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Land and Water
Application of the Biophysical Capacity to Change (BC2C) model to the Little River (NSW)
Ray Evans, Mat Gilfedder, and Jenet Austin
CSIRO Land and Water Technical Report No 16/04March 2004
© 2004, Murray-Darling Basin Commission and CSIRO
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Cover Photograph
Little River at Obley, 29/1/2004
Photographer: Mat Gilfedder © CSIRO
ISSN 1446-6171
Application of BC2C to the Little River
iii
Application of the Biophysical Capacity to Change (BC2C) model to the Little River (NSW) Ray Evans1, Mat Gilfedder2, Jenet Austin2
1. Salient Solutions Australia, Jerrabomberra
2. CSIRO Land and Water, Canberra
March 2004
CSIRO Land and Water Technical Report 16/04
Application of BC2C to the Little River
iv
Table of Contents
1 INTRODUCTION............................................................................................................ 6
1.1 Background and Objectives ................................................................................................... 6
1.2 Application of BC2C ............................................................................................................. 7
1.3 Links between Bio-physical and Socio-economic Modelling ............................................... 7
Scope of Work .................................................................................................................................... 8
2 OVERALL APPROACH TO PARAMETER ESTIMATION.................................... 9
3 GROUNDWATER RESPONSE TIMES IN THE LITTLE RIVER ........................ 10
3.1 Landscape Disaggregation ................................................................................................... 10
3.2 Groundwater Flow Systems................................................................................................. 12
3.3 Obtaining Geometric Properties for each Sub-Catchment................................................... 13
3.4 Groundwater Response Times ............................................................................................. 14
3.5 Groundwater Response Times ............................................................................................. 16
4 PARTITIONING OF DISCHARGE............................................................................ 18
5 EXCESS WATER PARTITIONING........................................................................... 20
6 SALT LOAD MODEL................................................................................................... 22
7 LEVELS OF CONFIDENCE IN PARAMETERS ..................................................... 24
7.1 Variation in Aquifer Properties............................................................................................ 24
7.2 Change in Recharge Due to Land Use................................................................................. 27
8 CONCLUDING REMARKS......................................................................................... 28
9 REFERENCES & FURTHER READING .................................................................. 29
Appendix A – Groundwater Response Model 30
Application of BC2C to the Little River
v
ACKNOWLEDGEMENTS
The authors acknowledge funding from NSW Agriculture and the “National Action Plan for Salinity and Water Quality” for the detailed application of the BC2C methodology to the Little River catchment, through the project: “Estimated Hydrological Responses to Land Use Change in the Little River Catchment”.
The authors acknowledge funding from the Murray-Darling Basin Commission for the development of the BC2C model through SI&E Grant Number D9004: “Catchment characterisation and hydrogeological modelling to assess salinisation risk and effectiveness of management options”, and also through Grant Number D2013: “Integrated Assessment of the Effects of Land Use Changes on Water Yield and Salt Loads”.
6
1 INTRODUCTION
1.1 Background and Objectives This report describes the application of the Biophysical Capacity to Change (BC2C) model to the Little River catchment. The Little River is a sub-catchment of the Macquarie River in the Central West region of NSW, just south of the City of Dubbo (Figure 1).
Dubbo
Yeoval
Wellington
Cumnock
Molong
�
�
�
�
�
Lit
tle
River
Macquarie
River
New
ell
Highw
ay
Mit
chel
lH
ighw
ay
Little River Catchment
Watercourse
Highways
0 20 4010 km
� NSW
VIC
QLD
Little River
Figure 1 Location of the Little River catchment.
The report has two objectives:
1) Document the application and parameterisation of the BC2C model in the Little River catchment (by way of example).
2) Generate groundwater time responses for the Little River.
This report describes how BC2C can be applied at a sub-regional scale, and forms one a series of reports documenting the BC2C model. This work has been undertaking collaboratively between two MDBC funded grants:
• D2013 which has the overall objective to predict the regional scale impacts of afforestation and other land use changes on mean annual and seasonal catchment water yield, groundwater recharge, and stream salinity, and
• D9004 which aims to produce a framework and suitable outputs to ensure that funding and resources for salinity management is targeted towards appropriate management activities.
7
1.2 Application of BC2C Biophysical Capacity to Change (BC2C) is a relatively simple method of modelling the responses of water and salinity to land use change using groundwater response functions. A prototype of this approach was used in the SALSA model developed by ABARE (Dawes et al. 2004), however, substantial development has occurred. Conceptually, a three-parameter logistic function is used to describe the trajectory of salt and water output from each sub-region in the catchment over time. This approach is most appropriate given the scale of the problems being considered within the catchment, the lack of technical data describing the hydrology of the catchment and the structure of the framework that has been developed. There is broad agreement that the shape of the logistic functions is appropriate to the problem, but the challenge is now to estimate the shape parameters using a set of variables inherent in the landscape and that are also easily measurable.
1.3 Links between Bio-physical and Socio-economic Modelling A linked bio-physical and socio-economic model of the Little River based on a Whole Farm approach (the “Little River Catchment Model”) has been developed by the NSW Department of Agriculture to examine economic issues of salinity management and policy development. This will provide a comprehensive description of the impact of land use change on dryland and river salinity and stream flows. The Model will be used to assess the net benefits of land use change in the Little River Catchment, including benefits to stakeholders downstream. It will provide the means to assess the economic impact of alternative policy options aimed at encouraging land use change and the extent to which farming systems would need to change to achieve an economically efficient reduction in river salinity.
BC2C has been used to provide a time series of the hydrological responses to land use change in different parts of the Little River Catchment, with an emphasis on relative differences across the catchment. A number of modelling studies have been undertaken in the Little River Catchment but substantial funds would be required to derive the relevant data from these to calibrate the water and salt responses at the scale required for the economic model.
8
Scope of Work The Little River Catchment Model operates on a sub-regional basis. Hence, each of the chosen sub-regions of the Little River (for instance, Cumnock, Baldry, Yeoval and Suntop/Arthurville) required estimates of the response over time, to changes in recharge, of stream flow, salt load and area of land salinised. Specifically, estimates of parameters for the response function proposed by Dawes et al. (2000, 2004) that relates the annual recharge to annual discharge are required for input to the economic model. Estimates should also be made of the range of possible values of parameters for the response function and provide an indication of the confidence levels.
To estimate the parameters required the following approach was adopted:
• Disaggregate the catchment to hydrologic sub-catchment level to allow representative response times to be calculated for each sub-catchment, both for the landscape character and for hydrogeology.
• Re-aggregated these estimates to the sub-regional level (based on the spatial discretisation from the socio-economic modelling) for input into the economic model.
This re-aggregation will also provide some measure of the variability of response that can be used to assess the final model outputs. Some consideration also needs to be given to whether the excess water partitioning coefficient approach of Dawes et al. (2000, 2004) is appropriate for this modelling exercise, or whether an approach can be adopted that uses available crop water use/soil measurements. This work will also contribute to the documentation of the Little River Catchment Model to ensure the hydrological component is transparent and that the process may be repeated for other catchments.
9
2 OVERALL APPROACH TO PARAMETER ESTIMATION The approach adopted to provide the necessary parameters for the economic modelling was based on the work of Dawes et al. (2000, 2004) which is reproduced in Appendix A.
The work reported here differed from the analysis of Dawes et al in that an attempt is made to specify explicit groundwater flow systems via a consideration of the topography and its stream/catchment network. Once individual catchments or flow system boundaries (objects) had been delineated (Section 3.2), a series of topographic and aquifer properties (Sections 3.1 & 3.3) were used to derive estimates of the parameters needed to fit the response curves (see Section 3.4 and Equation 17).
As with the analysis of Dawes et al., discharge was also partitioned into separate components (see Section 4). This work used a two-component discharge system, as opposed to Dawes et al’s three-component system. As will be discussed below in the section on groundwater flow systems, the definition of discrete groundwater flow systems leads to the assumption that no groundwater flow passes across the identified boundary. This means that the aquifer discharge component of Dawes et al. is effectively zero, and discharge can be resolved between that going to any stream network and that going to the land surface. Threshold values for the onset of discharge from the aquifer to the land surface were calculated for each catchment, using Darcy’s Law and based conceptually on catchment discharge capacity (see Stirzaker et al., 2002).
A simple salt load model (Section 6) was derived and input parameters estimated to allow the model to be applied for each sub-catchment.
Some consideration of the partitioning of excess water between runoff and recharge is given in Section 5 and a discussion of the confidence and sensitivity in parameter estimation is provided in Section 7.
10
3 GROUNDWATER RESPONSE TIMES IN THE LITTLE RIVER
3.1 Landscape Disaggregation The Little River catchment is made up of a series of local scale groundwater flow systems (GFS) (generally <5 km in hydraulic length). It was assumed that a local GFS is coincident with surface topography (see Section 2), and hence a Digital Elevation Model (DEM) could be used for the disaggregation. A stream-network was constructed from the DEM by extending the stream-network upstream until a certain minimum stream contributing area was reached. The minimum contributing area parameter was used to achieve a spatial disaggregation that approximated local knowledge of the distribution of groundwater flow across the broader Little River catchment. Sub-catchment boundaries were then defined using this generated stream-network.
These sub-catchment areas are taken to be approximations of individual groundwater flow systems, and form the fundamental unit for which a groundwater equilibrium time response can be calculated.
Landscape disaggregation – comparison The size of the minimum contributing area, which is required to initiate the stream network, affects the disaggregation. Three areas were considered: 250 ha, 500 ha, and 1000 ha (see Table 1).
Table 1: Comparison of the sub-catchment properties for a range of flow accumulation values.
Stream contributing area
Total number of sub-catchments
Mean sub-catchment area
Zonal thickness
(radius of largest circle which fits within the sub-catchment)
Mean
h=2(hmed-hmin)
250 ha 470 499 ha 775 m 81 m
500 ha 246 951 ha 1065 m 94 m
1000 ha 120 1937 ha 1548 m 113 m
1000-ha (small sub-catchments merged)
93 2500 ha 1787 m
(the mean ellipse length term as used was L=2956 m)
130 m
Sub-catchment areas were defined by using a stream-network with a minimum 1000 ha contributing area. The size was decided upon through:
1. Local knowledge of stream network 2. Assessment of the area of the individual sub-catchment units
Several very-small sub-catchments contained within the final sub-catchment analysis were considered to be an artefact of the disaggregation process. After consideration of the position of identified sub-catchments and how they had been generated by the process, sub-catchments smaller than 1000 ha in size were merged into their neighbouring sub-catchments to obtain a distribution of sub-catchments that was more consistent with the conceptual basis for identification of local groundwater flow systems (see Figure 2).
11
Figure 2: Disaggregation of Little River catchment into sub-catchments (using a 1000 ha minimum contributing area stream network)
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12
3.2 Groundwater Flow Systems A salinity province map is available for the Mid-Macquarie region (Figure 3). This shows the particular areas within the Little River where similar Groundwater Flow Systems (GFS) exist. The Little River catchment consists of Local scale GFSs.
Figure 3: Salinity provinces of the Little River catchment (with 1000ha stream network sub-catchments shown in black),
(see Table 2 for class descriptions)
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3.3 Obtaining Geometric Properties for each Sub-Catchment
Length The characteristic length (L) of each sub-catchment was given as the mean of the major and minor radii of an ellipse which best represents the sub-catchment area (see Figure 4). The ellipse is generated automatically using a command within the GIS. The “major-axis” of the ellipse was not used as a length scale, because the flow-path does not always correspond to this direction.
LminorLmajorLmajor
Lminor
Lmajor
Figure 4: Estimation of sub-catchment flow length using the “mean radius of an ellipse”
Height The height component (h) of the groundwater gradient could not be measured. Unfortunately, the total height drop within a sub-catchment is an unrealistic estimate of groundwater gradient. A more suitable way of estimating the gradient is to take the height term as being “twice the difference between the minimum height and the median height”.
hmax
hmin
hmedian
h
Figure 5: Estimation of the height component of groundwater gradient (h)
14
3.4 Groundwater Response Times
Time-scales A scaling argument is used to relate time-scale of groundwater response to key parameters (hydraulic conductivity, specific yield, aquifer thickness, flow-length, catchment gradient, and recharge rate). Three different processes contribute to the overall groundwater response (Gilfedder and Walker, submitted):
1. vertical filling (t1 = d’ S/ ∆R). (1) 2. lateral movement (t2 = S L2 / K d). (2) 3. gradient driven lateral movement (t3 = S L2 / K h). (3)
where:
d’ unsaturated zone representative thickness (m) d representative aquifer thickness (m) S representative storativity (specific yield) ∆R change in recharge rate (m/yr) L flow length of the GFS (m) K representative hydraulic conductivity of the aquifer (m/yr) h The change in groundwater elevation along the flow length (m)
Combining the time-scales The minimum of the three time-scales will dominate the overall response. In considering a range of catchments where the relative importance of the three processes may vary, a function is needed which can approximate this behaviour in a smooth manner. The “harmonic sum” is a simple way of approximating this behaviour, as it combines the time-responses in such a way that it approaches the minimum when that given process dominates:
321
mharmonicsu
t1
t1
t1
1t
++= (4)
The harmonic sum (tharmonic sum), provides an approximation of a 50% time-response over a range of conditions. It provides a simple way of combining the three time-scales smoothly, and in the absence of detailed modelling, can be used to parameterise a simple functional relationship which exhibits appropriate behaviour. The S-shaped logistic curve gives a reasonable approximation. This simple model of response to change weights changes in recharge to changes in discharge, according to a time scale and rate of change. The logistic function assumes independent annual recharge pulses, that the response is linear and additive, and that recharge from year to year is not correlated.
15
( ){ }slopehalf tttexp1
1D(t)
−+= (5)
where thalf is the time until 50% of the recharge has passed through the system (thalf = tharmonic sum), and tslope defines how steep the central portion of the curve is (and in this case has been set as tslope= thalf /4 ).
Parameterising the time-scales While h and L are determined directly as part of the DEM analysis, the hydrogeological properties can not. For each of the sub-catchment areas, parameter values were estimated using expert opinion for the time-scale equations (see Table 2). These were attached to the Salinity Province map, so that properties for each sub-catchment could be determined by area-weighting.
Table 2: Representative aquifer properties according to each Salinity Province in the Little River
Map unit Salinity Province
Representative aquifer K (m/day)
Representative aquifer
thickness (m)
Representative specific yield
(%)
1 Cudal Group 1 40 5
2 Low Relief Granites 1 25 5
3 High Relief Granites 1 20 5
6 Tertiary Volcanics 5 25 5
7 Permian and Triassic 1 20 5
8 Macquarie River Alluvium 5 50 5
9 South West Alluvium 5 20 5
10 Mesozoic Sediments 1 20 5
12 Ordovician Sediments 1 40 5
13 Dulladerry Volcanics 5 20 5
14 Upper Devonian Sediments 1 20 5
15 Gregra Group Sediments 1 40 5
16
3.5 Groundwater Response Times Groundwater response times were calculated using the timescales described in the previous section. For each sub-catchment:
1) Proportions of each Salinity Province were calculated 2) area-weighted values of K, d, S, were calculated 3) h and L were calculated; d’ was approximated as being equal to d 4) the time for 50% of the groundwater response (half time = thalf) was calculated.
The distribution of these thalf estimates is shown in the Figure 6 and 7.
7
10
5
4
8
6
3
8
3
8
5
8
5
7
5
5
8
7
3
1
10
3
87
3
3
1
7
4
11
2
6
5
9
2
1
8
7
6 5
6
2
6
2
2
5
4 6
3
4
8
5
5
1
3
5
3
1
3
6
3
4
5
2
2
6
5
5
3
3
46
2
4
5
4
3
2
4
4
4
2
3
5
23
2
4
1
32
5
3
4
6
5
2
8
7
3
7
5
10
10
8
79
5
5 86 6
6
25 6
5
62
5
8
8 8
3 8
2
83
5
5
11
0 10 205
Kilometres
Time_resp
0.5 - 1
1 - 2
2 - 3
3 - 4
4 - 5
5 - 6
6 - 7
7 - 8
8 - 9
9 - 10.6
Figure 6: Estimated groundwater response times (time for 50% response=– thalf) for each sub-catchment area.
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17
4.38
4.42
0.0
2.0
4.0
6.0
8.0
10.0
12.0
Value for each sub-catchment
Th
alf
(yr)
Figure 7: Range of 50 percentile response times (thalf) for each sub-catchment in the Little River. The mean and median values are shown (above and below the data).
The thalf value for each sub-catchment was used to parameterise the logistic curve (Equation 5). Figure 8 shows the overall area weighted response for the entire Little River (this is an indicative plot, since the effect of rainfall has not been included, and the amount of change has not been specified).
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 2 4 6 8 10 12 14 16 18 20
Time since change (yr)
Are
a w
eig
hte
d G
W r
esp
on
se
Figure 8: Area weighted Little River groundwater response.
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4 PARTITIONING OF DISCHARGE Discharge from the system (after groundwater response times have been allowed for), is partitioned into that flowing directly to streams (conceptually as baseflow) and that flowing to the land surface (seepage). The mechanism used to calculate this partitioning is related to the discharge capacity of the sub-catchment.
Conceptually, a groundwater system will most likely discharge to streams only under the steady state influence of a pre-development land-use. This assumption may be contravened where there are flat lower parts to uplands sub-catchments, where land discharge may have led to the development of waterlogged grasslands.
As recharge increases, the volume of water being transmitted through the aquifer will also increase. By an understanding of Darcy’s Law (which links the volume of groundwater flow, hydraulic conductivity, aquifer thickness and hydraulic gradient) and a recognition that both hydraulic conductivity and (effectively) aquifer thickness are constants, the increase in flow volume must be accompanied by an increase in hydraulic gradient. At some point in time if the flow volume increases in an unbounded fashion, the increasing hydraulic gradient will rise above the topographic gradient. Land discharge of groundwater will occur where this happens, manifest as the onset of land salinisation. The volume of water that can be transported by the aquifer at the hydraulic gradient just prior to the onset of land discharge has been termed the discharge capacity of the aquifer (Stirzaker et al., 2002).
Clearly, as recharge increases, so does discharge. Prior to the attainment of the discharge capacity, all the increased through-flow volume of groundwater must discharge to the receiving stream. Once the discharge capacity of the sub-catchment has been exceeded a proportion of the additional volume of groundwater (above the discharge capacity) will also continue to flow to the stream due to the increasing hydraulic gradient.
The point where the hydraulic gradient cuts the topographic gradient will be different for different catchments. Clearly, it will occur where the topographic gradient changes markedly (such as at the break of slope), or where it is at its lowest.
The conceptual model employed for this work defines the discharge capacity by an analysis of the topography of each sub-catchment. It takes the topographic gradient for the lowest 10% of the catchment and expresses it as a percentage of the total topographic gradient for the particular sub-catchment. It then assigns the hydraulic gradient for the discharge capacity based on the same proportion of the adopted catchment hydraulic gradient as calculated in Section 3.3. This hydraulic gradient is then applied via Darcy’s Law, with the specified aquifer properties to calculate a volume of groundwater flow. This is then converted to mm/yr of flow based on the sub-catchment area.
19
For example, suppose the hydraulic gradient for the sub-catchment calculated according to Section 3.3 was 0.01 and the total height difference for the same sub-catchment was 100 m . For the sub-catchment, analysis of the topography for the lowest 10% gave a 5 m height difference. Thus, the hydraulic gradient would be reduced to 5% (5 m/100 m) to give a discharge capacity hydraulic gradient of 0.0005. This would then be converted to a flow volume in m3/yr using Darcy’s Law and finally to mm/yr.
As the volume of groundwater discharge rises above the discharge capacity a simple partitioning between stream and land is employed. This is adopted to be in the ratio of 1:9 respectively. That is, the volume of groundwater discharging to the land surface was calculated as 90% of the difference between the total sub-catchment discharge and its Discharge Capacity.
The volume of groundwater discharging to the land is then divided by a discharge rate of 180 mm/yr to enable an estimate to be made of the area of land that might be affected by land salinisation. The value of 180 mm/yr was chosen to represent a typical bare earth evaporation rate for a saline site (that is, at a rate of about 0.5 mm/day).
20
5 EXCESS WATER PARTITIONING The excess water available after accounting for evapotranspiration was estimated using the relationship between land use, evapotranspiration and mean annual rainfall of Zhang et al. (1999). This is a coarse estimate and may introduce errors into the analysis. The discussion below seeks to place the Zhang method into the context of estimates of excess water derived from modelling studies based on soil moisture accounting.
Beverly et al. (2003) used a modelling approach in work in Victoria, the robustness and validity of which was evaluated in the upper Goulburn Broken Catchment in Victoria. They found that
Within this catchment the average annual rainfall ranges between 575-1700 mm and grazing is the dominant land use. Figure 9 shows the comparison between the mean annual evapotranspiration estimates for pasture derived using the broad scale Zhang approach and those derived using the catchment framework (their model).
The lower evapotranspiration results derived using the catchment framework relative to the broad scale Zhang approach are due to the lower fertility assigned to granitic areas within the study area. Unlike the Zhang approach, the catchment framework produces time-series responses at the land management scale rather than the broad scale and also discriminates between individual pasture species.
Figure 9: Modelled Evapotranspiration and annual rainfall relationships compared with the Zhang curves (reproduced from Beverly et al, 2003)
It is noted from Figure 9 that the estimates of both approaches are almost coincident at lower rainfalls and divergent as rainfall increases. It is felt that for the mean annual rainfall typical of the Little River catchment (less than 700 mm/yr) that the Zhang estimator provides reasonable estimates and that these are more or less consistent with the model results from Beverly et al. (assuming that the closeness of fit is applicable to the Little River catchment).
21
In a similar study in Queensland, Yee Yet and Silburn (draft) identified that the key determinants on the amount of deep drainage at any particular site is most controlled by soil properties of plant available water capacity (PAWC), rooting depth and saturated hydraulic conductivity (Ksat). Their study modelled 36 000 combinations of land use, climate and soil properties. They compared the modelled results with those of Zhang and concluded that:
• Variation in soil properties produced considerable variation for any given land use and climate. The variation was between 10 and 20% at mean annual rainfalls of about 600 to 700 mm/yr;
• Model runs of herbaceous plants most closely followed the Zhang curves but with the largest scatter about the central tendency;
• The Zhang curve appeared to over estimate ET for forests; and • Zhang curves did not match the model output for native grasses – the curves were
underestimating ET compared to the model.
In summary, the Zhang curves are a regression fit to a range of observational data worldwide that integrate a number of catchment and scale factors. Using the values derived from the regression will introduce some error into the process.
Modelling results of particular combinations of soils, climates and land uses show that there are gross similarities with the estimates derived from the Zhang curves. In detail, however, there appear to be departures between the Zhang curves and model outputs where specific soil properties have been used.
A model approach may produce a different set of results than those estimated from the Zhang curves, but the issue still remains as to whether these model outputs will be a better estimator of a catchment response given the complexity of the distribution of soil parameters and the need to simplify them as input to soil moisture models.
The ultimate approach would be to do a grid based modelling exercise based on actual descriptions of soils measured in the field. However, it is already known that this exercise would be more expensive to manage than the value of the resource being studied.
22
6 SALT LOAD MODEL The salt model routed salt through each sub-catchment/groundwater flow system and enabled the calculation of both load and concentration at any sub-catchment boundary down the stream network. The model assumed that groundwater salinity could be represented as an average for each sub-catchment, that all the salt that came to the surface via groundwater discharge was removed from the catchment during the annual time step, that the total salt mass that fell with rainfall exited the sub-catchment in overland flow only, and that groundwater didn’t entrain unsaturated zone salt stores as it discharged to the ground surface.
Groundwater salinities were assigned to each sub-catchment by area-weighted estimates derived from the limited groundwater salinity measurements in the catchment and values derived from expert workshops aimed at deriving the groundwater flow system attributes.
Figure 10: Distribution of groundwater salinity by sub-catchment(EC in microSiemens/cm).
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23
The general model was, LANDGWSTREAMGWRUNOFFTOTAL SSSS // ++= (6)
where STOTAL is the total salt mass leaving the sub-catchment and subscripts RUNOFF, GW/STREAM and GW/LAND are the salt mass due to runoff, groundwater discharge to streams and groundwater discharge to the land surface, respectively.
The salt mass at the sub-catchment outlet due to runoff was derived as,
)(10 3 TonnesAMS SALTFALLRUNOFF−××= (7)
where MSALTFALL is the mass of salt delivered via saltfall (assumed to be a constant 30 kg/ha/yr), A is the area of the sub-catchment in hectares and 10-3 is a conversion from kilograms to tonnes.
The salt mass at the sub-catchment outlet due to discharge of groundwater directly to streams was derived as,
GWSTREAMGWSTREAMGW CVS ×= // (8)
where VGW/STREAM is the volume of groundwater discharged to the stream and is calculated using the response conditions developed in Section 3 and subject to the threshold discharge capacity from Section 4, and CGW is the salt concentration of the groundwater.
The salt mass at the sub-catchment outlet due to the discharge of groundwater to the land was derived as,
GWLANDGWLANDGW CVS ×= // (9)
where VGW/LAND is the volume of groundwater discharged to the land and is calculated according to Sections 3 and 4 above, and CGW is the salt concentration of the groundwater.
It can be seen by the latter two equations that the total salt mass due to groundwater is just that due to total groundwater discharge. That is, there is no mechanism to account for the mobilisation of unsaturated zone salt stores.
24
7 LEVELS OF CONFIDENCE IN PARAMETERS The following section provides a simple sensitivity analysis as an indication of the variation in the response time and other key parameters as a result of possible variation in the input parameters. It is not a rigorous analysis. Individual parameters have been varied where there is some justification for variation in the experience of the authors. There has been no attempt to systematically combine parameter variations.
7.1 Variation in Aquifer Properties
Storativity/specific yield A value of 5% was chosen as typical of specific yield for all groundwater flow systems. This is at the higher end of typical values. Figure 11 compares thalf for the assumed case (5%) against a value of 1%. The relationship is linear, so there is a possible reduction by a factor of 5 lower.
0
2
4
6
8
10
12
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91
Sub-catchment
t hal
f (yr
)
S = 0.05
S = 0.01
Figure 11: Sensitivity of thalf to changes in specific yield.
25
Hydraulic conductivity A distribution of hydraulic conductivities was chosen based on discussion with local hydrogeologists when compiling the groundwater flow systems for the area. Figure 12 shows the effect on thalf when hydraulic conductivities are increased by a factor of 2.
0
2
4
6
8
10
12
14
16
18
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91
Sub-catchment
t hal
f (yr
)
base case
Hydraulic conductivity x 2
Hydraulic conductivity x 0.5
Figure 12: Sensitivity of thalf to changes in hydraulic conductivity
Sub-catchment length The length of the groundwater flow path in each sub-catchment was calculated based on approximating each sub-catchment by an ellipse and then taking the average of the major and minor axes. This was chosen as a systematic, but is subjective approach, to reflect the curvilinear nature of the groundwater flow paths. Figure 13 shows the effect on thalf of varying sub-catchment length upward by 1.5 and downward by 1.5. It is likely that each catchment will vary away from the adopted model in a unique way based on its shape (that is, how close it is to elliptical) and the interplay of within sub-catchment topographic influences on groundwater flow.
26
Sub-catchment height A parameter related to height was used together with sub-catchment groundwater flow path length to derive an estimator of catchment hydraulic gradient, as well as input to the calculation of time response parameter t3 (Eqn 15). Figure 14 shows the effect on thalf of variation in the height parameter by a factor of 1.5 increase and decrease.
0
2
4
6
8
10
12
14
16
18
20
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91
Sub-catchment
t ha
lf (y
r)
base case
Length x 1.5
Length/1.5
Figure 14: Sensitivity of thalf to changes in sub-catchment groundwater flow path length
0
2
4
6
8
10
12
14
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91
Sub-catchment
t hal
f (y
r)
base case
Height*1.5
Height/1.5
Figure 14: Sensitivity of thalf to changes in the sub-catchment height parameter
27
7.2 Change in Recharge Due to Land Use
Figure 15 shows the effect on thalf by varying ∆R, in t1 (Equation 13), between 1 and 100 mm. The method has assumed a constant ∆R value of 40 mm/yr as the magnitude of the change in recharge, where delta R should change as land use changes. The effect of the change is small, with a small number of sub-catchments varying up to about 50% in thalf as a result.
0
2
4
6
8
10
12
14
16
18
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91
Sub-catchment
t hal
f (yr
)
1mm
10mm
20mm
100mm
Figure 16: Sensitivity of thalf to variation in the change in recharge due to land use changes
28
8 CONCLUDING REMARKS The approach outlined in this report relies on combining a conceptual understanding of the way in which groundwater flow systems (GFS) operate with a range of parameters in a simple modelling framework. Parameters have been either estimated based on knowledge of the general systems operating in the Little River area, or have been measured from topographic analysis as surrogate estimates of key parameters. As such, very few of the parameters have been derived from actual measurements.
As examined in Section 7, the precise response time is relatively sensitive to variation in chosen parameters. BC2C should be viewed as a structured approach for providing response times across a sub-region, without putting too much weight on the exact values. Given the variability and paucity of data at this scale, BC2C is presented as a broad prioritisation tool for investigating effects of land-use change. If this model is run in a workshop setting, it provides a way of examining the interplay between parameters and response times.
The response times computed for the Little River in this report were much shorter than the generalised estimates in Dawes et al. (2004) of 30-60 years. BC2C gave a median response time of around 4 years (time taken for 50% of the response). The results were discussed with Alan Nicholson (DIPNR, Wellington), who was unsurprised, and felt that his own experience and observations of saline land changes in the catchments matched with response times of 5-10 years. In any case, the results from BC2C should be taken as a relative response time for prioritisation purposes, rather than as absolute response times.
It is acknowledged that all parameters can vary and that the choice of parameter values is to largely subjective. Wherever possible, parameter values have been chosen to fit within bounds that would occur naturally. It is also acknowledged that the combination of parameters as set out in this report is not unique, and it is plausible to parameters the equations with a different but equally valid set of values.
Summary
• Biophysical Capacity to Change (BC2C) uses groundwater flow systems (GFS) as a framework for providing estimates of groundwater response time to land-use change.
• BC2C has provided a simple and transparent method of estimating the relative groundwater response times across the Little River catchment, using readily available data and best available knowledge. It provides a useful data layer for implementation in socio-economic or other biophysical decision support tools.
• BC2C provides a structure for informal parameterisation and discussion within a workshop setting, of the effects of land-use change on catchment water and salt balances, and for exploring sensitivities.
29
9 REFERENCES & FURTHER READING Baker, P., Please, P., Coram, J., Dawes, W., Bond, W., Stauffacher, M., Gilfedder, M., Probert, M., Huth, N., Gaydon, D., Keating, B. Moore, A., Simpson, R., Salmon, L. and Stefanski, A., 2001. Assessment of salinity management options for Upper Billabong Creek catchment, NSW: Groundwater and farming systems water balance modelling, Milestone report for Dryland Salinity Theme 2 Project 3 of National Land and Water Resources Audit, MDBC, Canberra.
Beverly, C., Avery, A., Ridley, A. and Littleboy, M., 2003. Linking farm management with catchment response in a modelling framework, Proceedings of the 11th Australian Agronomy Conference, 2003.
Coram, J.E., Dyson, P.R., Houlder, P.A. and Evans, W.R., 2000. Australian Groundwater Flow Systems contributing to Dryland Salinity, Report by BRS for the Dryland Salinity Theme of the National Land and Water Resources Audit, Canberra.
Cresswell, R.G., Dawes, W.R., Summerell, G.K., Beale, G.T.H, Tuteja, N.K. and Walker, G.R., 2003. Assessment of Salinity Management Options for Kyeamba Creek, NSW: Data Analysis and Groundwater Modelling, CSIRO Land and Water Technical Report 26/03, CRC for Catchment Hydrology Technical Report 03/9, MDBC Publication 12/03, Murray-Darling Basin Commission, Canberra.
Dawes, W.R., Walker, G.R. and Evans, W.R., 2000. Biophysical modelling of surface and groundwater response. Background technical paper prepared for MDBC Groundwater Technical Reference Group.
Dawes, W.R., Gilfedder, M., Walker, G.R. and Evans, W.R., 2004. Biophysical modelling of catchment scale surface and groundwater response to land-use change, Journal of Mathematics and Computers in Simulation 64, 3-12.
Dawes, W.R., and Gilfedder, M. (draft). Background and Algorithms of the
BC2C Model, CSIRO Land and Water Technical Report, draft 2004.
Gallant, J.C. and Dowling, T.I., 2003. A Multi-resolution Index of Valley Bottom Flatness for Mapping Depositional Areas. Water Resources Research. 39(12) 1347, doi:10.1029/2002WR001426, December 2003.
Gilfedder, M., Smitt, C., Dawes, W.R., Petheram, C., Stauffacher, M. and Walker, G.R., 2003. Impact of increased recharge on groundwater discharge: development of a simplified function using catchment parameters, CSIRO Land and Water Technical Report 19/03, CRC for Catchment Hydrology Technical Report 03/6, MDBC Publication 05/03, Murray-Darling Basin Commission, Canberra.
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Gilfedder, M., Stauffacher, M., Walker, G.R. and Coram J., 2002. Characterising groundwater flow systems using a dimensionless similarity parameter, Proceedings of International Association of Hydrogeologists, International Groundwater Conference, 12-17 May 2002, Darwin NT [published as CD-ROM].
Jolly, I., Morton, R., Walker, G., Robinson, G., Jones, H., Nandakumar, N., Nathan, R., Clarke, R. and McNeill. V., 1997. Stream salinity trends in catchments of the Murray-Darling basin, CSIRO Land and Water Technical Report 14/97, Canberra, http://www.clw.csiro.au/publications/technical/tr14-97.pdf.
Nordblom, T., Bathgate, A. & Young, R., 2003. Derivation of supply curves for catchment water yields meeting specific salinity concentration targets. In: T. Graham, B. White, D. Pannell (Eds). Proceedings of the Australian Agricultural & Resource Economics Society Preconference Workshop – Dryland Salinity: Economic Issues at Farm, Catchment and Policy Levels. 11 February 2003, Fremantle, WA.
Smitt, C., Gilfedder, M., Dawes, W.R., Petheram, C. and Walker, G.R., 2003. Modelling the effectiveness of recharge reduction for salinity management, CSIRO Land and Water Technical Report 20/03, CRC for Catchment Hydrology Technical Report 03/7, MDBC Publication 06/03, Murray-Darling Basin Commission, Canberra.
Stirzaker, R, Vertessy, R and Sarre, A., 2002. Trees, water and salt. An Australian guide to using trees for healthy catchments and productive farms. Joint Venture Agroforestry Program, Rural Industries Research and Development Program. Canberra.
Walker GR, and M Gilfedder (draft) Land use change in salt affected upland catchments: Dimensional analysis of groundwater response times, paper submitted March 2003.
Yee Yet, JS, and Silburn, DM, (draft). Deep drainage estimates under a range of land uses in the QMDB using water balance modelling. Queensland Department of Natural Resources and Mines, Toowoomba.
Zhang, L., Dawes, W.R. and Walker, G.R., 1999. Predicting the effect of vegetation changes on catchment average water balance, CRC for Catchment Hydrology Technical Report 99/12, Canberra, [http://www.catchment.crc.org.au/pdfs/technical199912.pdf]
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Appendix A - Groundwater Response Model
The following is a brief discussion of the conceptual basis for the response model adopted in the work described above. It is reproduced from Dawes et al. (2000).
Assuming that recharge is linear and additive to the system, without interference or any correlation in time, we can define a weighting function that translates recharge added in any year to catchment discharge. The equation for discharge is:
( ) ( )∑ −−+= − in1ii0n ttDRRRD (A1)
where R0 is the initial equilibrium recharge, Ri is the recharge in Year i, and n is the current Year. The summation term may be from 1 to n, or from n-j to n where j is some maximum consideration time, and R0 is replaced by Rj-1.
The discharge-transfer function D(t) is a logistic function with the general form:
( ) ( )( )slopehalf tttexp11
tD−+
= (A2)
where thalf is the time such that D(thalf)=0.5, and tslope is a shape parameter related to the slope of the function. At t=thalf, dD/dt=1/(4 tslope). An example curve is shown below.
32
0.0
0.2
0.4
0.6
0.8
1.0
0 4 8 12 16 20
Time (Years) (T)
Res
pons
e F
unct
ion
(D)
D = 1 / (1 + exp[(xhalf - T)/xslope])
In addition, the total discharge D(t) must be split into three components: aquifer discharge (to some other catchment or to the river), stream discharge carrying salt with it, and land discharge causing direct salinisation. The simplest method for this is to define two thresholds - one for the beginning of stream discharge, and one for the beginning of land discharge.
So we can partition D(t) into:
( ) landstreamaquifer DDDtD ++= (A3)
( ) ( )
( )⎩⎨⎧
><
=min
min
minaquifer DtD,
DtD,
D
tDD (A4)
( )( )
( )( )⎪
⎩
⎪⎨
⎧
><<
<
−−=
max
maxmin
min
minmax
minstream
DtD,
DtDD,
DtD,
DD
DtD
0
D (A5)
Dland is inferred by difference between the three other quantities. The area of land salinised can be estimated by dividing Dland by a suitable maximum rate, which may be reverse-engineered from other SAP work, or by proportional change to areas estimated from other SAP work.
33
We anticipate that for many systems in Australia, D(t) will already be greater than Dmax. For some areas without surface drainage, Dmin = Dmax.
0
5
10
15
20
25
0 5 10 15 20 25 30
Time (Years)
Dis
char
ge (
mm
)
IncrementalStep Change
IncrementalRecharge Rate
Results of running a simple scenario are presented above. Discharge varies for an incremental increase in recharge (red) versus a step increase from 10 to 20 mm at Time Zero (green).
As a second example, the 1-dimensional groundwater model FLOWTUBE was run for an idealised aquifer, perfectly rectangular with uniform hydraulic and geometric properties. The recharge rate was step changed at Time=0 from 1000 m3/day to 2000 m3/day. The resulting discharge from the FLOWTUBE model was fitted to a response from the discharge-transfer function model, and is shown in the following figure.
34
500
1000
1500
2000
2500
0 10 20 30 40 50
Time (years)
Dis
char
ge
(m3 /d
ay)
Analytic Modelthalf=22, tslope=6
FLOWTUBEGroundwater Model
