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A soil water balance model for sloping landJ. S. Bircham a & A. G. Gillingham aa Whatawhata Hill Country Research Station , MAF , Private Bag, Hamilton , New ZealandPublished online: 20 Jan 2012.

To cite this article: J. S. Bircham & A. G. Gillingham (1986) A soil water balance model for sloping land, New Zealand Journalof Agricultural Research, 29:2, 315-323, DOI: 10.1080/00288233.1986.10426988

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New Zealand Journal of Agricultural Research, 1986, Vol. 29: 315-323 315 0028-8233/86/2802-0315$2.50/0 © Crown copyright 1986

A soil water balance model for sloping land

J. S. BIRCHAM A. G. GILLINGHAM Whatawhata Hill Country Research Station, MAF Private Bag, Hamilton, New Zealand

Abstract Simulation models of soil water bal­ance for flat land are not applicable to hill soils, principally because on the latter sites significant runoff can occur before the soil reaches field capacity. Part of the data from regular measure­ments of topsoil (0-75 mm depth) moisture con­tent over a 3-year period on the north aspect of a steepland yellow-brown earth soil was used to con­struct a simulation model which described changes in soil moisture to 150 mm depth during the year. Similar data collected on a south aspect of the soil and also on north and south aspects of a yellow­brown loam hill soil were used to evaluate the model. A 4-layer model was developed in which the rate of soil rewetting was empirically limited according to soil moisture content and evapotran­spiration rate was primarily soil-controlled. Pre­dicted topsoil moisture levels provided similar, but generally lower values compared to actual levels especially during the summer to late winter period: The greater discrepancy during early spring could be attributed to the role of unaccounted-for sub­surface flow downslope and/or rapid infiltration bypassing surface layers but contributing to actual moisture levels below the soil surface. Despite these limitations the modelling exercise enabled 2 major conclusions to be drawn which were not previously apparent. First, because of the low storage capacity of these soils the availability of moisture to pasture was highly dependent on rewetting frequency rather than total rainfall and, second, as a result of this, probably less than 50% of the total annual rainfall was involved in replenishing soil moisture at plant­available depths.

Keywords soil water; models; hill country; evapotranspiration

Received 20 March 1985: revision 2 December 1985

INTRODUCTION

Simulation models of the soil water balance for flat land (Scotter et al. 1979b; McAneney & Judd 1983) estimate changes in soil moisture with reasonable accuracy, and are potentially of considerable value to the agriculturalist. Unfortunately, the soil water balance models developed for flat land cannot be us~d .for hill land of variable slope and aspect, pnnclpally because they assume zero runoff unless the soil profile is at saturation capacity. In hill country, observations indicate that this is not so. In this paper, the development and evaluation of a soil water balance model for sloping land are described.

MODEL CONCEPTS

The model is based upon the daily soil water bal­ance equation (I) where Ri, AEi, ROi, Di, and Si represent the amount of rainfall, actual evapotran­spiration, runoff, deep drainage, and the change in soil moisture, respectively, occurring during day i.

Si = Ri - AEi - ROi - Di (I)

Runoffin this context includes water that moves rapidly through the entire profile via large pores and cracks, bypassing the matrix of the soil and the associated opportunity to contribute to soil moisture rewetting and storage. Deep drainage is water that passes through the profile at times when soil moisture status is greater than field capacity.

Actual evapotranspiration Potential or weather-controlled evapotranspiration (PE) is calculated using the PriestIey-Taylor (1972) method. Empirical estimates of global radiation (Rg) per day (Cal/cm2) falling on a horizontal sur­face (Charles-Edwards 1982) within latitudes lO­SS" only (Equation 2), are transformed (Equation 3) to mm water equivalents and corrected for slope and aspect using Revfeim's (1982) algorithm. Net radiation (Rn) is estimated (Equation 4) using the regression equation derived by Clothier et al. (1982). Mean daily air temperature (Tm) is calculated empirically using Equation 5, (Charles-Edwards 1982), but is not corrected for slope and aspect;

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316 New Zealand Journal of Agricultural Research, 1986, Vol. 29

Rg=(24.3-0.264 LAT)[1 + (0.0186 LAT-O.l2) SIN (21t (DAY + 101)/365)] 238.0 (2)

mm water/cm2 = Rg/54

Rn = 0.62 Rg - 0.24

(3)

(4)

Tm = (32.5 - 0.45 LAT)(l + (0.015 LA T - 0.10) SIN [21t (DAY + 101 - LAT/2)/365)] (5)

ASmax is the maximum soil water storage. The upper level is defined as field capacity (Sic) and the lower level as the field minimum value (Slm) measured in late summer-autumn. This value is lower than wilting point (Swp) since further soil drying can occur following plant wilt and conse­quently extend effective soil moisture storage beyond the level defined by wilting point. The Sim therefore expresses the level to which soil moisture can decline under field conditions. Actual evapo­transpiration (AE) is empirically derived (Equa­tions 6 and 7) and will be predominantly controlled by soil rather than plant factors as soil moisture level approaches Sim.

At levels of available soil water (ASl) greater than an arbitrarily determined critical level (ASc), AE is equal to PE - i.e., weather-controlled. For levels of available soil water less than ASc, AE is con­trolled by soil characteristics. The critical level of available water is defined as:

ASc = ASmax - k X ASmax

The empirical constant k determines when AE is soil-controlled. For example, a high k value (0.7) would imply that AE was at PE rates over a wide range of soil moisture conditions.

When ASi~ASc then AE = PE (6)

When ASi < ASc then AE/PE = ASi/ASc (7)

Soil rewetting Soil characteristics such as structure, organic matter content, and moisture status affect not only infil­tration rate (Dunne 1983) but also the storage capacity of the soil. By representing rainfall inten­sity as daily rainfall, and soil rewetting rate as a function of soil characteristics using daily time steps, runoff can be calculated as the difference between daily rainfall and daily rewetting after allowing for evapotranspiration. In this context the maximum possible daily infiltration into moisture storage would be the difference between saturation capacity (Sse) and field minimum moisture levels. However, on a dry, steepland soil, often only the surface few millimetres of the profile will be re­wetted during a rainfall event, almost regardless of

1.0 ~ ·u '" c. '" tJ

"0 ""iii ;;:: '0 0.5 c o .f:: o c. e

Il... 0.0+------,.----..,-------.-­

o 2 Duration (days)

3

Fig. 1 The soil rewetting function included in the model.

the intensity of rainfall. This does not occur during rainfall of low intensity and several days duration. A layer model with the surface layer controlling the rate of entry of water to the profile was therefore adopted. If surface crusting or hydrophobicity is not a problem, then the major determinant of soil rewetting is the available pore volume, which in clay/silt soils is a function of current soil moisture status. The moisture status of the surface layer of soil before rainfall can therefore be used to deter­mine the rate of rewetting .. In the following model, an empirically derived exponential relationship between the maximum possible rate of soil water recharge and time ensures that duration rather than intensity of rainfall tends to control the rate of soil rewetting. This relationship defines the minimum period of time for the surface layer to rewet from Sim to Sic as 3.3 days (Fig. 1). At levels of ASi < ASmax, the current moisture status of the surface layer is used to determine the maximum available moisture content possible one day later. If ASi > 0.68 ASmax, then the empirical rewetting relationship has no further limiting effect upon soil moisture recharge. Runoff occurs when rainfall exceeds infiltration into moisture storage within the surface layer plus actual evapotranspiration from the surface layer of the soil.

Transfer of moisture Moisture movement down the profile can occur rapidly via large pores and cracks, and may add to subsoil moisture storage. Alternatively downward moisture transfer from fine pores occurs when field capacity storage is exceeded. Because of the diffi­culty of estimating the contribution to subsoil moisture storage by the former mechanism, only downward moisture transfer from a higher soil layer is considered by the model to influence subsoil moisture levels. The model has 4 layers, each 37.5 mm deep and drainage from the jth to the (j + 1)

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Bircham & Gillingham-Soil water balance model

Table 1 Soil parameters of a 37.5 mm layer at the 4 sites.

Saturation Field Field capacity capacity minimum

Soil Aspect (mm water) (mm water) (mm water)

YBE North 18 15 5 South 20 17 7

YBL North 23 19 7 South 23 19 7

layer can occur only when Sj> Sic. The maximum amount per day that can be transferred is

Ssc U + 1) - Sic U + 1)

where Ssc is the moisture saturation capacity of the soil. With the exception of the surface layer, water is retained in the jth layer at levels greater than Sic only when the soil characteristics of the U + 1) layer prevent or slow the transfer of water. It there­fore is possible to have a perched water table and saturated subsurface flow. Deep drainage occurs when water flows from the lowest layer.

EXPERIMENTAL

Gravimetric determinations (0-75 mm) of soil moisture on 2 soil types - Waingaro steepland yellow-brown earth (YBE) of greywacke parent material, and Dunmore yellow-brown loam (YBL) of Mairoa ash parent material (Bruce 1978) - with slopes of about 30 and 20° respectively, were made

317

on both north and south facing aspects from Octo­ber 1970 until September 1973. Measurements were made weekly for the first 8 months and thereafter at 2-weekly intervals. All data were expressed as millimetres of water. The model was developed using the first 12 months of data from the north aspect of the steepland YBE site. The remainder of the available data were used to evaluate (vali­date) the model.

For the purpose of simulation, a pasture rooting depth of 150 mm with root proportions of 0.55, 0.25,0.15, and 0.05 by weight in each off our 37.5 mm deep layers of soil respectively was assumed (Sheath & Boom 1985). Saturation capacities and field capacities and minimums of the soils were estimated from 0-75 mm gravimetric moisture measurements (Table 1). A value of k = 0.1, which implies that AE is primarily soil-controlled, was assumed.

The soil profile was at field capacity at the end of September 1970 when the model runs com­menced. The 2 uppermost'layers of the computed moisture profile were summed to give a profile depth the same as the actual data (i.e., 0-75 mm). Runoff and deep drainage were also computed.

Paired t-tests and regression analysis were used to assess the performance of the model.

PERFORMANCE OF THE MODEL

Comparison with actual data (October 1970-September 1971) Actual and predicted levels of soil moisture were not significantly different for the north facing aspect of the YBE site during the first year (Fig. 2a). The regression for actual v. predicted soil moisture for

Table 2 The sensitivity of predicted levels of soil moisture (0-75 mm) to vari-ation in estimated saturation capacity and k value for the north aspect of the YBE site, during 1970-71 (40 values).

Saturation capacity (mm) k value

Paired (-test 18.0 16.5 19.5 0.1 0.2 0.3

Mean deviation -0.11 -0.97 0.38 -0.11 0.08 -0.40 SD mean 0.61 0.69 0.60 0.61 0.30 0.29 (-test value 0.18 1.41 0.63 0.18 0.27 1.38

NS NS NS NS NS NS Regression Intercept 0.20 2.00 1.10 0.20 2.40 3.00 SD 2.00 2.17 1.82 2.00 1.88 1.92 Coefficient 1.00 0.94 0.92 1.00 0.87 0.86 SD 0.11 0.12 0.10 0.11 0.10 0.10 r2 0.69 0.61 0.71 0.69 0.66 0.64

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318 New Zealand Journal of Agricultural Research, 1986, Vol. 29

(a)

30

20

10 E .§.

~ 0 co

S 40

30

20

0 0

(b)

N D M 1970

Steepland yellow-brown earth (North)

, ,

Steepland yellow-brown earth (South)

A M J J A s 1971

E Steepland yellow-brown earth (North)

.§. O~--------------------------------------------------------------------

Steepland yellow-brown earth (South)

O~r--O--'---N---r---D--+---J--'--F--'---M--'---A--'--M---'--J--'---J--'--A---r~S~

1971 1972

Fig.2 (and opposite) Actual (0----0) and predicted (0----0) levels of moisture (mm) in the 0-75 mm depth of soil on north and south facing aspects of the steep1and yellow-brown earth. (a) I October 1970-30 September 1971. (b) I October 1971-30 September 1972, (c) 1 October 1972-30 September 1973.

this period yielded a coefficient not significantly dif­ferent from unity (Table 2) and with a satisfactory level of correlation (r2 = 0.69).

Predicted levels of soil moisture for the 2 upper­most layers of the soil were not significantly affected

by changes to the estimated level of saturation capacity (at k = 0.1) or changes in k values (at a saturation capacity of 18.0 mm) (Table 2). How­ever, a decrease or increase of 1.5 mm in saturation capacity, while holding k at 0.1, had a substantial

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Bircham & Gillingham-Soil water balance model 319

E Steepland yellow-brown earth (North) ~ OL----------------------------------------------------------------~ co S 40

30~ ,

20 , ,

Steepland yellow-brown earth (South) O~----.-----_,----~----_,----_,~----._----r_----._----~----~----._----

o N D J F M AM J J A S 1972 1973

Table 3 Comparison of actual v. predicted levels of soil moisture (0-75 mm) for the period 1970-73.

YBE

Paired t-test North South

Mean deviation -1.94 -4.18 SO mean 0.45 0.50 n 98 98 t-test value 4.31 8.36

** ** Regression analysis Intercept 3.70 5.90 SO 1.34 1.75 Coefficient 0.91 0.93 SO 0.06 0.06 ,2 0.66 0.67 n 98 98

Regression analysis (intercept = 0)

Coefficient 1.08 1.14 SO 0.02 0.02

effect upon the predicted moisture level of the low­est layer (i.e., 112.5-150.0 mm depth) of soil. For saturation capacities of 16.5, 18.0, and 19.5 mm water per layer, drainage from the lowest layer for the 1970-71 period was 0, 8.5, and 36.2 mm of water respectively. With a value of 16.5 mm satu­ration capacity, the model predicted that the lowest layer would not be rewetted. This was because the low saturation capacity limited water entry into the

YBL

Combined North South Combined

-3.06 -0.94 -3.34 -2.14 0.35 0.54 0.48 0.37 196 101 100 201 8.74 1.74 6.95 5.78 ** NS ** **

3.20 7.20 8.60 7.40 1.04 1.59 1.46 1.12 0.99 0.76 0.81 0.80 0.04 0.06 0.05 0.04 0.72 0.63 0.73 0.67 196 101 100 201

1.12 1.01 1.09 1.05 0.02 0.02 0.02 0.01

surface layer and so induced greater runoff losses than at higher saturation capacity levels. No actual data are available to compare with model predic­tions for the 75-150 mm depth zone at that time.

Comparison with all available data Fig. 2 depicts actual and predicted levels of soil moisture for both the north and south aspects of the steep land YBE soil for the 1970-73 periop.

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320 New Zealand Journal of Agricultural Research, 1986, Vol. 29

40

30

20

E .s ~ C'C

s: 40

iii ... C'C

30

20

s: 40

30

20

(a)

(b)

q ~

~ '~\f\

0 N D J F 1970

o

o N D J F 1971

M

M

A. , ,

,f\ ~r';- q

,~tt; ,0

o

A M 1971

Yellow-brown loam (North)

Yellow-brown loam (South)

J J A S

, , ' 't5

Yellow-brown loam (North)

Ll-O_ 0.. o-o-D--O--U, 0...... /, -"0"" I, ~ ,. 0- -0' .0_ -0- ...0,. ''0.. ,

, ,'.... I

'd 'o...~

Yellow-brown loam (South)

A M J J A s 1972

Fig.3 (and opposite) Actual (0--0) and predicted (0--0) levels of moisture (mm) in the 0-75 mm depth of soil on north and south facing aspects of the yellow-brown loam. (a) 1 October 1970-30 September 1971, (b) 1 October 1971-30 September 1972, (c) 1 October 1972-30 September 1973.

Although there was a general similarity between both results, paired t-test analysis for either north or south or combined data (Table 3) indicated that overall, predicted levels were significantly lower than the actual values, especially on the south aspect. This aspect difference could be expected since the north aspect data included that upon

which model. development was based. The regres­sion analysis of actual v. predicted levels of mois­ture yielded coefficients not significantly different from unity. All the intercept terms were signifi­cantly greater :than zero. When the regression, in a more rigorous test of the I : 1 relationship between actual and predicted values, was forced through the

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Bircham & Gillingham-Soil water balance model

40

30

20

Q; ... CIl

~40

30

20

(c)

o N 1972

D M

origin, the coefficients were significantly greater than unity.

Fig. 3 shows actual and predicted levels of soil moisture for the YBL hill soil sites for the 1970-73 period. Again there was a close similarity between actual and predicted soil moisture levels especially in 1970-71 and in 1973. The paired t­test for the YBL sites, with the exception of the north aspect data, indicated that predicted values were again significantly lower than actual levels of soil moisture (Table 3). Regression analysis con­firmed this. However, when the regression was forced through the origin the coefficient for the north aspect relationship was not significantly dif­ferent from unity. It is therefore apparent that over the 3-year period the model predicted soil moisture conditions on the north aspect of the YBL hill soil more closely than on any other site.

DISCUSSION

This simple soil water balance model was developed from first principles and an assessment of the hill country environment. The same model parameters were used for both the steepland YBE and YBL hill soils, with only saturation and field capacities and minimum moisture levels being varied. Values for radiation and air temperature were derived from empirical functions with some allowance for vari-

321

p-~'

Yellow-brown loam (North)

Yellow-brown loam (South)

A M J J A S 1973

ation in cloud cover related to latitude but not with season. Except for global radiation corrections, the model does not include any modifYing effects of surface slope and is limited to a profile depth of only 150 mm. Nevertheless the predicted soil moisture values provide a realistic interpretation of changes during the year in the 0-7 5 mm depth zone especially relating to rewetting following rain­fall events.

Although the performance of the model com­pared to the actual data was adequate, the overall tendency was to underestimate soil moisture levels, especially during the 1971-72 year. Inspection of Fig. 2 and 3 shows that the initial discrepancy between actual and predicted values of soil mois­ture generally occurred over a 2-4 week period in September-October, particularly on the south aspect. Thereafter until December-January, the pattern of predicted levels followed actual levels of soil moisture. In general the model described the rewetting phase from autumn to early winter rela­tively well. There are several possible reasons for the poorer fit obtained during the drying phase in early spring.

According to the model, water entry into the sur­face layer is restricted if the moisture content of the surface layer is less than 0.68 Sic. However, even if the moisture content of the surface layer was at field minimum moisture level, only 16 mm of rain equally distributed over 3.3 days would be necessary to restore the surface layer to 6eld

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322 New Zealand Journal of Agricultural Research, 1986, Vol. 29

Table 4 Total annual rainfall and predicted runoff and drainage (mm water per year) for all sites in each year.

Total as percentage Year Soil Aspect Rainfall Runoff Drainage of rainfall

1970-71 YBE North 1644 1037 9 63.6 YBE South 1644 1094 133 74.6 YBL North 1644 983 63 63.6 YBL South 1644 1021 ISO 71.2

1971-72 YBE North 1935 1384 13 72.2 YBE South 1935 1416 115 79.1 YBL North 1935 1319 46 70.5 YBL South 1935 1331 122 75.1

1972-73 YBE North 1378 810 18 60.1 YBE South 1378 850 140 71.8 YBL North 1378 735 69 58.3 YBL South 1378 762 165 67.3

capacity. The difference between actual and pre­dicted levels of moisture in spring occurs princi­pally because the layer below the surface layer dries out and, in terms of the model structure, cannot be rewetted until the surface layer has a moisture content greater than field capacity. High evapo­transpiration rates in spring keep the moisture con­tent of the surface layer below field capacity most of the time. Since the transport processes used in the model seem adequate during the rewetting phase it appears that additional processes modify actual soil moisture levels in early spring.

As the biggest discrepancies between actual and predicted levels of soil moisture occur on the south aspects where predicted rates of evapotranspiration are lowest, it seems unlikely that overestimation of transpiration rate is the principal cause of the dis­crepancies between actual and predicted levels of soil moisture. If this was the major cause, the dis­crepancy would be greater on the north than the south facing aspect. Although there was some lati­tude related allowance for cloud cover, the greater seasonal effects could not be incorporated. There­fore, especially during the more cloudy seasons, AE may have been overestimated. This may partly explain why the model best simulated measured soil moisture levels when a relatively low k value was used which ensured that AE rate was predom­inantly soil-controlled. The higher k values derived from the results of Scotter et al. (1979a), McAneney & Judd (1983), and Parfitt et al. (1985a, b) relate to faster growth rate pastures on flat land and measured profile depths of 1 m or greater. The sig­nificance of such factors on the model performance have not been evaluated.

The higher values of measured compared to esti­mated soil moisture levels are probably related

more to the influence of water bypassing the sur­face layer of soil and contributing to the soil mois­ture storage of lower horizons. In addition there is the possibility of subsurface water flow downslope contributing to actual topsoil moisture levels.

On the steepland YBE sites with a definite and recurring track and intertrack microtopography, there is potential for a complex subsurface flow mechanism to occur. Runoff from steep intertrack slopes can collect on lower tracks and after infil­tration may contribute to soil moisture storage and pasture growth downslope. This pattern of uptake by pasture on slopes has been measured using a phosphorus isotope placed under track zones (Gil­lingham et al. 1980).

On the YBL hill soil in particular there is an increasing soil bulk density down the profile to about 700-900 mm depth below the surface. The pattern is similar but less pronounced on the steep­land YBE soil (Gillingham unpublished data). These profile characteristics would be expected to direct deep drainage downslope in preference to vertical movement. This hypothesis is consistent with observations of seepage from lower slopes, and the progression of soil drying and pasture wilt from slope top to bottom. Significant subsurface flow probably occurs in spring as the deviations between actual and predicted soil moisture levels are great­est on southern aspects (Fig. 2 and 3). Subsurface moisture levels and flow could be expected to be greater and persist longer on these areas because of associated low~r evapotranspiration rates.

The results of perhaps greatest practical interest from this study were obtained by totalling esti­mated water losses in runoff and deep drainage from each site (Table4). These revealed that even iftotal evapotranspiration on rain days was considered to

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Bircham & Gillingham-Soil water balance model

come from soil moisture storage, then the equiv­alent of60.1-79.1% of annual rainfall on the steep­land YBE soil, and 58.3-75.1 % on the YBL hill soil did not contribute to plant-available moisture stor­age in the surface 150 mm of soil. This model indi­cated that in the 1970-73 period, the steepland YBE soil stored only 404-598 mm and the YBL soil 451-598 mm of annual rainfall in the topsoil zone. These totals can be considered equivalent to annual AE estimates. When compared with an estimated annual PE for the measurement sites of about 1050 mm per year (Priestley & Taylor 1972), it is evi­dent that these hill slopes are in an effectively dry­land climate. Annual AE may be higher if some subsurface flow in spring contributes to plant-avail­able moisture downslope, and if capillary rise or deeper rooting of plants enables significant utili­sation of subsoil moisture from depths greater than 150 mm (Scotter et al. 1979a, b; McAneney & Judd 1983). If such mechanisms occur, the actual loss of water will be somewhat less than estimated above. However, even in years of low total rainfall, prob­ably less than half is potentially available for pas­ture growth.

On the measurement sites, as on the surrounding hill country, there was no evidence of significant surface runoff by overland flow as indicated by rill­ing or sediment ponding. The predominant method by which excess water movement occurs therefore i.s through the profile via large pores and cracks as noted by Scotter et al. (l979a) for a flat land site in Manawatu, and measured by Watt & Crouch ley (1985) on a gently sloping site in Hawke's Bay.

The application of fertiliser to improve soil fer­tility is the primary means of increasing pastoral production from hill country. Both the rate and degree to which this is achieved depend essentially on the available moisture regime. Although actual rainfall may be high the model suggests that the total effective rainfall may be quite low and similar to many dryland regions of New Zealand. In the absence of irrigation it is apparent that the poten­tial of these hill soils are limited primarily by the frequency of rainfall since their storage capacities are relatively low. In this context introduced pas­ture species are faced with the same limitations as indigenous species.

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Charles-Edwards, D. A. 1982: Physiological determinants of crop growth. Sydney Academic Press.

Clothier, 8. E.; Kerr, J. P.; Talbot, J. S. 1982: Measured and estimated evapotranspiration from well­watered crops. New Zealandjournal of agricultural research 25: 301-307.

Dunne, T. 1983: Relation of field studies and modelling in the prediction of storm runoff. Journal of hydrology 65: 25-48.

Gillingham, A. G.; Tillman, R. W.; Gregg, P. E. H.; Syers, J. K. 1980: Uptake zones for phosphorus in spring pasture on different strata within a hill paddock. New Zealand journal of agricultural research 23 : 67-74.

McAneney, K. J.; Judd, M. J. 1983: Pasture production and water use measurements in the central Wai­kato. New Zealand journal of agricultural research 26: 7-13.

Parfitt, R. L.; Joe, E. N.; Cook, F. J. 1985a: Water use and pasture growth on Judgeford silt loam. New Zealand journal of agricultural research 28: 387-392.

Parfitt, R. L.; Roberts, A. H. c.; Thomson, N. A.; Cook, F. J. 1985b: Water use, irrigation and pasture pro­duction on Stratford silt loam. New Zealand jour­nal of agricultural research 28: 393-401.

Priestley, C. H. 8.; Taylor, R. J. 1972: On the assessment of surface heat flux and evaporation using large scale parameters. Monthly weather review 100: 81-92.

Revfeim, K. J. A. 1982: Estimating global radiation on sloping surfaces. New Zealand journal of agricul­tural research 25: 281-283.

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