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Modelling the flow regime of an arid zone floodplain river, Diamantina River, Australia
Environmental Modelling & Software 18 (2003) 693–703 www.elsevier.com/locate/envsoft
Modelling the flow regime of an arid zone floodplain river, Diamantina River, Australia J.F. Costelloe ∗, R.B. Grayson, R.M. Argent, T.A. McMahon Centre for Environmental Applied Hydrology, CRC for Catchment Hydrology, Department of Civil and Environmental Engineering, University of Melbourne, Victoria 3010, Australia Received 22 March 2002; received in revised form 19 September 2002; accepted 19 December 2002
Abstract Arid zone, ephemeral rivers are characterised by discharge decreasing downstream in the lower reaches due to transmission losses. Modelling the flow regime of these rivers requires data on the spatial and temporal distribution of transmission losses in these reaches. In this study, a hydrological model is developed for a 330 km reach of the Diamantina River in southwestern Queensland, where the floodplain width varies from 5 to 60 km. Analysis of gauging station data at each end of the reach indicates that transmission losses are between 70 and 98% for floods with total discharge ⬍ 2300 GL. The flow routing and transmission losses are modelled using a grid-based, daily time-step conceptual model incorporating flow routing algorithms. Satellite images are used to identify the flow-paths used by the range of flood sizes and to identify threshold flow volumes for initiation of flow into new flow-paths. The grid-based approach allows for representative routing of flow through the reach and representation of spatial variability in transmission loss processes, including losses resulting from evaporation, channel/floodplain infiltration and terminal flow storage. A combination of gauging station data and satellite images is used in the calibration of the model parameters. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Ephemeral river; Arid zone; Transmission loss; Flow routing
1. Introduction 1.1. Arid zone floodplain rivers Arid zone (dryland) ephemeral and intermittent rivers are characterised by discharge decreasing in the lower reaches due to transmission losses (Knighton and Nanson, 1997). Many of these rivers flow into arid areas with low population bases and so there tends to be a paucity of gauged hydrographic data describing their flow regimes. Modelling the flow regime of these rivers requires data on the spatial and temporal distribution of transmission losses in the lower reaches. The interplay between discharge and transmission losses determines the extent and pattern of flow in most internally draining dryland rivers (Tooth, 2000) with major consequences
for the ecological response, and water resource and ecological modelling of the river system. Areas of enhanced transmission loss can have a high biological productivity as water loss from infiltration can support important areas of vegetation growth and in-reach surface water storages provide temporary refuges and resources for arid zone fauna. The complex flow paths and large transmission losses in dryland rivers, in combination with the paucity of hydrographic data, present challenges to the modelling of the flow regime (Knighton and Nanson, 1994). Transmission losses are due to the following factors (Knighton and Nanson, 1994): 앫 Infiltration to channel store and/or floodplain soils, 앫 Evapotranspiration, and 앫 Ponding in terminal storages, such as ephemeral pools, channels and other wetlands.
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Corresponding author: Tel.: 61-3-83447238; fax: 61-3-83446215. E-mail address: [email protected] (J.F. Costelloe).
The relative importance of these factors with respect to hydrology varies among arid catchments, depending
1364-8152/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1364-8152(03)00071-9
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on characteristics such as the size of the catchment, stream gradient, stream/floodplain sediments and seasonal timing of flow. Studies of small to medium sized catchments with low to moderate gradients in Arizona (Walters, 1990), India (Sharma and Murthy, 1995) and South Africa (Hughes and Sami, 1992) have found that infiltration to the near-surface channel aquifer was the major cause of transmission losses. The Orange River in South Africa flows through hot, arid regions with high evaporation rates and a study of that river (McKenzie and Craig, 2001), identified evapotranspiration as the principal cause of transmission losses. That study assumed insignificant losses due to bank storage or deep infiltration as the Orange River is underlain by bedrock and found evapotranspiration losses to be in the same order of magnitude as Class-A pan evaporation data for the region. In addition, the complex flow patterns of dryland, low gradient rivers enhance the potential for water loss to terminal in-reach storage. Transmission losses due to terminal flow storage in Australian dryland rivers and streams occur over a large range of flood magnitudes. Terminal flow storage was the primary immediate cause of transmission losses observed in a sub-bankful flow event in an arid zone stream with the transmission loss rate higher (13.2% per km) than for a bankfull event (5–6.9% per km, Dunkerley and Brown, 1999). Terminal storage is also recognised as an important loss process in flood events occurring in Cooper Creek, Lake Eyre Basin but was not quantified in comparison to other transmission loss processes (Knighton and Nanson, 1994). 1.2. Diamantina River, Lake Eyre Basin
The headwaters of the Diamantina River occur at elevations of 200–350 m in central Queensland. The entire river length is 1000 km to its terminus at Lake Eyre North (as the Warburton river) and its catchment area is 160,000 km2 with an average gradient of only 2.7 x 10 - 4m/m. The Diamantina River is a major river of the Lake Eyre Basin and the major contributor to Lake Eyre (Kotwicki, 1986). The lower and middle reaches are characterised by a complex system of braided/anastomosing channels and wide floodplains. Like many arid zone rivers, the Diamantina has few gauging station records along its 1000 km length with only one gauging station currently operating at Birdsville (began in 1949), one station at Diamantina Lakes that was decommissioned in 1988 and another station at Monkira that collected only flood-height data (Fig. 1). The catchment upstream of Diamantina Lakes comprises an area of 54,130 km2 and contains the greatest number of tributaries, highest elevation and highest rainfall. Rainfall is strongly summer dominant and related to the north Australian monsoon season. The median annual rainfall varies between 200–400 mm and the precipitation gradient decreases moving downstream. Large flood events are associated with monsoonal rainfall pushing further south into the Diamantina catchment and so large floods are often associated with heavy rainfall in the lower reaches. During moderate flood events the rainfall is more commonly confined to the upper catchment. The middle catchment, between the Diamantina Lakes and Birdsville gauging stations, has an area of 61,075 km2 and a river length of 330 km. The width of the channel/floodplain increases up to 60 km and the floodplains are dominated by self-mulching, cracking
The arid zone floodplain rivers of the Lake Eyre Basin, one of the world’s largest internally draining basins, have a number of distinguishing features that result in these rivers having amongst the most variable flow regimes in the world (Puckridge et al., 1998; Knighton and Nanson, 2001). The rivers develop over very low gradients and commonly have complex flow paths with extensive braided/anastomosing channel systems, resulting in floods with slow travel times (weeks to months). The rivers have greatly varying widths of active channel and floodplain. During large flood events, floodwaters can inundate thousands of square kilometres and the floodplain can be up to 60 km wide. The rivers predominantly transport clay-sized particles and areas of significant floodplain expansion and wetland development are covered by cracking clays (Nanson et al., 1986). Floodplain infiltration losses may be limited by the sealing of the swelling clay floodplain substrate once their crack capacity is exceeded (Knighton and Nanson, 1994). The flow regimes of these rivers are dominated by late summer flow events resulting from highly variable monsoonal related rainfall in the upper catchments.
Fig. 1. Location map of Diamantina River catchment (outlined). Gauging or flood height stations at Diamantina Lakes (1), Monkira (2) and Birdsville (3) are shown as triangles.
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clay soils. The aridity of the catchment increases downstream and the mean annual rainfall at Birdsville is only 169 mm and still summer-dominant. 1.3. Modelling approach The paucity of data regarding the hydrological characteristics of the Diamantina River catchment and its large size precludes the use of a data-intensive, physically based modelling approach. This study uses an initial inductive (“top-down”) approach by analysing available gauging station data in order to determine which elements need to be incorporated into the model structure for this catchment. A semi-lumped, conceptual model is then developed for the catchment that incorporates calibrated algorithms describing the hydrological processes that appear to be of most importance from the data analysis. An advantage of this approach is that it allows for testing of specific hypotheses regarding the behaviour of the catchment and arguably provides better insights into the physical processes driving the hydrology than does a purely inductive modelling approach. This approach is not a purely data-based, mechanistic approach as recently advocated by Mwakalila et al., (2001) as the initial data analysis is separate to the model construction and calibration. The use of a relatively simple conceptual model developed in conjunction with inductive data analysis also allows for the construction of a parsimonious model structure. This is a vital feature of any model developed for the data-poor environment of the Lake Eyre Basin. Limited work has been done on the modelling and quantification of the processes involved in transmission losses in the rivers of the Lake Eyre Basin. Analysis of gauging station data to determine transmission losses in a 420 km reach of Cooper Creek in the Lake Eyre Basin (Knighton and Nanson, 1994) demonstrated that the losses were extremely large and varied non-linearly with discharge. A simplified, whole of basin modelling approach was taken by Kotwicki (1986), using the RORB model (Laurenson and Mein, 1990) which included the Diamantina catchment. A more detailed rainfall-runoff-routing model was developed for Cooper Creek (Schreiber, 1997) using the Sacramento and IQQM models. In that study, streamflow was routed along a link-node representation of the channel system using a modified Muskingum routing procedure where the ‘k’ parameter varied as a function of discharge. The approach allowed for explicit flow routing through a simplified channel system and incorporated non-linear routing and transmission loss behaviour as discharge increased. The impact on transmission losses of variable flow paths used by different sized flood events was not addressed and the differing transmission loss processes were not considered separately. This study presents results from the application of a
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daily, semi-lumped, grid-based conceptual model of the flow regime of the Diamantina River, using remotely sensed data for model development and calibration. Gauging station data from the 330 km reach of the Diamantina River, between Diamantina Lakes and Birdsville, are analysed to determine the magnitude of transmission losses as a function of discharge. The hypothesized major loss processes of evapotranspiration, infiltration and terminal ponding, are modelled and their relative importance assessed. The grid-based model developed for the reach is calibrated and tested against gauging station data.
2. Analysis of flow data 2.1. Methodology Following the approach of Knighton and Nanson (2001), the analysis of flow behaviour using gauging station data from the Diamantina River used an eventbased methodology. Only two gauging stations exist on the Diamantina River. A gauging station at Diamantina Lakes (see Fig. 1) operated between November 1966 and December 1988 but has a poor rating (3% of estimated maximum discharge). However, cross-section and channel slope analysis of the Diamantina Lakes site has allowed discharges to be calculated up to the maximum measured stage with a reasonable level of confidence (Bullard et al., 2002). This station provides the only hydrological dataset for the upper reaches of the river. In the lower reaches, a more reliably rated (40% of estimated maximum discharge, 84% of maximum stage) gauging station operates at Birdsville, with records beginning in 1949. The maximum gauged discharge at Birdsville occurred at the peak of the fifth largest flood recorded at the gauging station since 1949. Midway between Diamantina Lakes and Birdsville, the Monkira station has recorded stage height data (often eventbased) between 1949–1962 and also recorded some later large flood events. Flow pulses at the Diamantina Lakes gauging station were correlated with flow pulses at Birdsville and transmission losses and travel times were compared. The correlation of pulses over the 330 km reach was facilitated by the flow occurring as discrete events and often starting and ending in zero flow at the upper and lower ends of the reach. Correlated flow events often contained more than one peak (particularly at the upstream gauging station) but had one welldefined maximum flow pulse peak at the downstream end. Travel times for flow events were calculated from the timing difference between the days of maximum discharge at the upstream and downstream gauging stations. A focus of the analysis of gauging station data is to derive information regarding the transmission losses and routing behaviour over a range of discharges. The pos-
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ition of the gauging stations downstream of long channel reaches precludes detailed examination of likely runoff processes in isolation from modification of the flow pulse through the channel system. 2.2. Results and analysis of flow data The degree of transmission loss between the two gauging stations is shown in Fig. 2 and illustrates very high losses in this reach, that vary non-linearly with discharge. The plot shows the ratio of downstream to upstream pulse volumes on the y-axis and the upstream input pulse volume (Diamantina Lakes) on the x-axis. Flow pulses with significant input from downstream of Diamantina Lakes have not been removed from the data. The transmission throughput varies non-linearly with flood size, with transmission losses of 70–98% for flood events ⬍ 2300 GL total volume at Diamantina Lakes and a maximum loss for floods of approximately 2000– 2200 GL total volume. The sharply increased transmission throughput of floods with total volumes of ⬎ 2300 GL is considered to reflect very significant runoff input from downstream of Diamantina Lakes due to heavier rainfall in the lower reaches associated with large floods (southerly incursion of the rain bearing systems). The data also points to transmission losses (as a percentage of the flood volume) decreasing with increasing size of large flood events. The initial stages of flooding and downstream local rainfall runoff may satisfy most of the infiltration losses and fill many in-reach stores, so restricting further transmission losses. The average total volume ratio (i.e. transmission) for all measured flood pulses was 0.17. The comparable 420 km Currareva-Nappa Merrie reach of Cooper Creek had an average volume ratio of 0.23 (Knighton and Nanson, 1994). In addition, the transmission versus discharge plot for that reach of Cooper Creek showed similar trends to those observed in Fig. 2. The Diamantina Lakes-Birdsville reach of the Diamantina and the Currareva-Nappa Merrie reach of Cooper
Creek both have similar complexly anastomosing channel/floodplain morphology and both occur in the mid to lower reach of their respective catchments. This area of the Lake Eyre Basin is known as the “Channel Country” and the width of the floodplain/channel section can reach between 50–60 km for both rivers. The travel time for floods in the Diamantina Lakes– Birdsville reach also vary non-linearly with discharge (Fig. 3). The travel times increase with increasing discharge, for floods of total discharge ⬍ 2300 GL, and then decrease as discharges increase over the 2300 GL threshold. For floods of total discharge ⬍ 2300 GL at Diamantina Lakes, a power function can be fitted to the travel time data to provide the following relationship; Travel time ⫽ 3.6Q0.26 R2 ⫽ 0.72, n ⫽ 34
(1)
The increase in travel time with discharge could be due to a combination of increasing flow retardance for larger floods and these floods using longer flow paths. A power function can also be fitted to the trend shown by floods of total discharge ⬎ 2300 GL (Fig. 3). The faster travel times for the larger floods reflect a probable decrease in flow retardance and more direct flood paths, as well as increased contribution from in-reach runoff. The Monkira-Birdsville section of the study reach has a dramatic widening of the channel network and an increase in available flow paths. Analysis of event based stage height data from Monkira (see location in Fig. 1) indicates that travel times decrease with increasing discharge in the Diamantina Lakes-Monkira section of the reach. However, floods in the Monkira-Birdsville section of the reach show a similar travel time pattern to that of the larger Diamantina Lakes-Birdsville reach (Fig. 3). Satellite images of two flood pulses demonstrate the different flow paths used by floods with different total volumes in the Monkira-Birdsville reach (Fig. 4). Floods approaching the 2300 GL total volume threshold flow into additional flowpaths than those utilised by smaller floods.
3. Flow modelling 3.1. Model structure and inputs
Fig. 2. Transmission losses of Diamantina Lakes to Birdsville reach of the Diamantina River.
The paucity of hydrological and catchment characteristic data for the Diamantina River requires a parsimonious modelling approach. The analysis of gauging station and satellite data indicates that the definition of flow paths for the range of flood discharges is a crucial feature for modelling the flow regime of the Diamantina River. In order to combine detailed routing capability with a parsimonious water balance model, the Diamantina Lakes–Birdsville reach of the Diamantina River has been modelled using a grid-based approach. The model was constructed using the Catchment Simulation Shell (CSS)
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Fig. 3. Travel time for Diamantina Lakes-Birdsville and Monkira-Birdsville reaches. Power function curves are fitted to data with total volumes at Diamantina Lakes of ⬍ 2300 GL and ⬎ 2300 GL.
software developed by the Cooperative Research Centre for Catchment Hydrology (CRCCH). The CSS software is written in Visual Basic 6 and provides a shell that allows the simple construction of grid-based models of catchments and handles all data inputs and outputs. The conceptual water balance algorithms are all contained in a single module that allows the modelling procedure to be tailored to the requirements of a specific catchment or modelling purpose. The grid-based structure allows for routing of flow between cells whilst using simple conceptual water balance algorithms calculated for each cell at each timestep. The structure also allows for some spatial representation of different morphological units of the reach (i.e. channels versus hillslope). The grid cell size used is 0.05∗0.05 degrees and the model runs at a daily timestep. The grid cell size was chosen to coincide with that of spatially interpolated rainfall data and its large size provided computational simplicity in limiting the number of cells in the model whilst retaining sufficient flexibility to represent flow paths and spatially variant elements. The inputs to the model are streamflow measured from the upstream (Diamantina Lakes) gauging station, a daily time-series of interpolated rainfall data and monthly mean areal potential evaporation values. The interpolated rainfall data were obtained from the Queensland Centre for Climate Applications. The rainfall data are interpolated on a 0.05∗0.05 degree grid (approximately 5∗5km) and represent the highest spatial resolution interpolated rainfall data available over Australia (Jeffrey et al., 2001). Daily evaporation values were derived from climatological mean monthly values of areal potential evaporation over the catchment extracted from an Australia-wide dataset (Australian Bureau of Meteorology, 2001). Previous work in temperate climates has found that use of mean climatological values of potential evaporation do not adversely affect the modelling of the water balance to any significant degree (Fowler, 2002). Given the likely high errors in measuring other aspects of the water balance, such as streamflow and rainfall, and difficulty in obtaining other variables for calculating the potential evaporation, it is
considered that use of mean monthly areal evaporation rates in the modelling is justified. The critical issue of defining flow paths between grid cells was achieved using topographic maps and satellite images (Landsat and NOAA-AVHRR). The satellite images were used to identify the flow-paths taken by the range of flood sizes and also to define land types. Available Landsat images of flood events representative of typical transmission loss behaviour identified by the gauging station data analysis, e.g. ‘large’ (total volume ⬎ 2300GL), ‘maximum loss percentage’ (1600–2300 GL) and ‘medium’ (80–1600 GL), were chosen to define the flow paths utilised by these floods (see Figs. 2 and 4). The topography of the catchment was found to be too flat and the topographic data too sparse to use in automatically generating flow patterns from a digital elevation model. In order to maintain accurate flow paths, cell connectivities were explicitly defined from topographic maps. In the complexly anastomosing channels of the Diamantina River, the model structure has to allow flow out of the cells from multiple directions to replicate the complex flow paths occurring at the scale of the grid cell. Different templates of cell connectivity are set for discharge ranges that result in distinctive flow patterns. Changes between connectivity templates are triggered by either the total volume of surface water in the Diamantina channel system or by the daily inflow discharge entering the reach at Diamantina Lakes. Four connectivity templates have been used in the model and define flow paths interpreted from satellite images for the following approximate pulse sizes; small ( ⬍ 80 GL total volume), medium (80–1600 GL), maximum loss size (1600–2300 GL) and large ( ⬎ 2300 GL). The explicit connectivity between cells utilises a tendigit code for each cell (e.g. 1000000604). The first digit (1) is used to maintain the code length and the following nine digits define the connectivity with the surrounding eight cells, ordered in a clockwise direction starting at the north-west (or top-left) cell. The fifth of the nine digits allows the cell to act as a sink, if necessary. Zero indicates that a particular surrounding cell is disconnected whilst any digit from 1–9 signifies connection and gives the proportion of the cell discharge that it received
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(e.g. 1000000010). In practice, a maximum of three outflow connections per cell was required. 3.2. Conceptual model structure
Fig. 4. Flow paths for different sized flood events shown in Landsat MSS images of the downstream half of the Diamantina Lakes to Birdsville reach of the Diamantina River. Image (1), taken after the passage of floodwaters in November 1985, shows the flow-paths used as an elevated vegetation response in white. Image (2) taken during a flood event in February 1986 shows floodwaters as black colour. Note the more extensive area of inundation and different flow paths used by the larger flood event.
(i.e 4 = 40%, 6 = 60% etc.). The sum of discharge proportions has to sum to one. In the example code given above, one cell receives 60% of the discharge whilst another receives 40%. In the case of a single connecting cell, the digit one denotes 100% discharge into that cell
A lumped parameter, water balance model is calculated for each grid cell at a daily time-step (Fig. 5). The conceptual model contains 12 parameters. Of these, two relate to the evapotranspiration process, two to the flow routing process and eight to the storage and water balance processes. Three land-type classes are used in the model. The first represents the primary channel system of the reach, the second covers the secondary channel system and extensive floodplains whilst the third comprises the remainder of the catchment. Separate parameter values are used for the different land types to capture some of the spatial variability driving the hydrological processes. Infiltration excess, or Hortonian overland flow, is commonly regarded as the dominant runoff process operating in hillslope areas of arid catchments due to the prevalence of surface crusts forming on the soils and limiting infiltration (Knighton and Nanson, 1997; Baird, 1997). Areas of vegetation concentration are zones of enhanced infiltration and act as sinks, trapping some of the runoff generated from areas of bare soils, hence limiting total runoff (Ludwig et al., 1999). The vegetation cover measured by area in these catchments is typically ⬍ 10% tree/shrub cover and ⬍ 30% grass cover but is not uniformly distributed. Vegetation tends to occur in clusters and is often most prevalent in drainage lines, channels and floodplains. The catchment drainage lines, from minor channel through to major channels and floodplains, have higher infiltration rates and capacities than much of the hillslope soil moisture store and form an important storage. Due to the flatness of much of the terrain, ponding of runoff and its exclusion from the integrated drainage network is also likely to be a significant cause of storage in addition to the soil moisture stores (Viney and Sivapalan, 1999). Runoff processes are modelled using a single bucket to represent the soil moisture store that requires filling to a calibrated amount before runoff occurs. Thus infiltration excess on the hillslopes is modelled by using a very small storage, while the size of the soil moisture store elsewhere will be a function of soil type, vegetation and the flatness of the terrain (terminal ponding). There was no pluviometer data available for the Diamantina catchment and so more complex modelling of the runoff processes (likely needing sub-daily time steps) was not considered warranted. Variations between the actual rainfall depth over any part of the catchment and that measured by the sparse raingauge network are as important a source of error on modelling runoff as are variations in rainfall intensity. The grid cell size is large in comparison with some
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Fig. 5. Flow diagram of conceptual water balance model for each grid cell. Loss processes are shown in gray and calibrated parameters are shown in bold italic type.
widths of the active channel and floodplain and so subgrid cell processes need to be considered in the conceptual modelling of the river flow, in particular, the grid cell scale relationship between storage and area inundated. The relationship between the discharge of a flood event and the area inundated is critical for measuring realistic transmission losses due to evapotranspiration and infiltration. The model uses Eq. (2) to divide the area of the cell into inundated and non-inundated portions, where SS is the calculated total surface storage in the cell and VM is a calibration factor that controls the shape of the curve. The form of Eq. (2) was chosen to reflect the likely control the channel morphology has on the sub-grid scale area of inundation and is asymptotic to 100% cell inundation. The shape of the curve is shown in Fig. 6 and decreasing VM results in an increased area of inundation within the pixel for a given storage. Area inundated ⫽ 1 ⫺ e(⫺0.01⫺SS/VM)
(2)
Losses due to evaporation are removed from the surface cell storage (see Fig. 5) at the areal potential rate and at a calibrated evapotranspiration rate when the surface
Fig. 6. Curves of function relating grid cell storage to the percentage of cell inundated. Two curves show impact of varying the VM parameter on the function shape.
store is empty. The maximum sub-surface store is set at a calibrated value and must be filled before flow out of the cell occurs. Losses due to deeper infiltration are then set at a calibrated daily rate. Following removal of water from the surface store due to evapotranspiration and infiltration, a proportion of the store is placed in a terminal cell store with a calibrated maximum volume. This simulates the terminal cell storage that is not available for further routing and is only depleted by evapotranspiration and infiltration to the subsurface store. The remaining water in the surface store is available for routing. A two-parameter kinematic storage, flow-routing iterative algorithm (Moore and Foster, 1990) is used for the routing and calculated the average daily (flow-available) storage and discharge within the cell. Discharge of baseflow from the sub-surface store back into the surface store for routing is set at a calibrated proportion of the sub-surface store. 3.3. Model calibration Calibration of the model for the mid-Diamantina reach was conducted on a trial and error basis, using the daily discharge data from Birdsville to provide optimum fits between observed and modelled data for flood events. The model was calibrated on data from two periods; 1973–1980 and 1979–1986, and the parameter sets were tested on the other period as a cross-validation exercise. The overlap between the two periods allows for the modelled stores to be equilibrated to likely initial conditions early on in the second calibration period. The 1973–1980 period contained a series of very large floods between 1973–1977 whilst the 1979–1986 period was much drier and characterised by small to medium floods except for one large event in 1981. The model performance was evaluated on three measures comparing the modelled to observed discharge records for specific flood pulses. These three measures are;
0.0001 750 4 1 30,000 3 0.3 25,500 0.0007 450 5 1 60,000 1 0.1 3500 0 40 1 1.1 30,000 0 0.1 500 0.0001 750 4 1 30,000 3 0.3 27,000 0.0007 500 4 1 60,000 1 0.1 5000 0 20 1 1.1 30,000 0 0.1 250 0.0001 750 4 1 30,000 3 0.3 24,000
Hillslope Primary Channel Flood-plain Flood-plain
Hillslope Primary Channel
0.0007 400 6 1 60,000 1 0.1 2000 Soil moisture return flow rate Soil moisture store (mm) Flow routing (timing) Flow routing (power) VM (storage-area parameter) Deep infiltration rate (mm/day) Percentile to terminal store Max. terminal storage (ML)
Calibration of modelled output for the 1973–1980 and 1979–1986 periods resulted in slightly different sets of parameter values (Table 1). The differences predominantly lay in the size of the soil moisture and terminal stores between the two periods. The wetter period of 1973–1980 required larger stores to best fit the modelled data to the Birdsville daily discharge record. The mean of the parameter values for the stores from the two calibration periods were used to generate a mean set of parameter values for use on both periods of data. The model
1979–1986
3.4. Modelling results
Table 1 Land-class dependent flow and storage parameter values from calibration of two time-periods (1973–1980 and 1979–1986)
Model accuracy is shown by volume ratios having values close to one and the difference in days and ARET values being as low as possible. Other traditional measures of model performance, such as the Nash efficiency criterion (NEC) (Nash and Sutcliffe, 1990) or the root mean square error (RMSE) are more affected by poor model fit for large floods and are not sensitive to maximising the model performance across the large range of discharges occurring in the Diamantina River. The definition of the extent of flooding for particular flood events was used in the “spatial” calibration of the model. The grid-based output was compared to Landsat images covering different flood events and the cell connectivities were set to enable a reasonable match between the modelled and actual spatial extent of the flooding at that time. The flood paths were defined from observed water flow during the flood event and from vegetation greening following the passage of floodwaters from images taken after the flood event (Fig. 4). Flow pulses with peak flow volumes of ⬍ 80 GL at Diamantina Lakes experience less transmission losses in percentage terms than higher volume floods and significantly less in absolute terms. Results during calibration indicated that the flow paths used by the smaller flows must occur in a well-connected “primary” channel system with less transmission losses (smaller soil moisture and terminal storages) than the larger floods. This required that the channel/floodplain system be defined by two land-classes, “primary channel” and “secondary channel/floodplain”, in addition to the “hillslope” class, even though this increased the number of adjustable parameters in the water balance model.
Mean parameter set
where To and Tm are the observed and modelled time to peak of the flood pulse, respectively.
Flood-plain
(3)
1973–1980
ARET (%) ⫽ 100 ∗|To⫺Tm| / To
Hillslope
1. Ratio between modelled and observed total flood volumes for specified flood pulses. 2. Absolute difference in days between the timing of peak flow for modelled and observed data. 3. Absolute relative error in time to flood peak (ARET, see Zhang et al., 2002) defined by
0 30 1 1.1 30,000 0 0.1 375
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Primary Channel
700
1.11 3 25 1.36 5 37 0.44 4 32 3.0 4 83 0.63 3 33
1.72 3 77
1.22 8 95 0.76 16 121 1.34 3 9 1.58 3 13
1979–1986 Parameter set Mean parameter set Floods ⬍10 GL/day discharge
Table 2 Summary of model performance measures
The quality of model fit is somewhat subjective and needs to be considered in the context of what is the best possible fit that might be considered possible given errors and uncertainties in primary input data. The sparseness and quality of precipitation data also sets a basic constraint on model fit. In this context, the fit between modelled and observed discharge data was generally satisfactory considering the large transmission losses and complexity of the Diamantina River. The larger floods (peak discharge ⬎ 100 GL/day at Birdsville) from the 1973–1980 period were modestly overestimated in volume (17% average overestimation, Table 2) but with reasonable timing and pulse shape fits. The modelled large flood of the 1979–1986 period (1981) had a poor timing and shape fit but reasonable volume estimation. The poor timing may be attributed to the modelled flow having to fill empty stores in the floodplain land-type thus slowing the modelled flow to a greater degree than the observed flow. The smaller floods (generally of peak discharges ⬍ 10 GL/day at Birdsville) were less well modelled with higher error and variability in the model performance measures and pulse shape fit. This is largely attributed to difficulties in accurately defining flow paths for these smaller floods and the magnified effects of errors when dealing with small flows. Two floods in the calibration period were particularly poorly modelled, these being the 1975 and 1984 events. The modelled 1975 flood was significantly overestimated with the modelled transmission losses being constrained by the water storage carried over from the extremely large 1974 flood event. The modelled 1984 flood was significantly underestimated and contained a large proportion of its flow volume derived from rainfall in the reach. It is quite likely that errors in rainfall measured for the reach, due to the sparse network of rainfall gauges in the catchment, are the main reason for poor performance in this case. The importance of having a terminal store in the modelling is shown by much of the short-term transmission loss being held in this store (Fig. 8) until it becomes depleted by the long-term loss processes of evapotran-
1.17 5 14
1973–1980 Parameter 1979–1986 Parameter Mean parameter set set set 1973–1980 Parameter set
4. Discussion
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Mean volume ratio Mean timing of peak error (days) Mean ARET (%) floods ⬎10 GL/day discharge Mean volume ratio Mean timing of peak error (days) Mean ARET (%)
1979–1986 data 1973–1980 data
performance measures for the two calibration-period parameter sets applied to both time periods and the mean set of parameter values are shown in Table 2. The fit between the modelled and observed discharge at Birdsville for both periods, using the mean set of parameter values, is shown in Fig. 7. The daily simulated time-series of terminal storage and evaporation and deep infiltration volume loss for the 1973–1980 period are shown in Fig. 8. These data are calculated for the channel and floodplain land-types and not for the hillslope land-type.
0.96 12 74
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Fig. 7. Modelled versus observed discharge at Birdsville gauging station for the period 1973–1980 and 1979–1986. Fit between modelled and observed flood pulses are reasonable for peaks but poor for very low flows (⬍100 ML/day).
앫 Explicit representation of routing and the spatial distribution of flooding. 앫 Influence of different land types on soil water storage and routing parameters.
Fig. 8. Daily simulated fluctuations in terminal storage and losses from evaporation and deep infiltration for the period 1974–1980.
spiration and deep infiltration. Losses due to deep infiltration are probably over-estimated as the calibrated infiltration rate was set between 1–3 mm/day and this is probably excessive in areas of cracking clay soils. Infiltration losses to deep aquifers are poorly constrained by field data and so the present model structure could significantly overestimate losses from this process. If the infiltration losses are overstated then the short-term loss to the terminal storage or the longer term loss via evapotranspiration would need to rise in compensation. It is possible that the average daily areal evaporation rate used in the model could underestimate the actual evaporation rates during and after the flood passage, particularly for smaller floods that are confined to a series of channels of widths ⬍ 100 m, where evaporation may approach the point potential rate.
5. Conclusions The use of a grid-based conceptual model shows considerable promise in the modelling of transmission losses and streamflow routing in the low gradient dryland rivers of the Lake Eyre Basin. This approach allows for two factors that are critical in estimating transmission losses and flow timings over a large discharge range.
The use of remote sensing data along with traditional flow data was critical in developing and calibrating the flow threshold and floodplain connectivity components of the model. Transmission losses during flood events are particularly sensitive to changes in flow paths used by different sized flood events. In the flat landscape of the Lake Eyre Basin, satellite images of flow events provide the best available data source for identifying patterns of inundation and objectively constraining cell connectivity templates used in the flow modelling of these river systems. The model will be further improved with additional information to constrain the modelling of the deep infiltration process. Another area requiring improvement is the switching of cell connectivity templates at threshold flow volumes. Ideally this should occur when individual cells reach threshold volumes or depths and not be dependent on the inflow volume at the upstream end or the contained total volume for all channel cells. Further work will examine mechanisms for achieving cell-level flow switching.
Acknowledgements Funding for this project was provided by the Natural Heritage Trust, an initiative of Environment Australia and forms part of a collaborative project (ARIDFLO) between the South Australian Department of Water Land and Biodiversity Conservation (SADWLBC), Queensland Environmental Protection Agency/Parks and Wildlife Service (QEPA/QPWS) and the Queensland Department of Natural Resources and Mines (QNRM). This work is also an associate project of the CRC for Catchment Hydrology. Gauging station data were supplied by QNRM and SADWLBC, revised rating data for the Diamantina Lakes gauging station were supplied by Paul
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Martin (QNRM), and the interpolated daily rainfall data were supplied by the Queensland Centre for Climate Applications (division of QNRM). References Australian Bureau of Meteorology, 2001. Climatic Atlas of Australia: Evapotranspiration. Australian Bureau of Meteorology publication. Baird, A.J., 1997. Overland flow generation and sediment mobilisation by water. In: Thomas, D.S.D. (Ed.), Arid Zone Geomorphology: Process, Form and Change in Drylands, second ed. John Wiley & Sons, pp. 165–184. Bullard, J.E., McTainsh, G.H., Martin, W.P., 2002. Establishing stagedischarge relationships in ephemeral rivers: a case study of the Diamantina River. Australia. J. Hydrology submitted. Dunkerley, D.L., Brown, K., 1999. Flow behaviour, suspended sediment transport and transmission losses in a small (sub-bank-full) flow event in an Australian desert stream. Hydrol. Process 13, 1577–1588. Fowler, A., 2002. Assessment of the validity of using mean potential evaporation in computations of the long-term soil water balance. J. Hydrology 256, 248–263. Hughes, D.A., Sami, K., 1992. Transmission losses to alluvium and associated moisture dynamics in a semiarid ephemeral channel system in southern Africa. Hydrol. Process 6, 45–53. Jeffrey, S.J., Carter, J.O., Moodie, K.B., Beswick, A.R., 2001. Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environ Modelling and Software 16, 309–330. Knighton, A.D., Nanson, G.C., 1994. Flow transmission along an arid zone anastomosing river, Cooper Creek, Australia. Hydrol. Process 8, 137–154. Knighton, A.D., Nanson, G.C., 1997. Distinctiveness, diversity and uniqueness in arid zone river systems. In: Thomas, D.S.G. (Ed.), Arid Zone Geomorphology: Process, Form and Change in Drylands, second ed. John Wiley & Sons, pp. 185–203. Knighton, A.D., Nanson, G.C., 2001. An event-based approach to the hydrology of arid zone rivers in the Channel Country of Australia. J. Hydrology 254, 102–123. Kotwicki, V., 1986. Floods of Lake Eyre. Engineering and Water Supply Department, Adelaide, Australia.
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Laurenson, E.M., Mein, R.G., 1990. RORB—Version 4 Runoff Routing Program User Manual. Monash University, Department of Civil Engineering. Ludwig, J.A., Tongway, D.J., Marsden, S.G., 1999. Stripes, strands and stipples: modelling the influence of three landscape banding patterns on resource capture and productivity in semi-arid woodlands, Australia. Catena 37, 257–273. McKenzie, R.S., Craig, A.R., 2001. Evaluation of river losses from the Orange River using hydraulic modelling. J. Hydrology 241, 62–69. Moore, I.D., Foster, G.R., 1990. Hydraulics and overland flow. In: Anderson, M.G., Burt, T.P. (Eds.), Process Studies in Hillslope Hydrology. John Wiley & Sons, pp. 215–254. Mwakalila, S., Campling, P., Feyen, J., Wyseure, G., Beven, K., 2001. Application of a data-based mechanistic modelling (DBM) approach for predicting runoff generation in semi-arid regions. Hydrol. Process 15, 2281–2295. Nanson, G.C., Rust, B.R., Taylor, G., 1986. Coexistent mud braids and anastomosing channels in an arid-zone river: Cooper Creek, central Australia. Geology 14, 175–178. Nash, J.E., Sutcliffe, J.V., 1990. River flow forecasting through conceptual models. Part 1, A discussion of principles. J. Hydrology 10, 282–290. Puckridge, J.T., Sheldon, F., Walker, K.F., Boulton, A.J., 1998. Flow variability and the ecology of large rivers. Mar. Freshwater Res 49, 55–72. Schreiber, S., 1997. Report on calibration of Cooper Creek daily flow simulation model, Hydrology Report No. 003001.PR/1, Surface Water Assessment Group, Queensland Department of Natural Resources. Sharma, K.D., Murthy, J.S.R., 1995. Hydrologic routing of flow in arid ephemeral channels. J. Hydraulic Engineering 121 (6), 466–471. Tooth, S., 2000. Process, form and change in dryland rivers: a review of recent research. Earth-Science Reviews 51, 67–107. Viney, N.R., Sivapalan, M., 1999. A conceptual model of sediment transport: application to the Avon River Basin in Western Australia. Hydrol. Process 13, 727–743. Walters, M.O., 1990. Transmission losses in arid region. J. Hydraulic Engineering 116 (1), 129–138. Zhang, S., Cordery, I., Sharma, A., 2002. Application of an improved linear storage routing model for the estimation of large floods. J. Hydrology 258, 58–68.
Modelling the flow regime of an arid zone floodplain river, Diamantina River, Australia J.F. Costelloe ∗, R.B. Grayson, R.M. Argent, T.A. McMahon Centre for Environmental Applied Hydrology, CRC for Catchment Hydrology, Department of Civil and Environmental Engineering, University of Melbourne, Victoria 3010, Australia Received 22 March 2002; received in revised form 19 September 2002; accepted 19 December 2002
Abstract Arid zone, ephemeral rivers are characterised by discharge decreasing downstream in the lower reaches due to transmission losses. Modelling the flow regime of these rivers requires data on the spatial and temporal distribution of transmission losses in these reaches. In this study, a hydrological model is developed for a 330 km reach of the Diamantina River in southwestern Queensland, where the floodplain width varies from 5 to 60 km. Analysis of gauging station data at each end of the reach indicates that transmission losses are between 70 and 98% for floods with total discharge ⬍ 2300 GL. The flow routing and transmission losses are modelled using a grid-based, daily time-step conceptual model incorporating flow routing algorithms. Satellite images are used to identify the flow-paths used by the range of flood sizes and to identify threshold flow volumes for initiation of flow into new flow-paths. The grid-based approach allows for representative routing of flow through the reach and representation of spatial variability in transmission loss processes, including losses resulting from evaporation, channel/floodplain infiltration and terminal flow storage. A combination of gauging station data and satellite images is used in the calibration of the model parameters. 2003 Elsevier Science Ltd. All rights reserved. Keywords: Ephemeral river; Arid zone; Transmission loss; Flow routing
1. Introduction 1.1. Arid zone floodplain rivers Arid zone (dryland) ephemeral and intermittent rivers are characterised by discharge decreasing in the lower reaches due to transmission losses (Knighton and Nanson, 1997). Many of these rivers flow into arid areas with low population bases and so there tends to be a paucity of gauged hydrographic data describing their flow regimes. Modelling the flow regime of these rivers requires data on the spatial and temporal distribution of transmission losses in the lower reaches. The interplay between discharge and transmission losses determines the extent and pattern of flow in most internally draining dryland rivers (Tooth, 2000) with major consequences
for the ecological response, and water resource and ecological modelling of the river system. Areas of enhanced transmission loss can have a high biological productivity as water loss from infiltration can support important areas of vegetation growth and in-reach surface water storages provide temporary refuges and resources for arid zone fauna. The complex flow paths and large transmission losses in dryland rivers, in combination with the paucity of hydrographic data, present challenges to the modelling of the flow regime (Knighton and Nanson, 1994). Transmission losses are due to the following factors (Knighton and Nanson, 1994): 앫 Infiltration to channel store and/or floodplain soils, 앫 Evapotranspiration, and 앫 Ponding in terminal storages, such as ephemeral pools, channels and other wetlands.
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Corresponding author: Tel.: 61-3-83447238; fax: 61-3-83446215. E-mail address: [email protected] (J.F. Costelloe).
The relative importance of these factors with respect to hydrology varies among arid catchments, depending
1364-8152/03/$ - see front matter 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S1364-8152(03)00071-9
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on characteristics such as the size of the catchment, stream gradient, stream/floodplain sediments and seasonal timing of flow. Studies of small to medium sized catchments with low to moderate gradients in Arizona (Walters, 1990), India (Sharma and Murthy, 1995) and South Africa (Hughes and Sami, 1992) have found that infiltration to the near-surface channel aquifer was the major cause of transmission losses. The Orange River in South Africa flows through hot, arid regions with high evaporation rates and a study of that river (McKenzie and Craig, 2001), identified evapotranspiration as the principal cause of transmission losses. That study assumed insignificant losses due to bank storage or deep infiltration as the Orange River is underlain by bedrock and found evapotranspiration losses to be in the same order of magnitude as Class-A pan evaporation data for the region. In addition, the complex flow patterns of dryland, low gradient rivers enhance the potential for water loss to terminal in-reach storage. Transmission losses due to terminal flow storage in Australian dryland rivers and streams occur over a large range of flood magnitudes. Terminal flow storage was the primary immediate cause of transmission losses observed in a sub-bankful flow event in an arid zone stream with the transmission loss rate higher (13.2% per km) than for a bankfull event (5–6.9% per km, Dunkerley and Brown, 1999). Terminal storage is also recognised as an important loss process in flood events occurring in Cooper Creek, Lake Eyre Basin but was not quantified in comparison to other transmission loss processes (Knighton and Nanson, 1994). 1.2. Diamantina River, Lake Eyre Basin
The headwaters of the Diamantina River occur at elevations of 200–350 m in central Queensland. The entire river length is 1000 km to its terminus at Lake Eyre North (as the Warburton river) and its catchment area is 160,000 km2 with an average gradient of only 2.7 x 10 - 4m/m. The Diamantina River is a major river of the Lake Eyre Basin and the major contributor to Lake Eyre (Kotwicki, 1986). The lower and middle reaches are characterised by a complex system of braided/anastomosing channels and wide floodplains. Like many arid zone rivers, the Diamantina has few gauging station records along its 1000 km length with only one gauging station currently operating at Birdsville (began in 1949), one station at Diamantina Lakes that was decommissioned in 1988 and another station at Monkira that collected only flood-height data (Fig. 1). The catchment upstream of Diamantina Lakes comprises an area of 54,130 km2 and contains the greatest number of tributaries, highest elevation and highest rainfall. Rainfall is strongly summer dominant and related to the north Australian monsoon season. The median annual rainfall varies between 200–400 mm and the precipitation gradient decreases moving downstream. Large flood events are associated with monsoonal rainfall pushing further south into the Diamantina catchment and so large floods are often associated with heavy rainfall in the lower reaches. During moderate flood events the rainfall is more commonly confined to the upper catchment. The middle catchment, between the Diamantina Lakes and Birdsville gauging stations, has an area of 61,075 km2 and a river length of 330 km. The width of the channel/floodplain increases up to 60 km and the floodplains are dominated by self-mulching, cracking
The arid zone floodplain rivers of the Lake Eyre Basin, one of the world’s largest internally draining basins, have a number of distinguishing features that result in these rivers having amongst the most variable flow regimes in the world (Puckridge et al., 1998; Knighton and Nanson, 2001). The rivers develop over very low gradients and commonly have complex flow paths with extensive braided/anastomosing channel systems, resulting in floods with slow travel times (weeks to months). The rivers have greatly varying widths of active channel and floodplain. During large flood events, floodwaters can inundate thousands of square kilometres and the floodplain can be up to 60 km wide. The rivers predominantly transport clay-sized particles and areas of significant floodplain expansion and wetland development are covered by cracking clays (Nanson et al., 1986). Floodplain infiltration losses may be limited by the sealing of the swelling clay floodplain substrate once their crack capacity is exceeded (Knighton and Nanson, 1994). The flow regimes of these rivers are dominated by late summer flow events resulting from highly variable monsoonal related rainfall in the upper catchments.
Fig. 1. Location map of Diamantina River catchment (outlined). Gauging or flood height stations at Diamantina Lakes (1), Monkira (2) and Birdsville (3) are shown as triangles.
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clay soils. The aridity of the catchment increases downstream and the mean annual rainfall at Birdsville is only 169 mm and still summer-dominant. 1.3. Modelling approach The paucity of data regarding the hydrological characteristics of the Diamantina River catchment and its large size precludes the use of a data-intensive, physically based modelling approach. This study uses an initial inductive (“top-down”) approach by analysing available gauging station data in order to determine which elements need to be incorporated into the model structure for this catchment. A semi-lumped, conceptual model is then developed for the catchment that incorporates calibrated algorithms describing the hydrological processes that appear to be of most importance from the data analysis. An advantage of this approach is that it allows for testing of specific hypotheses regarding the behaviour of the catchment and arguably provides better insights into the physical processes driving the hydrology than does a purely inductive modelling approach. This approach is not a purely data-based, mechanistic approach as recently advocated by Mwakalila et al., (2001) as the initial data analysis is separate to the model construction and calibration. The use of a relatively simple conceptual model developed in conjunction with inductive data analysis also allows for the construction of a parsimonious model structure. This is a vital feature of any model developed for the data-poor environment of the Lake Eyre Basin. Limited work has been done on the modelling and quantification of the processes involved in transmission losses in the rivers of the Lake Eyre Basin. Analysis of gauging station data to determine transmission losses in a 420 km reach of Cooper Creek in the Lake Eyre Basin (Knighton and Nanson, 1994) demonstrated that the losses were extremely large and varied non-linearly with discharge. A simplified, whole of basin modelling approach was taken by Kotwicki (1986), using the RORB model (Laurenson and Mein, 1990) which included the Diamantina catchment. A more detailed rainfall-runoff-routing model was developed for Cooper Creek (Schreiber, 1997) using the Sacramento and IQQM models. In that study, streamflow was routed along a link-node representation of the channel system using a modified Muskingum routing procedure where the ‘k’ parameter varied as a function of discharge. The approach allowed for explicit flow routing through a simplified channel system and incorporated non-linear routing and transmission loss behaviour as discharge increased. The impact on transmission losses of variable flow paths used by different sized flood events was not addressed and the differing transmission loss processes were not considered separately. This study presents results from the application of a
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daily, semi-lumped, grid-based conceptual model of the flow regime of the Diamantina River, using remotely sensed data for model development and calibration. Gauging station data from the 330 km reach of the Diamantina River, between Diamantina Lakes and Birdsville, are analysed to determine the magnitude of transmission losses as a function of discharge. The hypothesized major loss processes of evapotranspiration, infiltration and terminal ponding, are modelled and their relative importance assessed. The grid-based model developed for the reach is calibrated and tested against gauging station data.
2. Analysis of flow data 2.1. Methodology Following the approach of Knighton and Nanson (2001), the analysis of flow behaviour using gauging station data from the Diamantina River used an eventbased methodology. Only two gauging stations exist on the Diamantina River. A gauging station at Diamantina Lakes (see Fig. 1) operated between November 1966 and December 1988 but has a poor rating (3% of estimated maximum discharge). However, cross-section and channel slope analysis of the Diamantina Lakes site has allowed discharges to be calculated up to the maximum measured stage with a reasonable level of confidence (Bullard et al., 2002). This station provides the only hydrological dataset for the upper reaches of the river. In the lower reaches, a more reliably rated (40% of estimated maximum discharge, 84% of maximum stage) gauging station operates at Birdsville, with records beginning in 1949. The maximum gauged discharge at Birdsville occurred at the peak of the fifth largest flood recorded at the gauging station since 1949. Midway between Diamantina Lakes and Birdsville, the Monkira station has recorded stage height data (often eventbased) between 1949–1962 and also recorded some later large flood events. Flow pulses at the Diamantina Lakes gauging station were correlated with flow pulses at Birdsville and transmission losses and travel times were compared. The correlation of pulses over the 330 km reach was facilitated by the flow occurring as discrete events and often starting and ending in zero flow at the upper and lower ends of the reach. Correlated flow events often contained more than one peak (particularly at the upstream gauging station) but had one welldefined maximum flow pulse peak at the downstream end. Travel times for flow events were calculated from the timing difference between the days of maximum discharge at the upstream and downstream gauging stations. A focus of the analysis of gauging station data is to derive information regarding the transmission losses and routing behaviour over a range of discharges. The pos-
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ition of the gauging stations downstream of long channel reaches precludes detailed examination of likely runoff processes in isolation from modification of the flow pulse through the channel system. 2.2. Results and analysis of flow data The degree of transmission loss between the two gauging stations is shown in Fig. 2 and illustrates very high losses in this reach, that vary non-linearly with discharge. The plot shows the ratio of downstream to upstream pulse volumes on the y-axis and the upstream input pulse volume (Diamantina Lakes) on the x-axis. Flow pulses with significant input from downstream of Diamantina Lakes have not been removed from the data. The transmission throughput varies non-linearly with flood size, with transmission losses of 70–98% for flood events ⬍ 2300 GL total volume at Diamantina Lakes and a maximum loss for floods of approximately 2000– 2200 GL total volume. The sharply increased transmission throughput of floods with total volumes of ⬎ 2300 GL is considered to reflect very significant runoff input from downstream of Diamantina Lakes due to heavier rainfall in the lower reaches associated with large floods (southerly incursion of the rain bearing systems). The data also points to transmission losses (as a percentage of the flood volume) decreasing with increasing size of large flood events. The initial stages of flooding and downstream local rainfall runoff may satisfy most of the infiltration losses and fill many in-reach stores, so restricting further transmission losses. The average total volume ratio (i.e. transmission) for all measured flood pulses was 0.17. The comparable 420 km Currareva-Nappa Merrie reach of Cooper Creek had an average volume ratio of 0.23 (Knighton and Nanson, 1994). In addition, the transmission versus discharge plot for that reach of Cooper Creek showed similar trends to those observed in Fig. 2. The Diamantina Lakes-Birdsville reach of the Diamantina and the Currareva-Nappa Merrie reach of Cooper
Creek both have similar complexly anastomosing channel/floodplain morphology and both occur in the mid to lower reach of their respective catchments. This area of the Lake Eyre Basin is known as the “Channel Country” and the width of the floodplain/channel section can reach between 50–60 km for both rivers. The travel time for floods in the Diamantina Lakes– Birdsville reach also vary non-linearly with discharge (Fig. 3). The travel times increase with increasing discharge, for floods of total discharge ⬍ 2300 GL, and then decrease as discharges increase over the 2300 GL threshold. For floods of total discharge ⬍ 2300 GL at Diamantina Lakes, a power function can be fitted to the travel time data to provide the following relationship; Travel time ⫽ 3.6Q0.26 R2 ⫽ 0.72, n ⫽ 34
(1)
The increase in travel time with discharge could be due to a combination of increasing flow retardance for larger floods and these floods using longer flow paths. A power function can also be fitted to the trend shown by floods of total discharge ⬎ 2300 GL (Fig. 3). The faster travel times for the larger floods reflect a probable decrease in flow retardance and more direct flood paths, as well as increased contribution from in-reach runoff. The Monkira-Birdsville section of the study reach has a dramatic widening of the channel network and an increase in available flow paths. Analysis of event based stage height data from Monkira (see location in Fig. 1) indicates that travel times decrease with increasing discharge in the Diamantina Lakes-Monkira section of the reach. However, floods in the Monkira-Birdsville section of the reach show a similar travel time pattern to that of the larger Diamantina Lakes-Birdsville reach (Fig. 3). Satellite images of two flood pulses demonstrate the different flow paths used by floods with different total volumes in the Monkira-Birdsville reach (Fig. 4). Floods approaching the 2300 GL total volume threshold flow into additional flowpaths than those utilised by smaller floods.
3. Flow modelling 3.1. Model structure and inputs
Fig. 2. Transmission losses of Diamantina Lakes to Birdsville reach of the Diamantina River.
The paucity of hydrological and catchment characteristic data for the Diamantina River requires a parsimonious modelling approach. The analysis of gauging station and satellite data indicates that the definition of flow paths for the range of flood discharges is a crucial feature for modelling the flow regime of the Diamantina River. In order to combine detailed routing capability with a parsimonious water balance model, the Diamantina Lakes–Birdsville reach of the Diamantina River has been modelled using a grid-based approach. The model was constructed using the Catchment Simulation Shell (CSS)
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Fig. 3. Travel time for Diamantina Lakes-Birdsville and Monkira-Birdsville reaches. Power function curves are fitted to data with total volumes at Diamantina Lakes of ⬍ 2300 GL and ⬎ 2300 GL.
software developed by the Cooperative Research Centre for Catchment Hydrology (CRCCH). The CSS software is written in Visual Basic 6 and provides a shell that allows the simple construction of grid-based models of catchments and handles all data inputs and outputs. The conceptual water balance algorithms are all contained in a single module that allows the modelling procedure to be tailored to the requirements of a specific catchment or modelling purpose. The grid-based structure allows for routing of flow between cells whilst using simple conceptual water balance algorithms calculated for each cell at each timestep. The structure also allows for some spatial representation of different morphological units of the reach (i.e. channels versus hillslope). The grid cell size used is 0.05∗0.05 degrees and the model runs at a daily timestep. The grid cell size was chosen to coincide with that of spatially interpolated rainfall data and its large size provided computational simplicity in limiting the number of cells in the model whilst retaining sufficient flexibility to represent flow paths and spatially variant elements. The inputs to the model are streamflow measured from the upstream (Diamantina Lakes) gauging station, a daily time-series of interpolated rainfall data and monthly mean areal potential evaporation values. The interpolated rainfall data were obtained from the Queensland Centre for Climate Applications. The rainfall data are interpolated on a 0.05∗0.05 degree grid (approximately 5∗5km) and represent the highest spatial resolution interpolated rainfall data available over Australia (Jeffrey et al., 2001). Daily evaporation values were derived from climatological mean monthly values of areal potential evaporation over the catchment extracted from an Australia-wide dataset (Australian Bureau of Meteorology, 2001). Previous work in temperate climates has found that use of mean climatological values of potential evaporation do not adversely affect the modelling of the water balance to any significant degree (Fowler, 2002). Given the likely high errors in measuring other aspects of the water balance, such as streamflow and rainfall, and difficulty in obtaining other variables for calculating the potential evaporation, it is
considered that use of mean monthly areal evaporation rates in the modelling is justified. The critical issue of defining flow paths between grid cells was achieved using topographic maps and satellite images (Landsat and NOAA-AVHRR). The satellite images were used to identify the flow-paths taken by the range of flood sizes and also to define land types. Available Landsat images of flood events representative of typical transmission loss behaviour identified by the gauging station data analysis, e.g. ‘large’ (total volume ⬎ 2300GL), ‘maximum loss percentage’ (1600–2300 GL) and ‘medium’ (80–1600 GL), were chosen to define the flow paths utilised by these floods (see Figs. 2 and 4). The topography of the catchment was found to be too flat and the topographic data too sparse to use in automatically generating flow patterns from a digital elevation model. In order to maintain accurate flow paths, cell connectivities were explicitly defined from topographic maps. In the complexly anastomosing channels of the Diamantina River, the model structure has to allow flow out of the cells from multiple directions to replicate the complex flow paths occurring at the scale of the grid cell. Different templates of cell connectivity are set for discharge ranges that result in distinctive flow patterns. Changes between connectivity templates are triggered by either the total volume of surface water in the Diamantina channel system or by the daily inflow discharge entering the reach at Diamantina Lakes. Four connectivity templates have been used in the model and define flow paths interpreted from satellite images for the following approximate pulse sizes; small ( ⬍ 80 GL total volume), medium (80–1600 GL), maximum loss size (1600–2300 GL) and large ( ⬎ 2300 GL). The explicit connectivity between cells utilises a tendigit code for each cell (e.g. 1000000604). The first digit (1) is used to maintain the code length and the following nine digits define the connectivity with the surrounding eight cells, ordered in a clockwise direction starting at the north-west (or top-left) cell. The fifth of the nine digits allows the cell to act as a sink, if necessary. Zero indicates that a particular surrounding cell is disconnected whilst any digit from 1–9 signifies connection and gives the proportion of the cell discharge that it received
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(e.g. 1000000010). In practice, a maximum of three outflow connections per cell was required. 3.2. Conceptual model structure
Fig. 4. Flow paths for different sized flood events shown in Landsat MSS images of the downstream half of the Diamantina Lakes to Birdsville reach of the Diamantina River. Image (1), taken after the passage of floodwaters in November 1985, shows the flow-paths used as an elevated vegetation response in white. Image (2) taken during a flood event in February 1986 shows floodwaters as black colour. Note the more extensive area of inundation and different flow paths used by the larger flood event.
(i.e 4 = 40%, 6 = 60% etc.). The sum of discharge proportions has to sum to one. In the example code given above, one cell receives 60% of the discharge whilst another receives 40%. In the case of a single connecting cell, the digit one denotes 100% discharge into that cell
A lumped parameter, water balance model is calculated for each grid cell at a daily time-step (Fig. 5). The conceptual model contains 12 parameters. Of these, two relate to the evapotranspiration process, two to the flow routing process and eight to the storage and water balance processes. Three land-type classes are used in the model. The first represents the primary channel system of the reach, the second covers the secondary channel system and extensive floodplains whilst the third comprises the remainder of the catchment. Separate parameter values are used for the different land types to capture some of the spatial variability driving the hydrological processes. Infiltration excess, or Hortonian overland flow, is commonly regarded as the dominant runoff process operating in hillslope areas of arid catchments due to the prevalence of surface crusts forming on the soils and limiting infiltration (Knighton and Nanson, 1997; Baird, 1997). Areas of vegetation concentration are zones of enhanced infiltration and act as sinks, trapping some of the runoff generated from areas of bare soils, hence limiting total runoff (Ludwig et al., 1999). The vegetation cover measured by area in these catchments is typically ⬍ 10% tree/shrub cover and ⬍ 30% grass cover but is not uniformly distributed. Vegetation tends to occur in clusters and is often most prevalent in drainage lines, channels and floodplains. The catchment drainage lines, from minor channel through to major channels and floodplains, have higher infiltration rates and capacities than much of the hillslope soil moisture store and form an important storage. Due to the flatness of much of the terrain, ponding of runoff and its exclusion from the integrated drainage network is also likely to be a significant cause of storage in addition to the soil moisture stores (Viney and Sivapalan, 1999). Runoff processes are modelled using a single bucket to represent the soil moisture store that requires filling to a calibrated amount before runoff occurs. Thus infiltration excess on the hillslopes is modelled by using a very small storage, while the size of the soil moisture store elsewhere will be a function of soil type, vegetation and the flatness of the terrain (terminal ponding). There was no pluviometer data available for the Diamantina catchment and so more complex modelling of the runoff processes (likely needing sub-daily time steps) was not considered warranted. Variations between the actual rainfall depth over any part of the catchment and that measured by the sparse raingauge network are as important a source of error on modelling runoff as are variations in rainfall intensity. The grid cell size is large in comparison with some
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Fig. 5. Flow diagram of conceptual water balance model for each grid cell. Loss processes are shown in gray and calibrated parameters are shown in bold italic type.
widths of the active channel and floodplain and so subgrid cell processes need to be considered in the conceptual modelling of the river flow, in particular, the grid cell scale relationship between storage and area inundated. The relationship between the discharge of a flood event and the area inundated is critical for measuring realistic transmission losses due to evapotranspiration and infiltration. The model uses Eq. (2) to divide the area of the cell into inundated and non-inundated portions, where SS is the calculated total surface storage in the cell and VM is a calibration factor that controls the shape of the curve. The form of Eq. (2) was chosen to reflect the likely control the channel morphology has on the sub-grid scale area of inundation and is asymptotic to 100% cell inundation. The shape of the curve is shown in Fig. 6 and decreasing VM results in an increased area of inundation within the pixel for a given storage. Area inundated ⫽ 1 ⫺ e(⫺0.01⫺SS/VM)
(2)
Losses due to evaporation are removed from the surface cell storage (see Fig. 5) at the areal potential rate and at a calibrated evapotranspiration rate when the surface
Fig. 6. Curves of function relating grid cell storage to the percentage of cell inundated. Two curves show impact of varying the VM parameter on the function shape.
store is empty. The maximum sub-surface store is set at a calibrated value and must be filled before flow out of the cell occurs. Losses due to deeper infiltration are then set at a calibrated daily rate. Following removal of water from the surface store due to evapotranspiration and infiltration, a proportion of the store is placed in a terminal cell store with a calibrated maximum volume. This simulates the terminal cell storage that is not available for further routing and is only depleted by evapotranspiration and infiltration to the subsurface store. The remaining water in the surface store is available for routing. A two-parameter kinematic storage, flow-routing iterative algorithm (Moore and Foster, 1990) is used for the routing and calculated the average daily (flow-available) storage and discharge within the cell. Discharge of baseflow from the sub-surface store back into the surface store for routing is set at a calibrated proportion of the sub-surface store. 3.3. Model calibration Calibration of the model for the mid-Diamantina reach was conducted on a trial and error basis, using the daily discharge data from Birdsville to provide optimum fits between observed and modelled data for flood events. The model was calibrated on data from two periods; 1973–1980 and 1979–1986, and the parameter sets were tested on the other period as a cross-validation exercise. The overlap between the two periods allows for the modelled stores to be equilibrated to likely initial conditions early on in the second calibration period. The 1973–1980 period contained a series of very large floods between 1973–1977 whilst the 1979–1986 period was much drier and characterised by small to medium floods except for one large event in 1981. The model performance was evaluated on three measures comparing the modelled to observed discharge records for specific flood pulses. These three measures are;
0.0001 750 4 1 30,000 3 0.3 25,500 0.0007 450 5 1 60,000 1 0.1 3500 0 40 1 1.1 30,000 0 0.1 500 0.0001 750 4 1 30,000 3 0.3 27,000 0.0007 500 4 1 60,000 1 0.1 5000 0 20 1 1.1 30,000 0 0.1 250 0.0001 750 4 1 30,000 3 0.3 24,000
Hillslope Primary Channel Flood-plain Flood-plain
Hillslope Primary Channel
0.0007 400 6 1 60,000 1 0.1 2000 Soil moisture return flow rate Soil moisture store (mm) Flow routing (timing) Flow routing (power) VM (storage-area parameter) Deep infiltration rate (mm/day) Percentile to terminal store Max. terminal storage (ML)
Calibration of modelled output for the 1973–1980 and 1979–1986 periods resulted in slightly different sets of parameter values (Table 1). The differences predominantly lay in the size of the soil moisture and terminal stores between the two periods. The wetter period of 1973–1980 required larger stores to best fit the modelled data to the Birdsville daily discharge record. The mean of the parameter values for the stores from the two calibration periods were used to generate a mean set of parameter values for use on both periods of data. The model
1979–1986
3.4. Modelling results
Table 1 Land-class dependent flow and storage parameter values from calibration of two time-periods (1973–1980 and 1979–1986)
Model accuracy is shown by volume ratios having values close to one and the difference in days and ARET values being as low as possible. Other traditional measures of model performance, such as the Nash efficiency criterion (NEC) (Nash and Sutcliffe, 1990) or the root mean square error (RMSE) are more affected by poor model fit for large floods and are not sensitive to maximising the model performance across the large range of discharges occurring in the Diamantina River. The definition of the extent of flooding for particular flood events was used in the “spatial” calibration of the model. The grid-based output was compared to Landsat images covering different flood events and the cell connectivities were set to enable a reasonable match between the modelled and actual spatial extent of the flooding at that time. The flood paths were defined from observed water flow during the flood event and from vegetation greening following the passage of floodwaters from images taken after the flood event (Fig. 4). Flow pulses with peak flow volumes of ⬍ 80 GL at Diamantina Lakes experience less transmission losses in percentage terms than higher volume floods and significantly less in absolute terms. Results during calibration indicated that the flow paths used by the smaller flows must occur in a well-connected “primary” channel system with less transmission losses (smaller soil moisture and terminal storages) than the larger floods. This required that the channel/floodplain system be defined by two land-classes, “primary channel” and “secondary channel/floodplain”, in addition to the “hillslope” class, even though this increased the number of adjustable parameters in the water balance model.
Mean parameter set
where To and Tm are the observed and modelled time to peak of the flood pulse, respectively.
Flood-plain
(3)
1973–1980
ARET (%) ⫽ 100 ∗|To⫺Tm| / To
Hillslope
1. Ratio between modelled and observed total flood volumes for specified flood pulses. 2. Absolute difference in days between the timing of peak flow for modelled and observed data. 3. Absolute relative error in time to flood peak (ARET, see Zhang et al., 2002) defined by
0 30 1 1.1 30,000 0 0.1 375
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Primary Channel
700
1.11 3 25 1.36 5 37 0.44 4 32 3.0 4 83 0.63 3 33
1.72 3 77
1.22 8 95 0.76 16 121 1.34 3 9 1.58 3 13
1979–1986 Parameter set Mean parameter set Floods ⬍10 GL/day discharge
Table 2 Summary of model performance measures
The quality of model fit is somewhat subjective and needs to be considered in the context of what is the best possible fit that might be considered possible given errors and uncertainties in primary input data. The sparseness and quality of precipitation data also sets a basic constraint on model fit. In this context, the fit between modelled and observed discharge data was generally satisfactory considering the large transmission losses and complexity of the Diamantina River. The larger floods (peak discharge ⬎ 100 GL/day at Birdsville) from the 1973–1980 period were modestly overestimated in volume (17% average overestimation, Table 2) but with reasonable timing and pulse shape fits. The modelled large flood of the 1979–1986 period (1981) had a poor timing and shape fit but reasonable volume estimation. The poor timing may be attributed to the modelled flow having to fill empty stores in the floodplain land-type thus slowing the modelled flow to a greater degree than the observed flow. The smaller floods (generally of peak discharges ⬍ 10 GL/day at Birdsville) were less well modelled with higher error and variability in the model performance measures and pulse shape fit. This is largely attributed to difficulties in accurately defining flow paths for these smaller floods and the magnified effects of errors when dealing with small flows. Two floods in the calibration period were particularly poorly modelled, these being the 1975 and 1984 events. The modelled 1975 flood was significantly overestimated with the modelled transmission losses being constrained by the water storage carried over from the extremely large 1974 flood event. The modelled 1984 flood was significantly underestimated and contained a large proportion of its flow volume derived from rainfall in the reach. It is quite likely that errors in rainfall measured for the reach, due to the sparse network of rainfall gauges in the catchment, are the main reason for poor performance in this case. The importance of having a terminal store in the modelling is shown by much of the short-term transmission loss being held in this store (Fig. 8) until it becomes depleted by the long-term loss processes of evapotran-
1.17 5 14
1973–1980 Parameter 1979–1986 Parameter Mean parameter set set set 1973–1980 Parameter set
4. Discussion
701
Mean volume ratio Mean timing of peak error (days) Mean ARET (%) floods ⬎10 GL/day discharge Mean volume ratio Mean timing of peak error (days) Mean ARET (%)
1979–1986 data 1973–1980 data
performance measures for the two calibration-period parameter sets applied to both time periods and the mean set of parameter values are shown in Table 2. The fit between the modelled and observed discharge at Birdsville for both periods, using the mean set of parameter values, is shown in Fig. 7. The daily simulated time-series of terminal storage and evaporation and deep infiltration volume loss for the 1973–1980 period are shown in Fig. 8. These data are calculated for the channel and floodplain land-types and not for the hillslope land-type.
0.96 12 74
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Fig. 7. Modelled versus observed discharge at Birdsville gauging station for the period 1973–1980 and 1979–1986. Fit between modelled and observed flood pulses are reasonable for peaks but poor for very low flows (⬍100 ML/day).
앫 Explicit representation of routing and the spatial distribution of flooding. 앫 Influence of different land types on soil water storage and routing parameters.
Fig. 8. Daily simulated fluctuations in terminal storage and losses from evaporation and deep infiltration for the period 1974–1980.
spiration and deep infiltration. Losses due to deep infiltration are probably over-estimated as the calibrated infiltration rate was set between 1–3 mm/day and this is probably excessive in areas of cracking clay soils. Infiltration losses to deep aquifers are poorly constrained by field data and so the present model structure could significantly overestimate losses from this process. If the infiltration losses are overstated then the short-term loss to the terminal storage or the longer term loss via evapotranspiration would need to rise in compensation. It is possible that the average daily areal evaporation rate used in the model could underestimate the actual evaporation rates during and after the flood passage, particularly for smaller floods that are confined to a series of channels of widths ⬍ 100 m, where evaporation may approach the point potential rate.
5. Conclusions The use of a grid-based conceptual model shows considerable promise in the modelling of transmission losses and streamflow routing in the low gradient dryland rivers of the Lake Eyre Basin. This approach allows for two factors that are critical in estimating transmission losses and flow timings over a large discharge range.
The use of remote sensing data along with traditional flow data was critical in developing and calibrating the flow threshold and floodplain connectivity components of the model. Transmission losses during flood events are particularly sensitive to changes in flow paths used by different sized flood events. In the flat landscape of the Lake Eyre Basin, satellite images of flow events provide the best available data source for identifying patterns of inundation and objectively constraining cell connectivity templates used in the flow modelling of these river systems. The model will be further improved with additional information to constrain the modelling of the deep infiltration process. Another area requiring improvement is the switching of cell connectivity templates at threshold flow volumes. Ideally this should occur when individual cells reach threshold volumes or depths and not be dependent on the inflow volume at the upstream end or the contained total volume for all channel cells. Further work will examine mechanisms for achieving cell-level flow switching.
Acknowledgements Funding for this project was provided by the Natural Heritage Trust, an initiative of Environment Australia and forms part of a collaborative project (ARIDFLO) between the South Australian Department of Water Land and Biodiversity Conservation (SADWLBC), Queensland Environmental Protection Agency/Parks and Wildlife Service (QEPA/QPWS) and the Queensland Department of Natural Resources and Mines (QNRM). This work is also an associate project of the CRC for Catchment Hydrology. Gauging station data were supplied by QNRM and SADWLBC, revised rating data for the Diamantina Lakes gauging station were supplied by Paul
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