Improved Continuing Losses Estimation Using Initial Loss-Continuing Loss Model for Medium Sized Rural Catchments

Problem statement: The rainfall based design flood estimation techniqu es are commonly adopted in hydrological design and require a number of inputs including information on soil loss characteristics. Approach: A conceptual loss model known as the ‘Initial LossContinuing Loss (ILCL) model’ is widely used in Australia. Results: The Initial Loss (IL) occurs at the beginning of th e rainfall event, prior to the commencement of surfac e runoff and the Continuing Loss (CL) is the average rate of loss throughout the remainder of th e s orm. The currently recommended design loss values depicted in “Australian Rainfall and Runoff Vol. 1” for Queensland (Australia) has some basic limitations. This study investigated how more accur ate CL values can be estimated and derived for medium sized tropical Queensland catchments using l o term rainfall and streamflow data. Accuracy in CL estimation has got significant implications i n the estimation of design floods. Conclusion/Recommendations: The results showed that CL value is not fixed and constant through out the duration of the storm but the CL value deca ys with the duration of the storm.


PROBLEM STATEMENT
Flood estimation is often required in hydrologic design and has important economic significance [2] . Flood estimation and risk analysis in Australia involves an annual spending of the order of $650 million [4] . Rainfallbased flood estimation techniques are most commonly adopted and often require several inputs/parameters to convert design rainfalls to design floods [6,8] . Of the many inputs/parameters, the concept "loss" is an important parameter. Loss is the amount of precipitation that does not appear as direct runoff. Factors pertaining to loss in effect reduce the runoff during a flood event [2,7] .
In design flood estimation, simplified lumped conceptual loss models are commonly used because of their simplicity and ability to approximate catchment runoff behavior. Secondly, the detailed parameters needed for calculating individual loss components are generally not available. This is particularly true for design loss which is probabilistic in nature and for which complicated theoretical models may not be required. The common loss factors include rainfall intercepted by vegetation (interception loss), infiltration into the soil (infiltration), retention on the surface (depression storage), evaporation and loss through the streambed and banks. As these loss components are dependent on topography, soil characteristics, vegetation and climate; the components exhibit a high degree of temporal and spatial variability during high rainfall events. Many loss models do not account for the interception, depression storage and evaporation losses separately. Instead, such losses are considered as infiltration into the soil. In Australia, the most commonly adopted conceptual loss model is the initial loss-continuing loss model [1,4,6] . The initial loss occurs prior to the commencement of surface runoff and can be considered to be composed of the interception loss, depression storage and infiltration that occur before the soil surface is saturated. In design rainfall events, the continuing loss is computed as the average rate of loss that occurs up to the end of the rainfall event, after the initial loss is satisfied.

Selection of catchments:
This study was aimed at deriving new improved design losses for Queensland catchments. A total of 48 unregulated rural catchments were selected from the entire state of Queensland. The selection of catchments was done based on the catchment size, regulation, record lengths of rainfall and streamflow data. However, from these primarily selected catchments, final selection of catchments was done based on location of the pluviograph station, daily rainfall station, streamflow gauging station and the catchment boundary.
Catchment area: A primary selection parameter was size of the catchment; small or large. The loss (IL-CL) model which was used in this research is only suitable for small to medium size catchments and not suitable to compute the loss values for the larger catchments. The reason is that the process of computing loss values for larger catchments is different from the process of computing loss values for smaller catchments. It was observed that for larger catchments there is lack of uniformity in catchment characteristics than in smaller to medium sized catchments. Laurens on and Pilgrim [5] mentioned that catchment characteristic is a factor which affects the loss value. Australian Rainfall and Runoff [4] suggests the catchment area with an upper limit of 1000 km 2 can be considered as a small to medium sized catchments, which was taken as a guide to selecting the study catchments.

Regulation:
To select the study catchments, consideration was given to whether the study catchments were regulated or unregulated, as major regulation affects the natural rainfall-runoff relationship significantly. Gauging stations subject to major regulation (such as dams, gates, diversions and back water effect) were not included in this study. Also urbanization affects the catchment hydrology, so no urban catchment was selected. Only unregulated rural catchments were selected for this study. Topographic Maps of Australia (1:100000) were consulted to investigate the nature of streamflow network and nature of regulation in the selected catchments. Also the gauging authority was consulted to know about any recent changes of regulation and land use in the selected catchments.
Record length: It was aimed to have significantly longer record lengths for the length of the rainfall and streamflow data of the catchments under study, as more number of rainfall and streamflow events will produce more reliable results. Among collected data, the highest record length of streamflow data is 48 years and the lowest record length of streamflow data is 11 years. The mean and median values of streamflow record length are 30 and 31 years. A total of 132 pluviograph stations and 338 daily rainfall stations were selected from and near the selected catchments. The rainfall data were obtained from the Bureau of Meteorology (BoM), Australia.  After mapping the catchment boundary, an electronic layer of stream gauging stations were laid over the catchment boundary. The catchments whose location of the stream gauging station in the map was found away from the catchment boundary, that catchment was not selected as study catchment. Catchments were selected, when there was one or more pluviograph station or daily rainfall stations within the catchment boundary.
To select a rainfall streamflow event to estimate loss values the temporal pattern of the rainfall over the catchment is necessary. Catchments with only one pluviograph station but no daily rainfall station within the catchment boundary were selected as candidate catchments. As the catchments were small to medium in size, it was assumed that the temporal pattern of the pluviograph data was the representative temporal pattern of the whole catchment, provided the pluviograph station was located well inside the catchment boundary. But catchments with no pluviograph station inside or within 50 km of the catchment boundary were not selected as study catchments, though there was daily rainfall station within or near the catchment boundary. Again catchments having a pluviograph station close to the boundary and with daily rainfall stations within the catchment boundary were selected as study catchments. Because, it was assumed that when the pluviograph station and daily rainfall station are closely located, the temporal pattern of the daily rainfall station and the pluviograph station were same. Hence the pluviograph data can be used to proportion the daily rainfall data to obtain the representative temporal pattern of rainfall within the catchment. The distribution of the candidate catchments selected from all over the Queensland is shown in Fig. 1. The locations of the study catchments were identified by the electronic layer of catchment boundaries with in the Queensland boundary using Mapinfo Professional. Each study catchment is represented by a stream gauging station. A list of selected stream gauging stations numbers, streamflow names, location of stream gauging stations, latitude and longitude of stream gauging stations, catchment area and streamflow record length (start and finish date) is shown in Table 1.

Methodology (CL estimation):
In ARR [4] the continuing loss is defined as the loss that occurs at a constant rate after the commencement of the surface runoff. The procedure which was adopted in this analysis to compute the continuing losses was the same as the procedure adopted in ARR [4] i.e., the continuing loss is the rate of loss that occurred during the remainder of the storm.
The rates of continuing loss are constant as recommended in ARR [4] , however in reality the value could be decreasing with the time depending upon the soil cover and duration of the storm. In this study, it was investigated whether continuing loss rate is constant in nature or decays with the duration of the storm.
In this analysis Initial Loss and Continuing Loss (IL-CL) model was used to compute the initial loss and continuing loss values from the rainfall and streamflow events. ARR [4] recommended design median initial losses ranging from 15.0-35.0 mm and design median continuing loss 2.5 mm h −1 for eastern catchments of Queensland. Similarly for western Queensland catchments, the recommended median continuing loss is 1.4 mm h −1 . As per ARR recommendations, the design initial loss varies with the duration; however the design continuing loss does not vary with time but remain constant throughout the duration of the storm.
The water balance equation from the start of a rainfall event till the end of a runoff event may be expressed as: Where: R = Total rainfall of the event expressed in average depth of rainfall in mm over the catchment QF = Quickflow, assumed to be resulted from the rainfall event, expressed in mm t = Time elapsed between the start of the surface runoff till the end of the rainfall event (h) Since, QF is the total Streamflow (SFT) minus Baseflow (BF), Eq. 1 may be written as: where, both SFT and BF are expressed in mm.
As IL-CL model does not consider the temporal variability of losses. From Eq. 1 CL may be expressed as: To estimate QF in Eq. 3, separation of base flow from total streamflow was required. A lower limit of 0.0 mm h −1 and an upper limit of 20.0 mm h −1 were imposed for the continuing loss computation and events outside of this range were excluded from this analysis. As continuing loss value more than 20.0 mm h −1 , needs more detailed investigation.

RESULTS
The descriptive statistics of all the selected 969 rainfall streamflow events of IL and CL values are shown in Table 2 Hence it is observed that the continuing loss varies with the duration of the storm rather than it remains constant throughout the storm. Similar characteristics are expected from other catchments around the world.
To examine the effect of duration on continuing loss an analysis was performed with all the selected 969 rainfall events using a threshold value of 0.01 mm h −1 . To examine how continuing loss varies with the duration, the continuing losses of all the selected 969 rainfall events were plotted against their duration (duration between the end of initial loss and the end of the rainfall event) of all the events as shown in Fig. 2. The continuing loss for each catchment was examined against their durations of the remainder of the storm. It was observed that the continuing loss decays with duration i.e., it is not a single fixed value as recommended in ARR [4] .
In Queensland, the loss value varies with the location of the catchments. To examine the effect of duration in loss values for different regions of Queensland, the Queensland catchments were divided into two categories to compute storm losses such as eastern catchments and western catchments. The initial losses in western catchments are sometimes higher because the catchments are dryer than the eastern catchments. An investigation was performed to examine the effect of duration on continuing losses for different locations of Queensland catchments. Out of all selected 48 Queensland catchments 11 eastern catchments, 5 western catchments and 12 northern Queensland catchments were selected to examine the effect of duration on continuing loss values.   To examine how continuing loss varies with duration, the continuing loss and the duration of 270 rainfall events of 11 eastern Queensland catchments were plotted as shown in Fig. 3. It shows that, the continuing loss is not constant with storm duration but rather it decays with the duration. The equation of the decaying curve is shown in Fig. 3.
In Fig. 5 the continuing losses of 340 rainfall events of 12 northern catchments of Queensland are plotted against their respective durations to examine the effect of duration on continuing losses. Figure 5 shows that the continuing loss is not constant in respect of duration, but that it decays with respect to duration of the rainfall event. The equation of the decaying curve is shown in Fig. 5. Also the results of the continuing losses against their durations for few individual catchments are shown in Fig. 6.  [4] recommended that continuing loss rate is constant throughout the duration of the storm. However, using many years of data, derived continuing losses values found in this study are not constant. Rather, it is found that continuing loss value decreases with the increase of the duration of the rainfall event i.e., CL value is not a fixed single value for a catchment as recommended in ARR [4] but it decays with the increase in the duration of the storm. Hence, it was observed that the continuing loss of the Queensland catchments can be described as probability distributed losses.

CONCLUSION
This research analyzed how to improve the design continuing loss estimate for flood estimation in Queensland. The finding has important significance for design flood estimation. The following conclusions can be drawn from the analysis: • It was observed that the computed median CL value for western Queensland catchments was 12.86% higher than that of ARR recommended median continuing loss value • It is recommended in ARR that the continuing loss that occurs for a rainfall event is at a constant rate during the remainder of the storm. But this recommendation is not correct as per Fig. 2-6, which proved that the continuing loss decreases with the time i.e., it is not a single fixed value during the remainder of the storm. Hence, the continuing losses for the Queensland catchments are in reality probability distributed losses • This finding (probability distributed losses) is required to be confirmed with a larger data set. A larger data set is required to derive stochastic continuing losses for application with Joint Probability Approach as described by Ilahee et al. [3]