A modified model

The B&G model treats the pasture root zone as four separate layers, each of which is 37.5 mm thick, and then uses the simulated water content of the top 37.5 mm of soil to decide whether or not repellency limits infiltration. Infiltrating water has to cascade through all four layers before any excess drains into the deeper subsoil. Unverified assumptions had to

be made about the cascade process and the relative amounts of water uptake from the four layers.

To obtain a simpler model while preserving the feature of limited infiltration when the topsoil is dry, we calculated two daily water balances in parallel, as advocated by Scotter et al. (1979b) and Woodward et al. (2001) in order to obtain more realistic evaporation estimates during rewetting. The main (first) water balance is similar to that employed by Coulter (1973). It assumes an available water-holding capacity (Wa) for the root zone and

when this is exceeded, surplus water is lost immediately as drainage (D) or surface runoff. Evaporation (E) proceeds at the reference crop rate (E0) if available water is present, and

drops to zero once it is used up. The available water in the root zone at the start of the next day (Wn+1) is found in the usual way as

Wn+1 = Wn + I – D - E (1)

where I is the daily infiltration from rainfall on day n. Figure 4.2 suggests a value between 80 and 110 mm for the available water-holding capacity of the root zone. A value of 87 mm was chosen for Wa, as this was the difference between the two curves in Figure 4.1(b) and

the largest measured change with time in water storage in the top 350 mm of soil. Figure 4.1 indicates that there was uptake from below the 350 mm measurement depth, so this value will almost certainly be an underestimate of the total available water-holding capacity.

Figure 4.2 Modelled (

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The second water balance is specifically associated with the top 50 mm of soil and is calculated in parallel in much the same way, but a smaller available water-holding capacity (Ws,a) is assumed and the evaporation from the topsoil (Es) is estimated as some fraction of

E. The soil water content in the top 50 mm of the two N facing slopes ranged from

approximately 0.2 to 0.5 m3/m3 (Figure 4.3); therefore the available water storage capacity in the top 50 mm (Ws,a) was taken as 50 x (0.5 - 0.2) = 15 mm and the unavailable water as

Figure 4.3 Modelled (

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The amount of water uptake from the top 50 mm of soil depends on the root distribution and the dryness of the topsoil relative to the rest of the root zone. When the whole root zone is at field capacity, uptake will be largely dependent on the root density, so a large fraction of this uptake will be from the topsoil where the root density is the highest. Consequently, the topsoil initially dries out faster than the soil underneath, leading to a decreasing fraction of the uptake being tapped from the topsoil as the remaining water there becomes less available to plants. Trial and error suggested that Es (the uptake from

the top 50 mm) is reasonably well described by the equation

Es = E0Ws / (2Ws,a) (2)

Thus, at field capacity, half the water uptake by pasture is from the top 50 mm, with the fractional uptake decreasing in proportion to the available water remaining as the top 50 mm dries out.

Bircham and Gillingham (1986) used the Priestly and Taylor (1972) equation to estimate E0,

with Revfeim (1982) equations to estimate the effects of slope and aspect on solar radiation. However, rather than using actual solar radiation and air temperature data in the Priestley-Taylor equation, they used crude estimates of these variables obtained from empirical equations with only the latitude and Julian day as inputs, and not calibrated for New Zealand conditions. We also used Revfeim (1982) equations to correct the incoming radiation for slope and aspect, but used the version of the Penman-Monteith equation described by Allen et al. (1998) to estimate E0. The nearest NIWA site with solar radiation

data for the period of the study was at East Taratahi, about 30 km S of the site. Solar radiation, air temperature, dew point and wind run data from there were used to obtain daily estimates of the reference crop evaporation (E0). E0 is considerably less spatially

variable than rainfall, so obtaining proximal meteorological data was not as critical to its calculation.

Figure 4.4 Modelled drainage (+), repellency-induced runoff () and measured surface runoff

(for left- and for right-paired plots) for (a) 30oN (30o slope N aspect site), (b)

20o_{N (c) 30}o_{S, (d) 20}o_{S and (e) 30}o_{E (}

and  for sub-catchment I;  and  for sub-

It is acknowledged that using any estimate of E0 in hill country is, to some extent,

problematic as the assumptions implicit in its definition are not met. These assumptions include strictly vertical transfer of heat and water vapour with no advection in the air immediately above the pasture. Thus it only applies to ‘an extensive surface of green grass of uniform height’ (Allen et al. (1998), p. 23) which hill country, by definition, is not. Furthermore, hill country induces local updrafts and downdrafts, violating the neutral stability conditions implied in estimates of the aerodynamic resistance in the Penman- Monteith equation and its equivalent empirical factor in the Penman equation. Therefore, it remains to be shown that the above violations are minor enough to make conventional E0

estimates sufficiently accurate for use in water balance calculations in hill country.

The only meteorological measurement at the site was the cumulative rainfall between relatively infrequent site visits. However, daily rainfall and E0 values were needed for the

model. To derive daily rainfall estimates, data from Eastry Station (about 5 km away) were used in conjunction with the cumulative data from the trial site. Over the study period, the total rain at the site was only 75 % of that at Eastry Station, but a plot of the rainfall at the site and at Eastry for each of the sampling periods showed a strong correlation between them (R2 _{= 0.82). So, to obtain daily rainfall estimates, the daily rainfall at Eastry was}

multiplied by the total rainfall at the trial site for each period and divided by the corresponding rainfall for the equivalent period at Eastry.

Bircham and Gillingham (1986) assumed a critical moisture content of 68 % of field capacity. At moisture contents greater than this, they assumed that repellency effects (and therefore reduced infiltration) did not occur. At moisture contents smaller than the critical value, they use an exponential recharge function to relate the reduced infiltration rate to the topsoil water content. Given the lack of detailed data on repellency behaviour and the use of crude daily rainfall totals rather than detailed rainfall intensity data, we believe that a simpler, if somewhat similar, infiltration rate model is warranted. Trial and error led us to assume that when the water content in the top 50 mm of soil (Ws) is less than 0.25 m3/m3, and thus the

available water there (Ws) is less than 2.5 mm, the daily infiltration is limited to a set

maximum (Ir) of 5 mm. Otherwise, all the rainfall infiltrates and I = P where P is