 213 d a t a p o i n t s
Source
A n a l y s i s of v a r i a n c e of t r e n d s u r f a c e d a t a
TABLE I
4 203
3 207
2 210
212
D e g r e e s of freedom
3.13 0.88 21.94 0.58 3.11 0.53
3.33 0.94 25.63 0.58 3.62 0.52
6.96
44.19
3.54
F
5.87
37.83
3.56
20 c m
0 cm
0 cm
20 c m
Snedecor's
Mean square
99.9+
99.9+
95.0+
D
(%)
99.9+
99.9+
95.0+
m
(~)
20 c m
Confidence level 0 cm
$44,1~7
LEGEND
~700--
Contours in ft.O.D, a t 25ft. intervals
I]1 . . . .
Quarry
Clay- w i t h - f l i n t s
[]
Chalk
[]
Upper Greensand
[]
Gault
LOCATION MAP
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F i g . 1 . Sketch m a p of the s t u d y a r e a with a l o c a t i o n m a p . RESULTS F o l l o w i n g A l l e n a n d K r u m b e i n (1962) and H a r b a u g h (1964) a n a l y s i s of v a r i a n c e w a s u s e d to t e s t the s i g n i f i c a n c e of e a c h c o m p u t e d s u r f a c e and T a b l e I l i s t s the r e s u l t s : b o t h t h e q u a d r a t i c a n d c u b i c s u r f a c e s w e r e a s s o c i a t e d with c o n f i d e n c e l e v e l s > 9 9 . 9 % and it i s c o n c l u d e d t h e y a r e r e a l surfaces. The p e r c e n t r e d u c t i o n of t h e t o t a l s u m of s q u a r e s f o r e a c h s u r f a c e i s a m e a s u r e of how c l o s e l y that s u r f a c e f i t s t h e o b s e r v e d data. F r o m T a b l e II it is s e e n that t h e c u b i c s u r f a c e s a c c o u n t f o r the g r e a t e s t p r o p o r t i o n of the o b s e r v e d v a r i a n c e in t h e d a t a ; o n l y the c u b i c s u r f a c e s a r e d i s c u s s e d h e r e a f t e r 226
Geoderma, 3 (1969/1970)
and their computed regressions coordinates):
were (when U and V are the geographic
0 c m : pH t r e n d = 0 . 5 0 7 + 0 . 5 6 8 U + 0 . 4 8 4 V - 0 . 4 5 3 U 2 + 0 . 5 3 1 U V + 0 . 4 9 0 V 2 + 0.703U 3 + 0.141U2V - 0.322UV 2 + 0.506V 3 20 c m : pH t r e n d = 0 . 5 1 7 + 0 . 5 0 7 U + 0 . 7 6 7 V - 0 . 3 5 2 U 2 - 0 . 9 0 4 U V + 0 . 1 5 4 V 2 + 0.347U 3 + 0.180U2V - 0.250UV 2 + 0.332V 3 TABLE II % of total sum of s q u a r e s accounted for by s u r f a c e s Soil depth
Linear (%)
Quadratic (~)
Cubic (%)
0 cm 20 c m
3.27 3.30
40.97 37.65
48.05 44.14
6.4
F i g . 2 . C u b i c t r e n d s u r f a c e of s o i l pH, a t t w o d e p t h s , f o r t h e a r e a d e p i c t e d in F i g . 1 . G e o d e r m a , 3 (1969/1970)
227
In addition to the above data, the computer provided predicted and residual values at each location for the two depths. These computed values were entered at the appropriate grid intersection on the map and isopleths drawn and interpretations made according to the following c r i t e r i a . White (1961), using a s i m i l a r sampling technique on s i m i l a r soils 25 k~ east of this study a r e a , concluded that the standard e r r o r for a single positio] (sum of 3 cores) was +0.21 pH unit for surface s a m p l e s ( 0 - 1 5 cm) and +0.20 for the subsoil (15-75 cm). Hence a difference of > 0.6 (1~ ~ 0.05) between two positions indicated a change in soil reaction. It is convenient to r e g a r d residual values -> 1.0 pH unit as anomalous. F u r t h e r m o r e , discussion is r e s t r i c t e d to areas g r e a t e r than one sampling location o c c u r r i n g at both depths so as to minimise spurious results following localised contamination of the soil. The trend s u r f a c e s and the maps of r e s i d u a l s w e r e c o n s t r u c t e d with an isopleth interval of 0.5 pH unit, and for the trend s u r f a c e s the datum was neutrality = pH 6.4 (Davies, 1969). The cubic s u r f a c e s a r e displayed in Fig.2
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Fig.3. Map of r e s i d u a l s of cubic trend s u r f a c e of soil pH, at two depths, for the a r e a depicted in Fig.1. 228
Geoderma, 3 (1969/1970)
and the patterns of residuals in Fig.3 where positive or alkaline (observed predicted) and negative or acid (observed ~ predicted) a r e differentiated by shading. Acid a r e a s to be considered below are labelled with upper case letters and, similarly, alkaline a r e a s with lower case letters.
DISCUSSION Both surfaces (Fig.2) a r e closely s i m i l a r and a c c o r d with the prediction made in the introduction, t h e r e being an alkaline maximum zone over the Chalk, while to the north and south the trend is to acid values. The s i m i l a r i t y between the two surfaces is consistent with the general absence of strongly leached soils. In the north the isopleths -- pH 6.4 are s u b - p a r a l l e l and trend WSW-ENE matching the general strike of the Chalk outcrop and the isopleth 6.4 c o r r e s p o n d s with the top of the dip-slope adjacent to the s c a r p edge. Field mapping showed the soils on the dip-slope were developed in noncalcareous superficial deposits which thinned towards the s c a r p allowing the subjacent Chalk increasingly to influence pedogenesis. Alkaline values over the s c a r p c o r r e s p o n d with the o c c u r r e n c e of rendzinas. To the south the isopleths are lobate with a long axis trending slightly east of south contiguous with the generalised direction of a small dry valley. Chalky head mantled the lower slopes of the s c a r p and extended out over the Gault Clay and its distribution was possibly governed by funnelling down the valley. In the southwest c o r n e r values trend rapidly f r o m neutrality to moderate acidity where the soils were developed in the mildly acid Gault Clay. Although they exhibit minor differences the patterns of residuals at 0 and 20 cm a r e broadly similar. Explanations of these localised d e p a r t u r e s from the regional trend w e r e sought in t e r m s of generally accepted pedogenetic f a c t o r s utilising the information gained from the 54 profile descriptions. There are five acid a r e a s (one of which (D) is continuous at 0 cm but discontinuous at 20 cm) and a common explanation is adduced for a11 save a r e a C. Field mapping indicated that the soils in a r e a C were developed in an isolated a r e a of n o n - c a l c a r e o u s head, a dark yellowish brown (10 YR 4/6) neutral silty clay. A r e a s A and B c o m p r i s e soils f o r m e d on plateau deposits, chiefly clay-with-flints, and identified with the Winchester s e r i e s mapped elsewhere. These two anomalous a r e a s c o r r e s p o n d with woodland, w h e r e a s the same soils under cultivation conformed with the regional trend. These soils have been d e s c r i b e d by Avery (1964), Hodgson (1967) and J a r v i s (1968) as m o d e r a t e l y or strongly acid under woodland but near neutral under cultivation because of additions of chalk or lime. In a r e a s D and E the soils were developed in head o r in Gault Clay incorporating head. Again, the softs of these a r e a s were under woodland except for one profile under old permanent pasture; profiles on s i m i l a r parent m a t e r i a l s whose pH values conformed with the regional trend were nearly all cultivated, the exception was a gley under woodland. Soils under old pasture a r e often relatively acid whereas ground w a t e r gleys may be relatively alkaline. Thus, acidification under woodland, and ploughing and liming have differentiated otherwise s i m i l a r soils on s i m i l a r parent m a t e r i a l s . Only a relatively s m a l l part of the a r e a Geoderma, 3 (1969/1970)
229
w a s w o o d e d s o the r e a c t i o n s of t h e n o n - w o o d e d s o i l s g o v e r n e d t h e r e g i o n a l trend. T h r e e a r e a s of p o s i t i v e r e s i d u a l s w e r e i n v e s t i g a t e d . In t h e s m a l l e s t a r e a a no p r o f i l e s had b e e n d e s c r i b e d s o a f i r m e x p l a n a t i o n of t h i s a n o m a l y cannot b e p r o p o s e d . In a r e a b t h e s o i l s w e r e f r e e l y d r a i n e d and d e v e l o p e d in c h a l k y m a r l , c a l c a r e o u s h e a d o r c a l c a r e o u s c l a y e y h e a d o v e r G a u l t C l a y and n e a r l y a l l w e r e u n d e r b a r l e y o r wheat; an e x c e p t i o n w a s a c a l c a r e o u s g l e y u n d e r woodland. S i m i l a r s o i l s c o n f o r m i n g with t h e r e g i o n a l t r e n d w e r e a l l u n d e r p a s t u r e . In a r e a c the s o i l s w e r e c a l c a r e o u s g l e y s o r c a l c i m o r p h i c b r o w n s o i l s with s u b s o i l g l e y i n g and in a t o p o g r a p h i c p o s i t i o n w h e r e the g r o u n d w a t e r i s s u p p l e m e n t e d by l i m e - r i c h s p r i n g w a t e r a r i s i n g at t h e j u n c t i o n of the Chalk and U p p e r G r e e n s a n d .
CONCLUS~NS In c o n c l u s i o n , t h e a p p l i c a t i o n of t r e n d s u r f a c e a n a l y s i s in t h i s t r i a l a r e a was deemed successful since statistically significant surfaces were generated which a c c o r d e d with p r e d i c t i o n s b a s e d on t h e k n o w n p r o p e r t i e s of s o i l s f o r m e d on p a r e n t m a t e r i a l s s i m i l a r to t h o s e of t h e s t u d y a r e a . F u r t h e r m o r e , the residual values were generally explicable by commonly accepted i n f l u e n c e s on s o i l r e a c t i o n , n a m e l y l a n d u s e a n d g l e y i n g . T h e s e r e s u l t s s u g g e s t that the t e c h n i q u e m e r i t s f u r t h e r i n v e s t i g a t i o n a s an a i d in p e d o l o g i c a l r e s e a r c h . R e g i o n a l s o i l d e s c r i p t i o n s a r e o f t e n b a s e d on l a r g e s c a l e m a p p i n g and a n a l y t i c a l r e s u l t s f r o m a s m a l l n u m b e r of p r o f i l e s s e l e c t e d b y the s u r v e y o r a s r e p r e s e n t a t i v e of t h e m a p p i n g u n i t s . S a m p l i n g on a r e g u l a r g r i d f o l l o w e d b y t h e i n v e s t i g a t i o n of l a b o r a t o r y a n a l y t i c a l r e s u l t s u s i n g s t a t i s t i c a l t e c h n i q u e s s u c h a s t r e n d s u r f a c e a n a l y s i s m i g h t i m p r o v e the r e l i a b i l i t y of t h e i n t e r p r e t a t i o n s of the s u r v e y and t h e o b j e c t i v i t y of t h e r e g i o n a l d e s c r i p t i o n .
ACKNOWLEDGEMENT We a r e i n d e b t e d to o u r c o l l e a g u e M r . D.J. Unwin f o r t h e u s e of his deck of c o m p u t e r c a r d s c o n t a i n i n g the p r o g r a m m e . REFERENCES Allen, P. and Krtnnbein, W.C., 1962. Secondary trend components in the top Ashdown Pebble bed: a case history. J. Geol., 70: 507-538. Avery, B.W., 1964. The soils and land use of the d i s t r i c t around Aylesbury and Hemel Hampstead. Mem. Soil Surv. G. Brit., H.M.S.O., London, 216 pp. Chorley, R.J., 1964. An analysis of the aereal distribution of soil size facies on the Lower Greensand rocks of east central England by the use of trend surface analysis. Geol. Mag., 101: 314-321. Chorley, R.J. and Haggett, P., 1965. Trend surface mapping in geographical research. Trans. Inst. Brit. Geographers, 37:47-67. Davies, B.E., 1969. Tl~e interpretation of soil pH measured in 0.01M CaC12 solution. (unpublished). Gamin, S.A., 1968 Soils in relation to the physique and plant associations of an area in west Kent. unpublished B.Sc. Thesis, Geogr. Dept., Univ. Coll. Wales, Aberystwyth, 95 pp. 2"30
Geoderma, 3 (1969/1970)
Harbaugh, J.W., 1964. A c o m p u t e r m e t h o d f o r f o u r - v a r i a b l e t r e n d a n a l y s i s i l l u s t r a t e d by a study of o i l - g r a v i t y v a r i a t i o n s in s o u t h - e a s t e r n K a n s a s . State Geol. Surv. K a n s a s , Bull. 171, 58 pp. Hodgson, J.M., 1967. T h e s o i l s of the w e s t S u s s e x c o a s t a l plain. Bull. Soil Surv. Gt. B r i t . , 148 pp. J a r v i s , R.A., 1968. Soils of the R e a d i n g D i s t r i c t . M e m . Soil Surv. Gt. B r i t . , 150 pp. Nackowski, M . P . , M a r d i r o s i a n , C.A. and Botbol, J . M . , 1967. T r e n d s u r f a c e a n a l y s i s of t r a c e c h e m i c a l data. P a r k City D i s t r i c t , Utah. Econ. Geol., 62: 1072-1087. Shiue, C.J. and Chin, N.L., 1957. D i r e c t u s e of pH v a l u e s in s t a t i s t i c a l a n a l y s i s of soil r e a c t i o n s . Soil Sci., 84: 2 1 9 - 2 2 4 . White, G.C., 1961. A s u r v e y of the pH of s o i l s of E a s t M a l l i n g r e s e a r c h station. Ann. Rept. E a s t Malling R e s . Stat., 1960: 7 7 - 8 0 . Whitten, E.H.T., 1963. A s u r f a c e fitting p r o g r a m f o r t e s t i n g geological models which involve a r e a l l y d i s t r i b u t e d data. Office Naval R e s . , G e o g r a p h . B r a n c h , Tech. Rept., 2: 3 8 9 - 4 3 5 .
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231