Numerical Simulation of Soil Water Flux
S.1 Introduction
7.3 Results and discussion
7.3.1 A preliminary investigation
7.3.1.1 CONSERVB model calibration phase
Table 7.1 Soil system geometry and initial values for the two simulations.
INITIAL VALUES
JULIAN DAY 74# JULIAN DAY 89#
LAYER
SOIL THICK- WATER WATER
LAYER NESS CONTENT TEMP CONTENT
NUMBER m m3m-3
°c
m3m-31
\~~)
0.205 22.0 0.2302 O. 1 0.205 20.6 0.230
3 0.01 0.261 19.9 0.227
4 0.01 0.261 19.4 0.227
5 0.02 0.276 18.6 0.232
6 0.02 0.282 18.1 0.225
7 0.02 0.282 17.6 0.225
8 0.02 0.277 17.3 0.212
9 0.03 0.277 17.1 0.212
10 0.05 0.279 16.8 0.210.
11 0.05 0.260 16.6 0.210.
12 0.05 0.245 16.6 0.210
13 0.05 0.230 16.6 0.210.
•
14 0.05 0.230 16.6 0.210
#
•
Initialisation on julian day 74 was at 1200 hours.
Initialisation on julian day 89 was at 0800 hours . Estimated values.
cumulative evaporation was more than 4 mm above the measured value by julian day 86. It was apparent therefore, that the CONSERVe model was not accurately
simulating the soil water and energy balances when used with the previously specified initialisation values and Inputs. The model inputs were subsequently re-examined. For reasons that were discussed previously (Section 5.4), the hydraulic conductivity-water content relation was regarded as being only an approximation and, in the absence of experimental measurements, its accuracy could not be confirmed. For subsequent evaluation of the CONSERVe model the 'A' horizon K(9v) function was adjusted in such a way that model predictions for the first drying cycle matched the measured real-
system behaviour as best they could.
Table 7.2 Parameters used in the initialisation of CONSERVB for the two simulations.
PARAMETER
ROUGHNESS COEFFICIENT (zo) MEAN TOTAL POROSITY
- A horizon - e horizon SATURATED HYDRAULIC
CONDUCTIVITY ('A' horizon)
SOIL THERMAL CONDUCTIVITY (solid constituents only)
VOLUMETRIC HEAT CAPACITY OF DRY SOIL
VALUE 2.32 mm
0.56 m3m-3 0.46 m3m-3
6.0x10-4 m's-1 4.47 Wm-1 K-1
1.02x106 Jm-30C-1
The calibration of the CONSERVB model using the K(9v) function was achieved Simply by a trial and error process. If, when using the 'modified' K(9v) function, the model predictions provided a good description of real-system behaviour for both drying cycles then the model could be considered to be giving a valid solution. The 'B' horizon K(9v) function was left unchanged from the original Jackson (1972) estimation. This
estimation could reasonably be expected to be more accurate in the 'B' horizon than the 'A' horizon because of the smaller macro-pore volume, and probable greater uniformity of pore geometry.
Figure 7.4 Generalised shortwave albedo-soil water content input function.
20 18
....
16:-.:
OW' 140
"
CD 12.c ca
CD 10
>
ca ~ 8
- ...
0..c 6
en 4 2
0 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Water content Ct., v Iv)
To evaluate the sensitivity of the CONSERVB model to changes In the K(9v) function a log-linear regression function was fitted to the data pOints previously calculated using the procedure of Jackson (1972). The regression function was:
K
=
exp (0.688 9 v - 37.7)r 2 = 99.6%
. .. (7.1)
where K is hydraulic conductivity (m s-1) and 9y is water content (m3 m-3). The log-linear regression function (denoted "i') and the data pOints estimated using the Jackson procedure are shown in Figure 7.1. The CONSERVB model was run for the
first drying cycle initialised with the data points (the model interpolates linearly between these) and with the regression function. The results (Table 7.4) show an increase in cumulative evaporation of 2.5 mm from using the linear regression function. The high r2 value of the regression shows the regression function and the Jackson estimations to be very similar and hence the CONSERVe model appears very sensitive to the K(9y) input function.
A log-linear function between the measured hydraulic conductivity at 40% 9y (3.00X10-5 m S-1) and a value of 3.0x1 0-17 m s-1 at 4% 9y was substituted into the CONSERVe model for evaluation (function Iii, Figure 7.1). The results (Table 7.4) show a 10 mm decrease in cumulative evaporation during the first drying cycle as compared to the results using the K(9y) function estimated using the Jackson procedure. This result further emphasises the sensitivity of the CONSERVe model evaporation predictions to the K(9y) input function.
The log-linear K(9) function shown as 'ii' in Figure 7.1 was identified as a function with which the CONSERVe model gave good estimates of evaporation (Table 7.4) (refer to Section 7.3.2). As with the other K(9y) functions considered, the measured hydrauliC conductivity at 40% 9y remained unchanged as a part of the function. A log-linear function might provide a better approximation of the actual K(9y) function at 9y values greater than 12% than at lower values. To investigate this aspect further the
CONSERVe model was again run for the first drying cycle this time with a K(9y) function identical to function 'II' in Figure 7.1 at 9y values of 12% and greater, but with a
hydraulic conductiVity value at 4% 9y reduced to 3.0x10-17 (from 1.55x1 0-16 in the 'ii' function). This change had no effect on either the daily or cumulative evaporation predictions from CONSERVe. The log-linear 'ii' function in Figure 7.1 will be used as the 'A' horizon K(9v) function In the CONSERVe model for the subsequent model evaluation stages.
The extreme sensitivity of the CONSERVe model to the K(9y) input function in predicting evaporation is expected. During the field drying cycle the soil surface quickly becomes dry and thereafter the rate of evaporation is determined by the rate that water can be transported through the soli profile to the sites of evaporation. This rate of water transport is directly influenced by the soil hydraulic conductivity.
Table 7.3 Average dally meteorological input for the two simulation periods.
DAILY
JULIAN TOTAL MEAN AIR TEMPERATURE DEW POINT TEMP
DAY SOLAR WIND-
°c °c
RADIATION SPEEL
(1989) MJ m-2 m s-1 MIN MAX AVER MIN MAX AVER RUNI
74 20.0 6.05 12.9 25.9 17.6 4.5 12.3 8.1 75 20.5 7.98 10.3 24.3 17.1 -5.4 8.4 0.2 76 14.8 4.25 4.7 14.8 10.2 -3.5 3.0 -0.1 77 20.2 4.57 4.2 22.6 12.8 0.2 8.8 5.1 78 20.0 6.02 11.4 22.6 17.0 -0.8 9.2 4.9 79 6.7 6.31 10.5 17.4 12.9 -0.3 7.0 4.0 80 18.4 4.66 4.4 14.8 10.1 -0.9 2.4 0.8 81 13.4 3.43 3.9 17.7 11.1 0.8 8.9 5.7 82 12.0 5.30 10.5 19.6 14.7 7.6 12.0 9.9 83 18.3 6.42 10.7 27.5 18.6 7.8 12.9 11.5 84 16.7 5.15 9.5 23.6 14.8 3.4 9.6 7.7 85 18.3 4.65 8.7 21.6 13.7 3.3, 9.6 7.2 86 18.3 4.10 3.7 22.9 12.6 1.5 10.7 6.3 RUN II
89 17.3 4.59 7.6 23.2 13.3 4.4 9.5 7.0 90 14.1 3.75 10.4 18.0 13.0 6.7 10.3 8.6 91 16.7 4.73 8.5 21.4 13.3 6.0 12.3 8.7 92 16.7 3.48 4.8 17.0 11.1 2.7 10.1 7.0 93 15.6 3.44 5.7 17.7 11.7 3.1 10.0 7.3 94 16.5 2.85 7.7 19.8 13.2 4.3 11.0 7.8 95 16.5 4.09 3.3 19.8 11.1 0.8 10.9 6.8 96 13.9 3.48 9.8 18.6 12.9 8.0 9.8 8.7 97 15.9 6.43 10.1 20.6 14.6 7.9 12.7 10.2 98 6.5 3.78 7.7 15.9 12.4 6.0 12.0 9.7 99 13.0 3.75 7.1 15.0 11.4 0.2 6.8 4.4
Table 7.4
JULIAN DAY NUMBER
74 75 76 77 78 79 80 81 82 83 84 85 86 TOTAL
*
The effect of unsaturated hydraulic conductivity on simulated evaporation.
EVAPORATION RATE (mm d-1)
MEASURED SIMULATED
* AVER. STD DEV JACKSO~
K( &v) Fl NCTION
I II III
6.3 0.7 7.0 7.0 6.7 5.8
3.5 0.8 4.7 5.8 3.0 1.7
1.3 0.3 1.9 2.0 1.2 0.9
1.0 0.4 1.9 1.9 1.3 0.7
1.5 0.6 2.3 2.6 1.8 1.4
1.0 0.2 1.0 1.1 0.8 0.5
1.1 0.2 0.9 1.0 0.6 0.5
0.1 0.2 0.7 0.7 0.5 0.3
1.4 0.1 1.6 1.7 1.5 1.3
0.7 0.2 0.9 0.9 0.6 0.5
1.3 0.3 0.7 0.9 0.6 0.4
0.2 0.1 0.6 0.9 0.4 0.4
0.6 0.1 0.6 0.8 0.5 0.4
20.0 24.8 27.3 19.5 14.8
The hydraulic conductivity-volumetric water content (K(9v)) functions referred to as JACKSON, i, Ii and iii are described as follows:
JACKSON. Data points estimated using procedure of Jackson (1972) with the exception of K at 4% &v which was estimated from log-linear regression.
i. Log-linear regression line through the data points estimated from the Jackson (1972) procedure.
Ii. Straight line (log-linear) between measured K value of 3.00x1 0-5 at 40%
9v
and K value of 1.55x10-16 at 4% &v.iii. Straight line (log-linear) between measured K value of 3.00x1 0-5 at 40%
9v
and K value of 3.0x1 0-17 at 4% &v.Refer to Figure 7.1 for graphical presentation of the K(&v) functions described here.