A methodology to predict the impact of changes in forest cover on flow duration curves

Transcription

1 A methodology to predict the impact of changes in forest cover on flow duration curves Alice E. Brown, Thomas A. McMahon, Geoffrey M. Podger, Lu Zhang CSIRO Land and Water Science Report 8/06 February 2006

2 Copyright and Disclaimer 2006 CSIRO To the extent permitted by law, all rights are reserved and no part of this publication covered by copyright may be reproduced or copied in any form or by any means except with the written permission of CSIRO Land and Water. Important Disclaimer: CSIRO advises that the information contained in this publication comprises general statements based on scientific research. The reader is advised and needs to be aware that such information may be incomplete or unable to be used in any specific situation. No reliance or actions must therefore be made on that information without seeking prior expert professional, scientific and technical advice. To the extent permitted by law, CSIRO (including its employees and consultants) excludes all liability to any person for any consequences, including but not limited to all losses, damages, costs, expenses and any other compensation, arising directly or indirectly from using this publication (in part or in whole) and any information or material contained in it. Cover Photograph: From CSIRO Land and Water Image Gallery: File: PMA00622_09_07.jpg Description: The Warren River at the bottom of Heartbreak Trail near Pemberton, WA Photographer: Willem van Aken 2006 CSIRO. ISSN:

3 A methodology to predict the impact of changes in forest cover on flow duration curves Alice E. Brown 1, Thomas A. McMahon 2, Geoffrey M. Podger 1, Lu Zhang CSIRO land and water, Canberra Department of Civil and Environmental Engineering, The University of Melbourne CSIRO Land and Water Science Report 8/06 February 2006 Page iii

4 Acknowledgements This work was supported by funding from the Cooperative Research Centre for Catchment Hydrology under project 2E and the Murray Darling Basin Commission under project Integrated assessment of the effects of land use changes on water yield and salt loads (D2013). The first author was supported by a University of Melbourne Research Scholarship and the CRC for Catchment Hydrology. CSIR South Africa kindly provided data for the Biesievlei experimental catchment. Thiess Environmental Services provided data for the Pine Creek catchment. We thank Klaus Hickel and Richard Silberstein for their helpful comments on this report. Page iv

5 Executive Summary Afforestation has been recognised as a potential major land use change for Australia in the coming decades. This means that the impacts of afforestation on water security, salinity, and environmental flows need to be considered in catchment management planning. Significant progress has been made in our understanding of the relationship between vegetation and streamflow at the mean annual time scale. Unfortunately, our understanding of the impact of forest cover change on streamflow at shorter timescale is limited. One way to evaluate the effect of afforestation on a streamflow time series is to examine changes in a catchment s flow duration curve (FDC) following a change in forest cover. A FDC represents the relationships between the magnitude and frequency of streamflow for a catchment and provides an estimate of the percentage of time a given flow is equalled or exceeded. This report details the development of a methodology that predicts changes in a daily FDC following a change in forest cover. This methodology uses a five-parameter model, referred to as the FDC model, to describe the shape of the observed FDC for current vegetation conditions. To predict the changes in the FDC under altered forest cover, the parameters of the FDC model are adjusted based on an estimated change in mean annual streamflow. In order to develop a methodology to adjust the FDC for a change in forest cover, the effect of vegetation on each of the parameters of the FDC model needs to be understood. Analysis of streamflow data from paired catchment studies showed that for the afforestation and deforestation experiments changes can occur in all parameters of the FDC model under altered vegetation conditions. For perennial streams, the major changes are seen in the conditional median flow parameter and parameter that describes the low flow section of the FDC. For intermittent streams or streams that become intermittent after vegetation change the conditional median flow parameter and the cease to flow percentile may change. The linkage between the estimated change in mean annual streamflow and the parameters of the FDC model comes from the knowledge that the area under the FDC must be equal to the mean annual streamflow. Thus, a methodology has been developed that uses an estimated change in mean annual streamflow to adjust the parameters of the FDC model. This methodology has been applied to two experimental catchments that have a large percentage increase in forest cover, Pine Creek in Victoria and Biesievlei catchment in South Africa. These catchments have undergone a 100% and 98% change from pasture to pine plantation. Data from the pre-treatment periods in these catchments were used to develop FDCs for the initial forest cover. The change in mean annual streamflow was then calculated using a mean annual water balance model. The parameters of the FDC model were then adjusted to ensure that the predicted FDC achieved a mass balance with the new mean annual flow. Comparisons were then made between the predicted and observed FDCs for the pine plantations in these two catchments and showed good results, with a coefficient of efficiency of 0.7 and 0.95 in the Pine Creek and Biesievlei catchments respectively. Page v

6 Table of Contents Acknowledgements... iv Executive Summary...v Table of Contents... vi Table of Figures... vii Table of Tables... ix 1. Introduction Observed streamflow responses to forest cover changes Changes in mean annual streamflow due to afforestation Streamflow regime and flow duration curve Changes in flow duration curves from paired catchment studies Linking the mean annual streamflow to the FDC Adjusting the FDC for changes in forest cover Parameterisation of the Flow Duration Curve Impact of vegetation on model parameters Procedure for adjusting the FDC for vegetation change Step 1: Change in mean annual streamflow Step 2: Parameters of annual flow duration curves Step 3: Cease-to-flow percentile or 95 th percentile flow Developing a simple bucket model to adjust the 95 th or CTF percentile Developing an automated method to estimate, k Finding a solution to the bucket model Understanding how the parameters affect the model fit Developing an automated procedure to fit the bucket model Adjusting the bucket size for a change in land use Step 4: Conditional Median (initial estimate) Step 5: Lower exponent (initial estimate) Step 6: Achieving mass balance Application of the model to Pine Creek and Biesievlei catchment Pine Creek - An example of adjusting the FDC for afforestation in ephemeral streams Step 1: Estimating streamflow under new vegetation type Step 2: Parameters of annual flow duration curves Step 3: The cease-to-flow percentile Step 4: Conditional median (initial estimate) Step 5: Lower Exponent (initial estimate) Step 6: Achieving mass balance Biesievlei An example of adjusting the FDC for afforestation in a perennial stream Step 1: Estimating streamflow under new vegetation type Step 2: Parameters of annual flow duration curves Step 3: The cease-to-flow percentile Step 4: Conditional median (initial estimate) Step 5: Lower Exponent (initial estimate) Step 6: Achieving mass balance Discussion Conclusions References Appendix A: Example of recession constant calculation Identifying the recessions Identifying and removing the surface flow component Separating the interflow and baseflow Determining the recession constant for the entire time series Page vi

7 Table of Figures Figure 1: Relationships between mean annual streamflow and rainfall for catchments under different vegetation cover (after Zhang et al., 2001)... 2 Figure 2: Time series and flow duration curve for a) ephemeral stream (dry 55% of the time), and b) perennial stream. From left to right, the 3 charts are: 1) time series, 2) time series plotted using log-scale, 3) FDC curve plotted on log-scale for the same period... 3 Figure 3: Typical flow duration curves for perennial and ephemeral streams Figure 4: Flow duration curves (1 year period) for the Redhill catchment (near Tumut, NSW). 1-year-old pines, and 8-year-old pines. (after Vertessy, 2000) Figure 5: Flow duration curves for Wights catchment in south-western Australia (Based on a water year from April-March). (Data courtesy of Department of Environment, WA)... 5 Figure 6: Flow duration curve from Glendhu experimental catchments (NZ) during the calibration period (both catchments tussock) years after pine plantation established years after pine plantation established (from McLean, 2001) Figure 7: Linking the Zhang curves to the FDC. Using the Zhang Curves (a), the change in mean annual streamflow can be predicted (Δ Streamflow). This is linked to the FDC (b) as the shaded area between the FDC for Grass and FDC for forest is equal to Δ Streamflow... 7 Figure 8: Normalising the FDC to achieve common parameter space... 8 Figure 9: Flow chart showing the key steps in adjusting the FDC for land use change.12 Figure 10: Relationship between mean annual rainfall and mean annual runoff for grass and forested catchments, adopted from Zhang et al. (2001) Figure 11: Figure showing the soil water storage at which stream ceases to flow. While soil water storage (S) is above the stream invert, baseflow occurs Figure 12: Single bucket model used to model the percentage of time the flow occurs in a given catchment. In figure A, S base is the S max refers to the soil water storage above S base, Figures B and C show two possible configurations of S base and S ET, which the shaded area representing the soil water storage available for evapotranspiration Figure 13: ET function proposed by Farmer et al., 2003 and adopted in the simple bucket model Figure 14: Examples of surface flow, interflow and baseflow in hydrograph recessions19 Figure 15: Examples of different flow components in recessions Figure 16: Procedure for determining the change from interflow to baseflow (in a recession 28 days in length). A, shows Line 1 fitted through the first 2 points and Line 2 fitted through the last 27 points. B, shows Line 1 fitted through the first 3 points and Line 2 fitted through the remaining 26 points. C, shows the two lines that have the maximum weighted R 2 (9 points in Line 1 and 20 points in Line 2). D shows the Line 1 fitted through the entire recession Figure 17: S max and S ET that match mass balance for the bucket model. Any point on the line shown will achieve a mass balance between the total observed flow and flow from the bucket model Page vii

8 Figure 18: Combinations of S max and S ET that give match on 95 th percentile flow. The solid line shows the different S max and S ET that result in the 95 th percentile flow from the bucket model equalling the observed 95 th percentile flow Figure 19: Point where bucket model will match both mass balance and 95%ile flow. The point of intersection (marked by the black dot) of these two lines gives the most satisfactory fit for the bucket model Figure 20: No solution to bucket is possible with current recession constant as the two lines do not intersect Figure 21: Impact of adjusting k, on the mass balance curve. Increasing k (i.e. bucket drains more slowly) moves curve to the right, decreasing k (i.e. bucket drains more quickly) move curve to the left Figure 22 : Flow diagram of steps to find a solution to the bucket model Figure 23: Typical relationship between the conditional mean and conditional median.26 Figure 24: Observed FDCs in Pine Creek under forested and Figure 25: Observed and fitted FDCs for the 4 calibration years Figure 26: Recessions used to define the recession constant, baseflow sections have been used to determine a recession constant of k = Figure 27: Figure showing the observed flow and bucket model flows for the calibration period Figure 28: Figure showing the observed flow and bucket model flows for the equilibrium period Figure 29: Relationship between conditional mean and median for the 4 years used as a calibration period Figure 30: Predicted FDC for grazing and pine plantation and the observed FDCs for the calibration period (first 3 years of data) and for the last three years of treatment (assumed to be close to new equilibrium conditions) Figure 31: Observed FDCs in Biesievlei under native vegetation and forest Figure 32: Observed and fitted FDCs for pre-treatment period Figure 33: Recessions used to determine the recession constant. Recession has been determined to be k = Figure 34: Figure showing the observed flow and bucket model flows for calibration period Figure 35: Figure showing the observed flow and bucket model flows for equilibrium period Figure 36: Relationship between conditional mean and median for the 9 years used as a calibration period Figure 37: Observed and predicted FDC for pre-treatment and post-treatment vegetation types Figure 38: FDCs using monthly Data from Pine Creek. Calibration period represents 0% forest cover and uses 4 years of monthly data, new equilibrium represents 100% forest cover and using 3 year of monthly data Page viii

9 Table of Tables Table 1: Summary of experimental catchment groups (Details and key references can be found in Best et al., 2003a) Table 2: Results for the Mann-Kendall test for trend at the 0.05 level of significance. Values are the number of catchments showing a statistically significant trend in positive or negative direction Table 3: FDC parameters for the 4 years used as the control period Table 4: FDC parameters for the 10 years used as the control period Page ix

10 1. Introduction Afforestation is recognised as a potential major land use change for Australia in the coming decades. This means that the impacts of afforestation on water security, salinity, and environmental flows need to be considered in catchment management planning. Significant progress has been made in our understanding of the relationship between vegetation and streamflow at the mean annual time scale. The model developed by Zhang et al. (2001) to predict the impact of forest cover changes on mean annual streamflow has proven to be robust in Australia and has been used to assess the impact of vegetation changes at a regional scale (Zhang et al., 2003). While changes in mean annual streamflow associated with afforestation are important, it is perhaps even more significant to predict the effects of afforestation on streamflow at shorter time scales. This is because models for water allocation, water quality, and environmental flows all require the ability to predict how monthly or daily flow time series will be affected by changing land use. For example, water allocation models such as the Integrated Quantity and Quality Model (IQQM) (Simons et al., 1996) and Resource Allocation Model (REALM) (Diment, 1991) use daily or monthly catchment inflow data. Unfortunately, our understanding of the seasonal impact of forest cover change on streamflow is limited and there have been no effective tools available for predicting changes at shorter time scales. It is generally understood that afforestation affects not only rainfall interception, which directly influences surface runoff, but also deep drainage (Zhang et al., 1999). The impact on deep drainage determines the amount of baseflow in a catchment. However, it is difficult to quantify these changes where no detailed experimental data are available. The degree of control on these processes by vegetation depends upon climate, soil, and other catchment characteristics. One of the difficulties in predicting changes in streamflow at the monthly or daily time step is to decide on a method that can capture the characteristics of the streamflow time series in the simplest way possible. This is important when comparing two time series as the difference needs to be quantified using well-defined statistics, such as the mean and the variance. A commonly used approach for making such predictions is to rely on detailed physically based models or statistical models derived from paired-catchment studies (Vertessy et al., 1993; Scott and Smith 1997). These methods are either difficult to apply due to the extensive data requirements or constrained by local data, so an alternative approach is required. One way to evaluate the effect of afforestation on a streamflow time series is to examine changes in a catchment s flow duration curve (FDC) following a change in forest cover. A FDC represents the relationships between the magnitude and frequency of streamflow for a catchment and provides an estimate of the percentage of time a given flow is equalled or exceeded. The adoption of the flow duration curve (FDC) as a method to summarise the key features of a time series of streamflow, allows the identification of differences between two streamflow time series. Another useful feature of a FDC is the ability to display flow variability. It also has direct application in hydrology for hydropower, water allocation, and water quality management. Most studies involving FDC analysis aim to provide information on the relationships between flow and frequency for catchments under static land-use (Fennessey and Vogel, 1990). However, the main aim of this study was to develop a procedure for predicting responses in a catchment s FDC following a change in forest cover. This requires identification of appropriate models that can be manipulated to reflect observed responses within a procedure that is simple enough for practical use. This report describes the development of a methodology to predict how a FDC based on daily data will change following a change in forest cover. Section 2 introduces the concept of flow duration curves and describes observed changes in FDCs from paired catchment studies. Section 3 details the development of a FDC adjustment methodology with its assumptions, parameterisations, and operational procedure. Section 4 applies the methodology to two paired catchment studies where a significant change in forest cover has occurred. The strengths and limitations of the FDC model are discussed in Section 5, including the potential adjustments to the methodology for monthly data. Page 1

11 2. Observed streamflow responses to forest cover changes 2.1. Changes in mean annual streamflow due to afforestation Before describing responses in daily streamflow following forest cover changes, it is important to understand changes in mean annual water balance. Forested catchments have a lower mean annual streamflow than non-forested catchments, and changes in vegetation cover (e.g. afforestation or clearing) will result in changes in mean annual streamflow. The work of Zhang et al. (1999, 2001) has provided a robust estimator for the impact of afforestation or tree clearing on mean annual streamflow. Figure 1 shows the generalised curves that describe the relationship between mean annual rainfall and mean annual streamflow. These relationships are based on observed data from over 250 catchments around the world, covering a variety of climates and vegetation types and are robust when considered over such a range of conditions Mena annual water yield (mm) Grass Forest Mean annual rainfall (mm) Figure 1: Relationships between mean annual streamflow and rainfall for catchments under different vegetation cover (after Zhang et al., 2001) Streamflow regime and flow duration curve The streamflow regime of a catchment represents its flow characteristics such as distribution of the flow and its variability. A FDC is a simple and powerful tool that provides a statistical overview of the distribution of flow at the outlet of a catchment. It is a graphical and statistical summary of the flow variability and distribution. The shape is determined by the size and physiographic characteristics of the catchment and the associated rainfall pattern. The shape is also influenced by water resources development and land use type (Smakhtin, 1999). The FDC is widely used in hydrology as it provides an easy way of displaying the complete range of flow. It is adopted in this project as it provides a useful measure of how the distribution of streamflow may alter following a change in forest cover. A FDC can be constructed from daily streamflow data by ranking the flow from the maximum to the minimum, and determining the percentage of time each flow value is exceeded (Figure 2). Page 2

12 a) Flow(mm/day) Flow(mm/day) Flow(mm/day) Days Days Percentage of time that flow is exceeded b) Flow(mm/day) Flow(mm/day) Flow(mm/day) Days Days Percentage of time that flow is exceeded Figure 2: Time series and flow duration curve for a) ephemeral stream (dry 55% of the time), and b) perennial stream. From left to right, the 3 charts are: 1) time series, 2) time series plotted using log-scale, 3) FDC curve plotted on log-scale for the same period. The FDC for a given catchment represents several key characteristics of the streamflow time series. For example, in Figure 3, the high-variability perennial stream will only exceed a flow of 0.1 mm/day (averaged over the catchment) for about 50% of the time. For the ephemeral stream, there is no flow for approximately 57% of the time. By displaying flows in this fashion, a better appreciation of the complete range of streamflow and its variability can be observed. The general slope of the curve represents streamflow variability, while the x- intercept indicates the perennial or ephemeral nature of the stream. For regulated catchments, flow duration curves will be relatively flat indicating more constant flow, while for catchments with highly variable rainfall and little water storage capacity, the slopes of flow duration curves will be very steep. The perennial or ephemeral nature of a stream can be clearly identified by examining the x-intercept or the percentage of time the flow is greater than zero. Page 3

13 Flow (mm/day) perennial stream with low variability perennial stream with high variability ephemeral stream Percentage of time flow is exceeded Figure 3: Typical flow duration curves for perennial and ephemeral streams. A FDC may be depicted for different time intervals, such as months or days. It can be based on all the flows in a given year (annual flow duration curve) or for a subset of annual flows (seasonal flow duration curve). In this project, we have focused on the FDC constructed from daily flow data for an annual time period. However, with some adjustments, we believe that the methodology could also be applied to monthly data (see section 5) Changes in flow duration curves from paired catchment studies Brown et al. (2005) provided examples of the change in the FDC for three experimental catchments following forest cover modification. These examples are presented here to demonstrate how a catchment s FDC could be affected by a change in vegetation cover. Figure 4 depicts the change in FDC due to pine afforestation in the Red Hill catchment (located about 50 km west of Canberra, within the Murrumbidgee basin). Red Hill has a catchment area of 195 ha, winter-dominant rainfall and an average annual rainfall of 866 mm (Hickel, 2001). Prior to conversion to pines, the catchment was predominately used for grazing. Streamflow data from year 1 and year 8 following planting of the pines were used to represent the pre- and post- treatment conditions. The data from these two years were chosen because of the similar annual rainfalls of 887 mm and 879 mm, respectively. The FDC indicated that there is approximately a 50 % reduction in high flows (0 to 5 th percentiles on FDC). Low flows (70 th to 100 th percentile on the FDC) have become zero indicating a 100% reduction. The FDC indicates that the Red Hill catchment moves from being a highly variable perennial stream to an ephemeral stream following the establishment of the pine plantation. Page 4

14 10 Grass. Annual Rainfall = 887 mm Trees. Annual Rainfall = 879mm 1 Flow (mm/day) Percentage of time flow is exceeded Figure 4: Flow duration curves (1 year period) for the Redhill catchment (near Tumut, NSW). 1- year-old pines, and 8-year-old pines. (after Vertessy, 2000). Figure 5 shows the response to conversion of native forest to pasture in the Wights catchment in south Western Australia. The Wights catchment is part of a series of paired catchment experiments in that region. The interplay between the local groundwater system and vegetation plays an important role in the hydrological response of these catchments in particular the change in streamflow observed when native forest is replaced by pasture. The response is related to an increase in the area of groundwater discharge (Schofield, 1996). As with Figure 4, it is shown that all sections of the FDC are affected by the change in vegetation type. Comparing the FDC for pasture ( ) with a period of similar climatic conditions for native vegetation ( ) a 50 % change in high flows can be expected when changing from forest to pasture and a 100 % change in low flows Flow (mm/day) Percentage of time flow is exceeded Average Annual Rainfall = 1002 mm Average Annual Rainfall = 800 mm Average Annual Rainfall = 963 mm Average Annual Rainfall = 1008 mm Average Annual Rainfall = 914 mm Average Annual Rainfall = 1020 mm Average Annual Rainfall = 884 mm Figure 5: Flow duration curves for Wights catchment in south-western Australia (Based on a water year from April-March). (Data courtesy of Department of Environment, WA). Figure 6 depicts a different response to pine afforestation than the previous examples. These data are from the Glendhu experimental catchments in New Zealand. The control and treated catchments have mean annual rainfalls of 1310 mm and 1290 mm respectively. The treatment involved the planting of 67% of the catchment with Pinus radiata (McLean, 2001). As there is little difference between the control and the treated catchments FDC for the pre- Page 5

15 treatment period, thus the changes in high and low flows have been assessed through comparison of the control and the treated catchment at various stages after treatment. The relative reductions in flows are uniform for all parts of the flow duration curve with ~30 % reduction in both low and high flows Flow (mm/day) Percentage of time flow exceeded Control Control Control Treated Treated Treated Figure 6: Flow duration curve from Glendhu experimental catchments (NZ) during the calibration period (both catchments tussock) years after pine plantation established years after pine plantation established (from McLean, 2001). The response seen in the Red Hill and Wights catchments are typical of drier areas where annual evapotranspiration of forests approaches annual precipitation, while the response seen in Glendhu is typical of wetter areas where annual precipitation is greater than the annual evapotranspiration. It should be noted that rainfall seasonality could also affect the responses of the FDCs to land-use change. In the Mountain Ash catchments in southern Australia, Watson et al. (1999) noted that in wetter catchments all flows respond to climatic and vegetation changes in unison with the changes in the mean flow, however, in the drier parts of the study area changes in low flows are accentuated Linking the mean annual streamflow to the FDC The procedure outlined in Section 3 to adjust the FDC for changes in forest cover uses a top-down or downward approach to model development (Sivapalan et al., 2003). This approach differs from the physically based modelling approach in that it tries to capture the overall response of a catchment based on the analysis and interpretation of the observed response data. The level of process understanding included in a model is based on analysis of the data, rather than the notion that a particular process must be included in the modelling. The mean annual water balance model of Zhang et al. (1999) and Zhang et al. (2001) is a good example of the downward modelling approach. It provides a practical tool known as the Zhang curves for predicting the long-term consequences of afforestation or deforestation on mean annual evapotranspiration at the catchment scale. This model is based on observed data and has the advantage over traditional process based models in that the required input data (mean annual rainfall and percentage forest cover) are readily available at both the catchment and regional scale. By linking the Zhang curves to a parameterisation of FDC, a methodology has been developed that allows the impact of vegetation change on the FDC to be predicted. The linkage between the Zhang curves and the parameterisation for the FDC comes primarily from the knowledge that the area under the FDC must be equal to the mean annual streamflow. While the Zhang curves produce an estimate of the mean annual evapotranspiration, it is a simple matter to change this estimate to an estimate of mean annual streamflow. By assuming that the relative change in soil water storage is minimal, the mean annual streamflow is calculated as the difference between the mean annual rainfall Page 6

16 and the mean annual evapotranspiration. Figure 7 shows the link between the Zhang curves and the area under the FDC. Figure 7: Linking the Zhang curves to the FDC. Using the Zhang Curves (a), the change in mean annual streamflow can be predicted (Δ Streamflow). This is linked to the FDC (b) as the shaded area between the FDC for Grass and FDC for forest is equal to Δ Streamflow In order to develop a methodology to adjust the FDC for a change in forest cover, the following steps were undertaken: parameterise the FDC (Section 3.1); determine the effect of vegetation on each of the parameters of the FDC model based on paired catchment data (Section 3.2); and develop a methodology for adjusting the FDC parameterisation in accordance with the estimates of change in streamflow predicted from the Zhang curves (Section 3.3). Page 7

17 3. Adjusting the FDC for changes in forest cover 3.1. Parameterisation of the Flow Duration Curve Various methods are used to parameterise the FDC (Cigizoglu and Bayazit, 2000). These methods have generally been used to produce regionalised FDCs (Meunier, 2001; Fennessey and Vogel, 1990) or to predict FDCs for ungauged catchments (Holmes et al., 2002). However, investigations into the changes in the FDC resulting from change in a catchment s vegetation are limited. Burt and Swank (1992) used a regression model relating the percentile flow in a control and a treated catchment during a seven-year control period. This allowed the FDC for the treated catchment to be predicted using the FDC from the control catchment in the post treatment period. While this improves our understanding of the impact that vegetation has on the FDC it does not provide a methodology for predicting the impact of proposed forest cover changes on a catchment s FDC. In order to develop a predictive methodology it is first necessary to determine a parameterisation of the FDC that captures the key components of the curve. It is also important that the parameterisation be linked to known catchment properties and/or predicted changes in streamflow. Figure 8 shows the method used to normalise the FDC of perennial and ephemeral streams. Firstly, the cease-to-flow (CTF) percentile is established (Figure 8a). The CTF percentile is defined as the ratio of the number of non-zero flow days to the total number of days. A non-zero flow day is defined as any day on which flow is greater than or equal to a specified threshold value (adopted here as mm/day). A FDC is then constructed using only the days on which flow is greater than the threshold value as streamflow measurements below this value are considered unreliable (Figure 8b). The FDC for the days of flow is then normalised by dividing all flow values by the conditional median (Figure 8c). The conditional median is defined as the median flow of the days on which flow occurs. Finally, the FDC is plotted in log-normal space (Figure 8d) to produce a Normalised FDC (NFDC). This normalisation procedure results in all of the NFDCs intersecting the origin. a Flow CTF Percentile Percentage of time flow is exceeded Determine the CTF percentile and determine the FDC for days when flow occurs b Flow Percentage of time flow is exceeded Ephemeral Stream Perennial Stream Divide All flows by the median (P 50 ) d log (Flow/P50) Normal Probability Plot in log-normal Space to generate the normalised FDC c 100 Flow/P Percentage of time flow is exceeded Figure 8: Normalising the FDC to achieve common parameter space Three models were developed and tested to determine the most appropriate one to describe the shape of the NFDC (Figure 8d). These models are discussed in detail in Best et al., 2003b. The three models were compared to determine which of the parameterisations gave the most robust fit to a range of flow duration curves. Equation 1 describes the final model Page 8

18 used to parameterise the FDC. This model has five-parameters and involves fitting an exponential curve to the upper and lower sections of the NFDC. P yˆ P s exp F c1 s exp F c x CTF x CTF c1 1 c 2 1 CTF x 2 CTF x CTF 2 x CTF Equation 1 where: ŷ is the predicted flow, F -1 is the inverse of the standard normal cumulative distribution, P 50 is the median of the non-zero flow days, CTF is the cease-to-flow percentile (expressed as a percentage), x is a flow percentile value (0-100%) and s, c 1, c 2 are curve fitting parameters. A cease to flow threshold value for flow of mm/day has been adopted for all catchments. The s, c 1 and c 2 parameters relate to different sections of the FDC, s being the slope at the origin of the NFDC and c 1 and c 2 being the exponents for the upper and lower sections of the NFDC, respectively. Given a model that describes the shape of the FDC (referred to as the FDC model), the next step is to understand how changing vegetation affects the model parameters. This was done using data from paired catchment studies Impact of vegetation on model parameters To investigate how the model parameters change with time, the parameters for the FDC model were determined for the FDC for each year of record for each of the afforestation and deforestation paired catchment studies listed in Table 1. The Mann-Kendall non-parametric test for trends (Mann, 1945; Kendall, 1975) was used on the different periods depending on the type of treatment to determine whether the observed changes were statistically significant. The Mann-Kendall test was used in this analysis as in many of the paired catchment studies steady state conditions are not reached under the new vegetation conditions and a test for change in the mean was inappropriate. The same test period was used for the control catchment, in which no change in vegetation had occurred. This approach was adopted as it allowed an investigation into the cause of the trend. For example, if a trend in the median flow were due to a climatic change then it would be expected that both the control and the treated catchment would show a significant and similar trend, but if the change were due to an alteration to vegetation then the trend would only be detected in the treated catchment. Page 9

19 Table 1: Summary of experimental catchment groups (Details and key references can be found in Best et al., 2003a). Experimental catchment group Number of treated catchments (number of control catchments) Treatment 1 Type South Africa Cathedral Peak 2 (1) A Jonkershoek 5 (1) A,D Mokobulaan 2 (1) A Westfalia 1 (1) A Witlip 1 (1) D New Zealand Glendhu 1 (1) A Australia Collie Basin 3 (1) D Red Hill 1 (1) A 1. A denotes afforestation experiments, D denotes deforestation experiments The Mann-Kendall test was used to test for significant trends in the control and treated catchments. As only catchments with large areas of treatment are likely to show a trend, 16 paired catchment studies all with at least 50% of the area treated were used for this analysis. Table 2 shows a summary of the results for the model parameters for the control and the treated catchments. A number of the afforestation catchments in South Africa have long treatment histories with more than one planting rotation. Where this was the case, the period of record was divided to allow trends to be detected during the first and second rotation. The clear-felling of the catchment at the end of the first rotation was also considered as a deforestation experiment. Table 2: Results for the Mann-Kendall test for trend at the 0.05 level of significance. Values are the number of catchments showing a statistically significant trend in positive or negative direction. Treated catchments Control catchments Model parameters Model Parameters Median CTF s c1 c2 Median CTF s c1 c2 Treatment 1. A (13) D (5) A denotes afforestation experiments, D denotes deforestation experiments. The number in brackets indicates the number of experiments in each treatment type. indicates an increase in parameter value and indicates decrease in parameter value. Table 2 shows that significant changes can occur in all parameters under altered vegetation conditions. However, the major effects are in the median flow parameter and lower exponent for perennial streams and in either or both of the conditional median flow and the CTF percentile for intermittent streams or streams that become intermittent after vegetation change. For the catchments reported in Table 2, 4 of the 13 afforestation catchments, 3 of the 5 deforestation catchments were intermittent at some point during the period of record. Given the methodology established to parameterise the FDC and an understanding of how each of the parameters changes following a change in forest cover, we seek to develop a methodology to link the estimated change in streamflow from the Zhang curves to this parameterisation. The change in streamflow predicted by the Zhang curves is linked to the median of the non-zero flow days by an empirical relationship. This empirical relationship varies depending on the rainfall of the catchment. In high rainfall areas, all the change in streamflow are reflected as changes in the median, as under forested conditions, the flow remains perennial. In lower rainfall areas, it is possible that no change will occur in the Page 10

20 median of the non-zero flow days and the change in streamflow will be entirely reflected as a change in the CTF percentile. We hypothesise that the response of the FDC to forest cover change occurs in two ways, depending on the rainfall. When forest cover is increased in high rainfall areas, it is anticipated that the proportional reductions in all flow percentiles are similar, while for catchments in lower rainfall areas the higher percentiles (lower flows) are reduced by a greater proportion than the higher flows. These differences are because in high rainfall areas while there is an increase in evapotranspiration when forest cover is increased there is no significant drawdown of soil moisture stores. However, in lower rainfall areas a combination of increases in evapotranspiration and an increase in soil moisture draw caused by the greater depth of tree roots results in larger proportional reduction in low flows compared to high flows. Therefore, in catchments with high rainfall, we hypothesise that the exponents do not change significantly under altered land use conditions. However, for lower rainfall areas, we anticipate that the CTF percentile or c 2 parameter would be altered as a result in changes to the low flow conditions. Changes are expected in the model parameters when the percentage forest cover is altered. The changes in model parameters depend on the type of treatment and prevailing climatic conditions. The results indicate that the major changes occur in the parameters relating to the median flow and the low flow section of the FDC. The change in the low flow portion is reflected in the change in the CTF and c 2 parameters in Table 2. Section 3.3 provides the methodology for linking predictions of change in mean annual streamflow to the parameterisation of the FDC Procedure for adjusting the FDC for vegetation change Figure 9 shows the methodology for adjusting the FDC for forest cover change. The method has six steps, with each of these steps described in detail in Sections 3.4 to 3.9 respectively, starting with estimating the change in mean annual streamflow and finishing with the adjustment of conditional median flow to ensure that the area under the FDC is equal to the predicted mean annual streamflow. The data required to use the methodology are: 1. daily flow data under static land use conditions; 2. daily rainfall data; 3. daily point potential evapotranspiration (PET) data; 4. current percentage forest cover; and 5. proposed percentage forest cover. Page 11

21 Collate data for the catchment: rainfall, flow, PET, current percentage forest cover, new percentage forest cover Step 1 Use mean annual water balance model to predict change in water yield when going from current percentage forest cover to new percentage forest cover Step 2 Divide observed flow data into water years and fit FDC curve parameterisation to each annual FDC. Determine mean slope Determine mean upper exponent Step 3 Determine CTF percentile for new percentage forest cover Step 4 Initial estimate of conditional median flow for new percentage forest cover Step 5 Initial estimate of lower exponent Step 6 Adjust median to get mass balance Adjust lower exponent Adjusted FDC for new percentage forest cover Figure 9: Flow chart showing the key steps in adjusting the FDC for land use change Step 1: Change in mean annual streamflow Given a proposed change in forest cover, the change in streamflow can be estimated using the Zhang curves. The Zhang curves were developed to estimate the change in evapotranspiration when going from one vegetation type to another. Assuming that the change in the soil water storage and recharge terms are negligible over the long term, the water balance can be simplified to streamflow equalling rainfall minus actual evapotranspiration. Thus, an estimate of mean annual evapotranspiration can be changed into an estimate of mean annual streamflow. Figure 10 shows the relationship between mean annual rainfall and mean annual streamflow based on the equations developed by Zhang et al. (1999). Equation 2 gives the expression for calculating the evapotranspiration under a given percentage forest cover and Equation 3 gives the expression used to change the ET estimate into an estimate of streamflow (Zhang et al., 2001). Page 12

22 Mean annual water yield (mm) Forest - observed Grass - observed Mixed veg. - observed Grass Forest Rainfall (mm) Figure 10: Relationship between mean annual rainfall and mean annual runoff for grass and forested catchments, adopted from Zhang et al. (2001) P 1 P ETf f f P 1410 P 1100 P P 1410 P 1100 Equation 2 where, f is the fraction of forest cover, P is the mean annual rainfall, and ET f is the estimated actual total annual evapotranspiration in mm for a specific percentage forest cover f. WY P ET Equation 3 f f where WY f is the predicted mean annual streamflow, P is the mean annual rainfall and ET f is the mean annual evapotranspiration as calculated from Equation 2. The change in streamflow (WY) is calculated from the proportional change in streamflow predicted from the Zhang curves and the observed mean annual streamflow for the current forest cover, as given in Equation 4. WY WY current proposed WY WYcurrent _ observed WYcurrent Equation 4 where, WY current_observed is the observed streamflow under current land use, WY current and WY proposed are the streamflows predicted from the Zhang curves under current forest cover and proposed percentage forest cover respectively. As is seen from the scatter in Figure 10, a large number of catchments do not fall on the Zhang curves. It is considered that the proportional change in streamflow is more accurate than the absolute values. Therefore, the streamflow under new forest cover is determined as the sum of the mean annual streamflow under current vegetation and the proportional change in streamflow predicted from the Zhang curves as given in Equation 5. WY WY WY Equation 5 new current _ observed where, WY new is the predicted streamflow under proposed forest cover, WY current_observed is the observed streamflow under forest cover (determined from the observed flow time series in the catchment) and WY is the change in streamflow determined from Equation 4. Page 13

23 3.5. Step 2: Parameters of annual flow duration curves The daily annual flow duration curve is defined as the flow duration curve for a complete year constructed from daily flow data from that year. To minimise the difference between the soil water storage at the beginning of each year, a water year has been adopted as the annual time unit. In determining the water years, it was decided not to split either the wet or the dry flow periods. Therefore, the start of the water year is defined as being the first day of the month following the cumulative average driest three-month period. For example, if February, March and April gave the driest three-month average, then the water year would start on May 1 st and finish on April 30 th. Once the start of the water year is determined, the observed flow data is divided into water years, the observed FDCs are then calculated and the FDC model parameters determined for each water year. The FDC parameters are the CTF percentile, the conditional median and three curve fitting parameters for the NFDC, referred to as the slope, upper exponent and lower exponent. The slope, upper exponent and lower exponent are s, c 1 and c 2 in Equation 1, respectively. The CTF percentile and the conditional median are determined directly from the observed data while the curve fitting parameters are fitted using a two stage iterative process: 1. The slope and then the upper and lower exponents are adjusted to minimise the sum of squared error of the difference between the observed and fitted FDCs. 2. The slope and then the upper and lower exponents are adjusted to achieve a mass balance between the fitted curve and the observed data. Once the parameters for each annual FDC have been determined, the mean slope and mean upper exponent can be determined. It is assumed that these two parameters remain unchanged following a change in forest cover. However, to ensure that only excellent fits are used to determine the mean slope and upper exponent only years with a coefficient of efficiency greater than 0.97 are used in the calculation of the mean slope and upper exponent. Equation 6 gives the expression used to calculate the coefficient of efficiency (Nash and Sutcliffe, 1970) between the observed and the fitted curve. CofE CTF O P i1 1 Equation 6 2 CTF log( O) log( O ) i1 log log 2 where O is the observed percentile flow and P is the predicted percentile flow. Thus the closer the coefficient of efficiency is to one the better the fit. The logarithm of the values is used to give more weight to low flow values. The CofE has only been calculated between the first percentile and the CTF percentile, thus zero flows are not considered. This is because the CTF percentile is calculated from the observed time series, thus there is no difference between the fitted and observed FDCs between the CTF percentile and 100 th percentile Step 3: Cease-to-flow percentile or 95 th percentile flow As was shown in section 2.3, vegetation has a greater affect on the lower flow section of the FDC than the high flow section. The low flows (represented by the 95 th percentile for perennial streams and the CTF percentile for ephemeral streams) are controlled by interception, soil type and depth, the ability of vegetation to extract water from the soil moisture store, and the pattern of rainfall. When a catchment s vegetation is changed, catchment interception and amount of water extracted from the soil moisture store will be effected. The Zhang curves provide us with an estimate of how the total evapotranspiration may change under different percentage forest cover. However, it does not indicate how vegetation affects the individual processes, such as interception loss and transpiration from the soil water store. In Australia, it is recognised that clearing of native vegetation for agriculture has led to increased recharge and hence increased groundwater levels. These Page 14

24 elevated groundwater levels are the result of less total actual evapotranspiration by agricultural crops and pastures compared with forests Developing a simple bucket model to adjust the 95 th or CTF percentile Cease-to-flow conditions occur when the soil water storage is below the stream invert, as shown in Figure 11. This section describes the development and adjustment of the simple bucket model for a change in forest cover. The simplest conceptualisation of this system is a single bucket model where the relationship between precipitation (P), evapotranspiration (ET) and streamflow (Q) is mediated by the soil water storage. The bucket model has been conceptualised as shown in Figure 12A. The maximum soil water storage, S max, represents the maximum soil water possible above the baseflow threshold (S base ). The threshold for evapotranspiration is given by S ET, while the soil water storage at which streamflow ceases is given by S base. ET Soil water storage (S) Q direct Q bas e Figure 11: Figure showing the soil water storage at which stream ceases to flow. While soil water storage (S) is above the stream invert, baseflow occurs. Page 15

25 P I ET P I ET P I ET S max Q direct S max Q direct S max Q direc t S ET S base Q base S base Q base S base Q base S ET S ET A B C Figure 12: Single bucket model used to model the percentage of time the flow occurs in a given catchment. In figure A, S base is the S max refers to the soil water storage above S base, Figures B and C show two possible configurations of S base and S ET, which the shaded area representing the soil water storage available for evapotranspiration. The water balance of the bucket model is given by S S P I ET Q Q Equation 7 t t t t t direct base 1 t t where S t-1 is the storage at the previous time step, P t is the rainfall, I t is the interception, ET t is the actual evapotranspiration, Q direct is the surface or quick flow and Q base is the baseflow. The order in which water is added and subtracted from the bucket to achieve the storage at the end of a day is important and should represent the order in which the processes occur. Therefore, the interception loss is removed from the rainfall and the remaining rainfall is added to the storage in the bucket. If the storage exceeds S max then direct runoff occurs and is calculated as in Equation 8. Once Q direct has been determined, ET is calculated based on Equation 9. Once the ET has been estimated, Q base can be calculated as shown in Equation 10. Thus, the storage at the end of a day can be calculated. 0 St 1 P I S max Qdirect Equation 8 St1 P I S max St 1 P I S max The ET of vegetation is a function of soil water storage in the root zone, leaf area index and potential evapotranspiration. In order to keep the bucket as simple as possible and as our main interest is going from agricultural crops or pasture to plantation forestry, the relationship between actual ET and PET shown in Figure 13 has been adopted. A linear interpolation between the forest and grass curves has been adopted for partial forest cover in a catchment as shown in Equation 9. Page 16

26 Relative Evapotranspiration Rate ET/PET FOREST GRASS Relative Soil Water Store (Root Zone) Figure 13: ET function proposed by Farmer et al., 2003 and adopted in the simple bucket model. ET ET ET grass forest total RSWS t t g PETt RSWS 0 PETt RSWSt PETt f fet S t1 forest t (1 f ) ET Pt I S t Q S direct ET RSWS RSWS 0.4 RSWS grass where RSWS is the realtive soil water storeage and max S ET t t RSWS t RSWS t t t 0 is the percentage forest cover 0 Equation 9 0 S PI Q ETS Qbase t ln( k) S PI Q ETS S PI Q ET S where k is the recession constant t1 t t direct base t1 t t direct t basse t1 t t direct base Equation 10 As shown in Equation 10, the baseflow is calculated assuming a simple linear storage model. This requires an estimation of the recession constant. As the bucket model is calibrated to observed flow, the recession constant has been estimated from the observed time series of daily streamflow following the procedure outlined in Section Page 17

27 The recession from a simple linear storage can be expressed as: Q t Q 0 exp( t) Equation 11 where Q t is the discharge at time t, Q 0 is the initial discharge, and is a constant. The exp(- t) term can be replaced by the recession constant, k. This recession constant can be used to determine the amount of baseflow released from the simple bucket model as shown in Equation 10. Figure 12B and C show two possible configurations of the bucket model, one in which the threshold of ET is greater than the threshold for baseflow and one in which the threshold for ET is less than the threshold for baseflow. The shaded regions in these two diagrams refer to the range in which soil water storage is available for transpiration. To adjust the bucket model for the predicted change in streamflow or ET, it is assumed that k, S max and S base are not impacted by change in vegetation. Therefore, only S ET can be altered to allow the ET to change. Under conditions where a stream goes from being perennial to ephemeral, it is anticipated that the S ET would change from being above S base to below S base. S base therefore provides a point of reference for both S max and S ET and has been set to equal zero. In order to account for the different rates of interception between grasses and forest, an interception store has been added to the model. For simplicity, interception has been taken as a constant (Farmer et al., 2003). The interception has been taken as 1mm of rainfall for fully grassed catchments and 4 mm fully forested catchments. A linear function between these two values has been used to allow for the partial forest cover in a catchment Developing an automated method to estimate, k There are numerous methods available for estimating baseflow recession constant, k. Many methods rely upon plotting recessions on a logarithmic axis and using an averaging technique (Nathan and McMahon, 1990). Others use filtering methods to separate the baseflow component of flow and then estimating the recession from the filtered baseflow (CRC for Catchment Hydrology, 1996). One of the major problems with these techniques is making a distinction between the components of the recession; surface flow, interflow and baseflow. The distinction between interflow and baseflow is very difficult to estimate. Quite often, these methods are subjective and the result for the same time series differs depending on the practitioner. As the method outlined in this report aims to adjust the FDC in a reproducible manner, a methodology for determining recession constant is required that does not depend on the subjective decisions of the practitioner. The method developed for determining the recession constant works by identifying the three major components of a hydrograph recession namely, surface flow, interflow and baseflow (Figure 14). When plotted in log space, there are six possible combinations of the components of the streamflow recession (see Figure 15): 1. Surface flow only 2. Surface and interflow 3. Surface, interflow and baseflow 4. Interflow only 5. Interflow and baseflow 6. Baseflow only According to Nathan and McMahon (1990), it is possible to distinguish between the parts of a recession based on the values of the different recession constants. Typically for daily data the range for recession constants have been found to be, for surface flow, for interflow and for baseflow, thus it should be possible to separate out the baseflow recession from surface flow and interflow based on the slope when plotted in logarithmic space (Figure 15) Page 18

28 Flow (m 3 /sec) Daily flow time series Surface runoff Interflow Baseflow /07/ /08/1972 8/09/ /09/ /10/1972 7/11/ /11/ /12/1972 Date 6/01/ /01/ /02/1973 7/03/ /03/1973 Figure 14: Examples of surface flow, interflow and baseflow in hydrograph recessions 4 ln (Flow (m 3 /sec)) Surface runoff Interflow Baseflow Number of Days since start of recession Figure 15: Examples of different flow components in recessions Once the recessions are identified from the time series, they are classified into one of the six categories based on the slope. Recessions that fall into categories without a baseflow component are rejected (Categories 1, 2 and 4). The remaining recessions are then analysed by trying to fit lines of best fit to identify the baseflow component. The method works by: 1. Identifying every recession over 5 days in length. A recession is defined as a period of flow during which the flow is not increasing. Gaps and small rises in the streamflow time series cause the start of a new recession. Page 19

29 2. Identifying and removing the surface flow component. We first calculate a recession constant for each segment in the recession (see Appendix A). The segment identified as having a recession constant less then 0.8 is considered as surface flow. All segments above the lowest segment that have a recession constant less than 0.8 are also considered as surface flow. The threshold value of 0.8 for surface flow is based on the recommendations in Nathan and McMahon (1990). 3. Separation of interflow and baseflow. The baseflow and interflow are separated by determining the change in slope in the recession. This is achieved by fitting two lines through the natural log of the flow values in an iterative manner as shown in Figure 16. A line, Line 1, is fitted through the first two points of the recession and the R 2 is determined. A second line, Line 2, is fitted through the remaining points plus the last point in Line 1 and the R 2 of this line is determined (Figure 16A). The weighted R 2 is then determined by multiplying the R 2 for Line 1 with the number of points in Line 1 and adding this to the R 2 for Line 2 multiplied by the number of points in Line 2 and diving by the total number of points. This procedure is followed along the entire length of the recession, increasing the number of points in Line 1 and deceasing the number of point in Line 2 until Line 1 is fitted through the entire recession (Figure 16 B D). The maximum weighted R 2 is then determined (Figure 16C). This identifies the point where the slope of the recession changes. Flow (m 3 /sec) Flow (m3/sec) 10 1 R 2 Line1 = 1 R 2 Line2 = Change Factor = Days in recession 10 C R 2 Line1 = R 2 Line2 = A Change Factor = Days in recession Flow (m3/sec) Flow (m3/sec) B Change Factor = R 2 Line1 = R 2 Line2 = Days in recession D Change Factor = R 2 Line1 = Days in recession Points in line 1 Points in line 2 Line of best fit (line 1) Line of best fit (line 2) Figure 16: Procedure for determining the change from interflow to baseflow (in a recession 28 days in length). A, shows Line 1 fitted through the first 2 points and Line 2 fitted through the last 27 points. B, shows Line 1 fitted through the first 3 points and Line 2 fitted through the remaining 26 points. C, shows the two lines that have the maximum weighted R 2 (9 points in Line 1 and 20 points in Line 2). D shows the Line 1 fitted through the entire recession. 4. Once the point of change is determined, the recession constant for both sections of the recession can be determined. If both sections of the recession have a recession constant greater than 0.93 (based on the lower limit for recession constant for baseflow in Nathan and McMahon, 1990), then potentially the entire recession is baseflow. However, if the difference in the recession constants of the two sections is greater than 0.005, then the recession is considered to have two distinct components and the upper section is considered interflow and lower section is baseflow. If the difference in recession constant is less than then the all points in the recession are considered baseflow and the recession constant is determined for the entire recession (excluding any points considered as surface flow). If the lower section of the recession has a recession constant, less than 0.93, then all points in the recession are considered to be interflow. Page 20

30 5. The previous steps are repeated for all recessions more than 5 days in length. The overall baseflow recession constant is then determined by taking a weighted average of the recession constants for each of the individual recessions based on the length of each recession. i.e. the recessions with the greatest number of days gets the greatest weighting. The result is a single number that represents the base-flow recession constant. This is used in Equation 10 to control the baseflow from the bucket model at each time step. Appendix A provides an example of the procedure outlined above Finding a solution to the bucket model Initially, the bucket model is calibrated to give both a mass balance and the best fit to the low flow section of the FDC. The bucket model is then used to adjust either the CTF percentile or the 95 th percentile flow depending on the nature of the stream. Where a stream is perennial, the bucket model is calibrated to ensure mass balance and to give a good fit for the 95 th percentile flow. A good fit of the 95 th percentile flow is defined as being within 1 percentile of the observed 95 th percentile flow (i.e. if the observed 95 th percentile flow is 0.01mm/day, the 0.01 mm/day flow should lie between the 94 th percentile and 96 th percentile when the bucket model is calibrated). A similar approach is adopted for ephemeral streams. However, in this case, the bucket model is calibrated to ensure mass balance and a good fit on the CTF percentile, again the predicted CTF percentile from the bucket should be within 1 percentile of the observed CTF percentile. With both perennial and ephemeral streams, it is assumed that mass balance is satisfied if the total flow from the bucket model is within 1% of the total flow observed in the catchment Understanding how the parameters affect the model fit The bucket model described in Section has three parameters, S max, S ET and k. S max controls the available soil moisture for baseflow, S ET controls the depth to which water can be extracted by evapotranspiration from the bucket and the recession constant, k, controls the rate at which water flows from the soil moisture store as baseflow. Different combinations of S max, S ET and k give different fits to the observed time series. The recession constant, k, is initially estimated using the method outlined in Section Once the recession constant is estimated the bucket model is run to determine the combination of S max and S ET that will give mass balance. Figure 17 shows the different combinations of S max and S ET that give mass balance for Glendhu catchment with a recession constant of Page 21

31 Combinations of S max and S ET that give mass balance Smax S ET Figure 17: S max and S ET that match mass balance for the bucket model. Any point on the line shown will achieve a mass balance between the total observed flow and flow from the bucket model. From Figure 17 it can be seen that many combinations of S max and S ET give mass balance for the bucket model. The question then becomes which of these combinations, if any, gives a satisfactory fit (i.e. with a 1 percentile error) to the 95 th percentile flow. This is resolved by looking at the difference between the observed 95 th percentile flow and the 95 th percentile flow from the bucket model. As with the mass balance, a large number of combinations of S max and S ET gave a satisfactory fit for the 95 th percentile flow as shown in Figure 18. The intersection of these two lines gives the best solution to the bucket model for a given recession constant, k. Figure 19 combines Figure 17 and Figure 18 to show how the two curves relate to each other. The intersection point provides the most satisfactory model fit based on the two criteria (mass balance and match on 95 th percentile flow or CTF percentile). Page 22

32 Combinations of S max and S ET that match 95 th percentile flow 70 Smax S ET Figure 18: Combinations of S max and S ET that give match on 95 th percentile flow. The solid line shows the different S max and S ET that result in the 95 th percentile flow from the bucket model equalling the observed 95 th percentile flow Bucket model will achieve mass balance Bucket model will match 95 th percentile flow Smax S ET Figure 19: Point where bucket model will match both mass balance and 95%ile flow. The point of intersection (marked by the black dot) of these two lines gives the most satisfactory fit for the bucket model. From Figure 19 it can be seen that the two curves intersect, thus a satisfactory fit to the bucket model could be found without adjusting the recession constant. However, in analysis of our data, these two curves do not intersect for some catchments, as shown in Figure 20. In this situation, a satisfactory fit to the bucket model could not be found and the recession constant, k, needed to be adjusted. Figure 21 shows the impact that adjusting k by 10% has on the volume curve. Adjusting k effectively alters the proportion of quick flow (or spill from the bucket) and baseflow (flow from the soil moisture store). Page 23

33 Match of 95%ile flow Mass Balance line 70 Smax S ET Figure 20: No solution to bucket is possible with current recession constant as the two lines do not intersect k from observed time series k decreased by 10% k increased by 10% Smax S ET Figure 21: Impact of adjusting k, on the mass balance curve. Increasing k (i.e. bucket drains more slowly) moves curve to the right, decreasing k (i.e. bucket drains more quickly) move curve to the left. Once we understand how each of the parameters (S max, S ET and k) affects the fit of the bucket model, it is possible to develop an automated procedure for determining the parameters that will give us a satisfactory fit for either the 95 th percentile and the mass balance, or the CTF percentile and mass balance. As k is calculated from the observed flow data, the aim is to get the most satisfactory fit for our two criteria with the smallest adjustment possible to the recession constant Developing an automated procedure to fit the bucket model Figure 17 and Figure 18 showed that a large number of combinations of S max and S ET would give either a mass balance or a fit to the 95 th percentile flow. Thus, any automated procedure for determining the most suitable parameters for the bucket model needs to ensure that both the mass balance and low flow criteria are met. This is achieved by firstly determining the range of mass balance solutions for a given catchment and determining if a fit for the 95 th percentile flow or the CTF percentile could be achieved with the current k Page 24

34 value; if not then k needs to be adjusted. Figure 22 provides a flow diagram showing the steps involved in finding an appropriate fit for the bucket model. Determine S ET required for S max = 1 using the k calculated from streamflow record Increase k Find maximum value of S ET that will give mass balance No Is the 95 th or CTF percentile from bucket greater than 95 th or CTF percentile observed? Yes Determine S ET required for S max = 1 using current k value Increase S max, determine S ET required to achieve mass balance Is 95 th or CTF percentile from bucket within 1% of 95 th or CTF percentile observed? No YES Finish Figure 22 : Flow diagram of steps to find a solution to the bucket model Following this procedure, the parameters of the bucket model can be determined that will provide a unique solution that gives both mass balance and a match on the low flow section of the FDC. The bucket model is then used in the FDC adjustment methodology to predict the change in either the CTF percentile or the 95 th percentile flow. Therefore, it is considered appropriate that the simple bucket model is fitted to match these sections of the FDC. By achieving mass balance, we can adjust the bucket size for the change in mean annual streamflow estimated during step 1 (Section 3.4) Adjusting the bucket size for a change in land use The concept of using a simple bucket model is driven by the need to be able to predict the impact of vegetation on the low flow section of the FDC. This section of the curve is primarily driven by a change in baseflow. The ability of the deep-rooted vegetation such as forest to extract water from the soil store is much greater than short rooted grass. Therefore, to adjust Page 25

35 the bucket for a change in vegetation we needed to adjust depth to which the vegetation can extract water via transpiration from the bucket. This is achieved by assuming that after a change in vegetation the S max, S base and k parameters of the bucket model are unchanged. This means that to match the change in streamflow predicted from the Zhang curves the only parameter that can be adjusted is S ET. Increasing S ET results in greater streamflow from the bucket, which would be anticipated following a reduction in forest cover. Decreasing S ET results in a reduction in streamflow which would be expected following an increase in forest cover. Once S ET is adjusted to achieve mass balance with the mean annual streamflow for the proposed forest cover (predicted during step 1), the CTF percentile and/or the 95 th percentile flow can be determined from the daily flow time series output from the bucket model. In some cases the S ET needs to be moved in the opposite direction of that expected for the change in forest cover (i.e. S ET increased when the forest cover increased), this is because the change in interception and ET function associated with new forest cover cause sufficient changes in streamflow without a need to change the bucket size. When this occurred, the S ET value is not altered Step 4: Conditional Median (initial estimate) Once the CTF percentile for the new percentage forest cover is determined, the next parameter to be adjusted is the conditional median. This is achieved by creating catchment specific relationships between the annual conditional mean and the annual conditional median of the observed time series. The annual conditional mean and median are determined from the streamflow during the water years defined in Step 2 (Section 3.5). Figure 23 shows a typical relationship between the conditional mean and median. Once the relationship between the conditional mean and median is established, the new conditional median is estimated based on the estimated mean annual flow under the new forest cover. This method is used provided the coefficient of determination (R 2 ) is greater than 0.6. The conditional mean for the new forest cover conditions is determined by dividing the mean annual flow predicted in Step 1 by the CTF percentile for the proposed forest cover (predicted from Step 3). Figure 23: Typical relationship between the conditional mean and conditional median. Page 26

36 3.8. Step 5: Lower exponent (initial estimate) The determination of the lower exponent (c 2 ) depends on the nature of the streamflow at the catchment outlet. For ephemeral streams, the lower exponent is estimated based on the slope (s) of the NFDC and the knowledge that the CTF percentile will equal the threshold value. For perennial streams, the lower exponent is estimated based on the 95 th percentile flow from the bucket model. With an estimate of the CTF or 95 th percentile flow and the slope, we can rearrange Equation 1 to determine the lower exponent required to intercept the CTF percentile or the 95 th percentile flow. Equation 12 and Equation 13 give the expressions for determining the lower exponent for ephemeral and perennial streams respectively log TV 10 expf c2 1 s P50 c2 1 P log10 expf 0.95c2 1 s P50 c2 Equation 12 Equation 13 where s is the slope and c 2 is the lower exponent as defined in Equation 1, F -1 is the inverse of the standard normal cumulative distribution, P 50 is the median of the non-zero flow days. TV is the threshold value below which it is assumed zero (taken as mm/day), P 95 is the 95 th percentile estimated from the bucket model. As it is not possible to determine the inverse of the standard normal cumulative distribution of a value of 1, is adopted for ephemeral streams (Equation 12). For perennial streams the calculation is based on the 95 th percentile flow, hence the inverse of the standard normal cumulative distribution of 0.95 is adopted (Equation 13). This procedure provides an initial estimate of the lower exponent, however, the combination of s, c 1, c 2 and P 50 produced from the above steps do not necessarily give mass balance i.e. the area under the FDC does not equal the estimated mean annual streamflow as predicted by Equation 5. Where mass balance is not achieved, P 50 is then adjusted and c 2 is recalculated as described in Section Step 6: Achieving mass balance The slope and upper exponent are estimated in Step 2 by taking the mean of the annual slopes and upper exponents. The conditional median for the new percentage forest cover is then calculated from the recession relationship between the conditional mean and median from the observed flow data (Step 4), the lower exponent is then calculated based on the combination of the output from the bucket model and mean slope (Steps 2, 3 and 5). These parameters provide an initial estimate of the FDC under the new forest cover. However, it is important that the area under the FDC equals the mean annual streamflow predicted by Equation 5. If the area under the FDC does not equal the predicted mean annual streamflow the conditional median, P 50, is adjusted to ensure mass balance. The lower exponent is then recalculated using Equation 12 or Equation 13 to ensure that the lower portion of the FDC intersects either the 95 th percentile flow or the CTF percentile determined from the bucket model. Page 27

37 4. Application of the model to Pine Creek and Biesievlei catchment The methodology described in Section 3 to predict the impact of forest cover changes on the FDC was applied to two experimental catchments. In these catchments daily streamflow data prior to and following changes in forest cover due to afforestation are available, thus allowing the predictions to be compared to the observed responses. These examples represent two types of response: one in which there is a substantial change in the percentage of time flow occurs and the other in which the stream remains perennial. They also represent examples with varying length of streamflow record. These catchments were chosen to illustrate the methodology using varying amounts of streamflow data for current land use conditions Pine Creek - An example of adjusting the FDC for afforestation in ephemeral streams Pine creek is a small experimental catchment located in south-eastern Australia. In the late 1980 s, 100% of the catchment was changed from grazing to pine plantation, resulting in significant changes in streamflow. Figure 24 shows the observed FDCs for Pine creek for the grazing and pine plantation. Figure 24: Observed FDCs in Pine Creek under forested and Although there is no pre-treatment data for the Pine Creek catchment, it is considered appropriate to use the first 4 years of record as representative of the grazing conditions as the pines are only in the early stages of development and are unlikely to have a significant impact on the catchment s hydrology. The analysis was based on water years defined as 1 st May to the 30 th April. Below is a worked example of the methodology outlined in Section 3 for adjusting the FDC for change in percentage forest cover. Page 28

38 Step 1: Estimating streamflow under new vegetation type Old percentage forest cover = 0% (100% grazing) New percentage forest cover = 100% (100 % pine plantation) Mean annual rainfall = 830 mm Observed mean annual streamflow for 100% grazing = 109 mm ET and streamflow for current and proposed percentage forest cover as predicted from Zhang curves (Zhang et al., 2001) for rainfall of 830mm. ET zhang_old = 571 mm WY zhang_old = 259 mm ET zhang_new = 732 mm WY zhang_old = 98 mm ET % reduction zhang _ new WY ET zhang _ current zhang _ old 62% WYpredicted WYobserved _ current WYobserved _ current % reduction _ water _ yield WYpredicted 109 ( ) WY 41mm predicted where ET zhang is the evapotranspiration calculated from Equation 2 and WY zhang is the streamflow calculated from Equation Step 2: Parameters of annual flow duration curves The first 4 years of the data in Pine Creek were used to develop a set of parameters from which the relationship between the conditional mean annual flow and the conditional median could be determined. These parameters are also used to determine the mean slope and upper exponent of the NFDC. Figure 25 shows the observed and fitted FDCs for Pine Creek during the calibration period. Table 3 lists the parameters from this 4-year period. Figure 25: Observed and fitted FDCs for the 4 calibration years. Page 29

39 Table 3: FDC parameters for the 4 years used as the control period. Water Year CTF percentile Conditional Median Slope Upper Lower C of E 1 Mean 1989/ / / / C of E is the coefficient of efficiency between the observed and predicted FDC as defined in Equation 6. In Table 3, only 1989/1990 has a coefficient of efficiency (CofE) greater than Hence, the slope and upper exponent are taken as and 0.28 respectively Step 3: The cease-to-flow percentile The recession constant was determined using the method outlined in Section Figure 26 shows the observed hydrograph recessions and the parts of the hydrograph that were used to determine the recession constant. Figure 26: Recessions used to define the recession constant, baseflow sections have been used to determine a recession constant of k = With the recession constant determined, the bucket model was calibrated to the observed flows during the four-year calibration period (Figure 27). This model was calibrated to ensure a mass balance between the observed and predicted flows and match the CTF percentile. In order to achieve a match on both mass balance and the CTF percentile the recession constant has changed from to and S ET and S max were determined to be and 171 mm respectively. When S ET was adjusted to achieve mass balance with the streamflow predicted from Step 1, the S ET did not change. This indicated that in order to achieve mass balance S ET would need to be changed in the opposite direction from that anticipated, thus S ET was not altered but retained at Figure 28 shows the observed flows, and model output from the bucket model for grazing and pine plantation for the end of the period of record. It can be seen from Page 30

40 Figure 28, that while the simple bucket model did not match the observed flow at the end of the period of record, nevertheless, the length of the period of flows and no flow were similar. Running the bucket model for the period of observed rainfall gives a cease-to-flow percentile of 85% for grazing and 42% for pine plantation observed Daily flow Daily flow from Bucket model 10 1 Flow (mm/day) Jan-1990 Date 01-Jan-1992 Figure 27: Figure showing the observed flow and bucket model flows for the calibration period 10 2 Observed daily flow (new forest cover) Daily flow from bucket model (old forest cover) Daily flow from bucket model (new forest cover) 10 1 Flow (mm/day) Jan-2000 Date Figure 28: Figure showing the observed flow and bucket model flows for the equilibrium period Page 31

41 Step 4: Conditional median (initial estimate) Figure 29 shows the mean to median relationship for the water years during the calibration period. Figure 29: Relationship between conditional mean and median for the 4 years used as a calibration period. The conditional mean under the new forest cover was determined from the combination of Step 3 and Step 1. The mean annual streamflow for the pine plantation was determined as 41 mm, dividing this by the CTF percentile (42%), gave a conditional daily mean of 0.27 mm/day. The conditional median was then estimated from the regression relationship shown in Figure 29, this resulted in an estimate for the conditional median under pine plantation of mm/day Step 5: Lower Exponent (initial estimate) As the CTF percentile is less than 100%, the lower exponent was determined by ensuring that the CTF percentile (42%) is equal to the threshold value of 0.001(Equation 12). The initial estimate for the lower exponent was determined to be Step 6: Achieving mass balance The above procedure has given us a FDC for the adjusted land use. However, it did not achieve mass balance with the predicted streamflow from step 1. In order to achieve mass balance the median and thus the lower exponent needed to be adjusted respectively to and to With the parameter of the FDC for pine plantation determined, the predicted FDC for the new vegetation type was calculated. The same procedure was used to predict the FDC for current vegetation conditions. Figure 30 shows the observed and predicted FDCs for grazing and the pine plantation. The final three years of data have been chosen as the being close to the new equilibrium condition to illustrate how the predicted FDC matches the observed FDC for the post-treatment period. Page 32

42 Predcited FDC (Post - treatment forest cover) Observed FDC (Post - treatment forest cover) Predcited FDC (Pre - treatment forest cover) Observed FDC (Pre - treatment forest cover) Flow (mm/day) Percentage of time flow is exceeded Figure 30: Predicted FDC for grazing and pine plantation and the observed FDCs for the calibration period (first 3 years of data) and for the last three years of treatment (assumed to be close to new equilibrium conditions) Although the predicted FDCs for the grazing and the pine plantation are not identical to the observed FDC, the methodology does pick up the key characteristic of the observed FDC, i.e. the large change in the percentage of time streamflow occurs. The coefficient of efficiency (as calculated by Equation 14) for the predicted and observed FDC under pine plantation is 0.70, and the coefficient of efficiency for the predicted and observed FDC under grazing is The square root of the values has been used in Equation 14 to give a more weight to the lower flows. CofE i i1 O O P O 2 Equation 14 Page 33

43 4.2. Biesievlei An example of adjusting the FDC for afforestation in a perennial stream The Biesievlei experimental catchment is part of the Jonkershoek study catchments in South Africa. 98% of the catchment was changed from native vegetation to pine plantation, resulting in significant changes in streamflow. Figure 31 shows the observed FDCs for the Biesievlei catchment for the calibration period and the period when the Biesievlei catchment appears to have reached a new equilibrium. Figure 31: Observed FDCs in Biesievlei under native vegetation and forest For the analysis a water year from the 1 st April to the 31 st March was adopted. Below is a worked example of the methodology outlined in Section 3 for adjusting the FDC for a change in the percentage of forest cover in the Biesievlei catchment. Page 34

44 Step 1: Estimating streamflow under new vegetation type Current percentage forest cover = 0% Proposed percentage forest cover = 98% Mean annual rainfall = 1047 mm Observed mean annual streamflow current = mm ET and streamflow for current and proposed percentage forest cover as predicted from Zhang curves (Zhang et al., 2001) for rainfall of 1105 mm. ET zhang_current = 645 mm WY zhang_current = 402 mm ET zhang_proposed = 867 mm WY zhang_proposed = 180 mm Proportional change in streamflow ETzhang _ proposed ETzhang _ current % reduction _ water _ yeild 55.3% WY zhang _ current WYpredicted WYobserved _ current WYobserved _ current % reduction _ water _ yield WYpredicted 620 ( ) WY 277mm predicted Step 2: Parameters of annual flow duration curves The first 10 years of the data were used to develop a set of parameters from which the relationship between the conditional mean and median could be determined. These years have also been used to determine the mean slope and upper exponent. Figure 32 shows the observed and fitted FDCs for the calibration period. Table 4 shows the parameters for the fitted FDCs. Figure 32: Observed and fitted FDCs for pre-treatment period. Page 35

45 Table 4: FDC parameters for the 10 years used as the control period. Water CTF Conditional C of Slope Upper Lower Year percentile Median E Mean Conditional Mean C of E is the coefficient of efficiency between the observed and predicted FDC as defined in Equation 6. The values of the mean slope and the mean upper exponent are and 0.03 respectively Step 3: The cease-to-flow percentile Figure 33 shows the observed hydrograph recessions and the portions of the hydrograph used to determine the surface flow, interflow, and baseflow. The baseflow sections of the recessions are used to define the recession constant. Figure 33: Recessions used to determine the recession constant. Recession has been determined to be k = With the recession constant determined, the bucket model was calibrated to the observed flow during the calibration period (Figure 34). This model was calibrated to ensure mass balance and match for the 95 th percentile flow. This resulted in S ET = 72.2 mm and S max = 161 mm. In order to achieve mass balance and a match to the 95 th percentile flow the recession constant, k, was changed from to Page 36