HRUs and stream segments (reaches) are used within the J2000 model for distributed topographic and physiological modelling. In this study, the HRU delineation made use of a digital elevation model, with slope, aspect, solar radiation index, mass balance index and topographic wetness being derived. Before the delineation process, gaps within the digital elevation model were filled using a standard fill algorithm from ArcInfo (Jenson and Domingue, 1988). The AML (ArcMarkupLanguage) automated tool (Pfennig et al., 2009) was used for the HRU delineation, with between 13 and 14 HRUs km-2 being defined (Pfannschmidt, 2008). After the delineation of HRUs, dominant soil, land-use and geology properties were assigned to each. The hydrological topology was defined for each HRU by identifying the adjacent HRUs or stream segments that received water fluxes.

Rainfall and relative humidity are the two main parameters that are regionalised within the J2000 model. While a direct regionalisation using an inverse-distance method (IDW) and the elevation of each HRU can be applied to rainfall data, the regionalisation of relative humidity requires the calculation of absolute humidity. The regionalisation of rainfall records was applied by defining the number of weather station records available and estimating the influence on the rainfall amount for each HRU. A weighting for each station using the distance of each station to the area of interest was applied to each rainfall record, using an elevation correction factor (Krause, 2001). The relative humidity and air temperature measured at set weather stations were used to calculate the absolute humidity. Absolute humidity was thereafter regionalised using the IDW method, station and HRU elevation. After the regionalisation had been applied, the absolute humidity was converted back to relative humidity through calculation of saturated vapour pressure and the maximum humidity.

The J2000 model is divided into calculations that impact surface water and groundwater processors. The J2000 model distributes the regionalised precipitation (P) calculated for each HRU using a water balance defined as 1P=R+Intmax+ETR+ΔSoilsat, where R is runoff (mm) (RD1 – surface runoff; RD2 – interflow), Intmax is vegetation canopy interception (mm), ETR is “real” evapotranspiration and ΔSoilsat is change in soil saturation. The surface water processes have an impact on the amount of modelled runoff and interflow, while the groundwater processors influence the upper and lower groundwater flow components.

Lateral routing was responsible for water transfer within the model and included HRU influxes and discharge through routing of cascading HRUs from the upper catchment to the exit stream. HRUs were either able to drain into multiple receiving HRUs or into reach segments, where the topographic ID within the HRU dataset determined the drain order. The reach routing module was used to determine the flow within the channels of the river using the kinematic wave equation and calculations of flow according to Manning and Strickler. The river discharge was determined using the roughness coefficient of the stream (Manning roughness), the slope and width of the river channel and calculations of flow velocity and hydraulic radius done during model simulations.

The lake evaporation rate was based on the ETP calculated by J2000 and an estimated lake surface area. The lake was modelled as a unique HRU (water as the land-cover type), with a variable area which was estimated using remote sensing data from Landsat 8 and Sentinel-2 and the measured lake water level at G3T001 (Fig. 1). To infill lake surface area when remote sensing data were not available, a relationship was created between the estimated lake's surface area and the measured water level between 2015 and 2017. Where lake water level data were not available (before 1999), an average long-term monthly value was used for the lake evaporation calculations.

To account for missing streamflow data between 2007 and 2017, an empirical mode decomposition (EMD) (Huang et al., 1998) was applied to the measured water level data at the sub-catchment outlet (G3T001) (Fig. 1) between 1994 and 2018 (Fig. 8a). EMD is a method for the decomposition of non-linear and non-stationary signals into sub-signals of varying frequency, so-called intrinsic mode functions (IMFs), and a residuum signal. By removing one or more IMFs or the residuum signal, certain frequencies (e.g. noise) or an underlying trend can be removed from the original time-series data. This approach was successfully applied to the analysis of river runoff data (Huang et al., 2009) and forecasting of hydrological time series (Kisi et al., 2014). In this study, EMD filtering was used to remove high-frequency sub-signals from simulated runoff and measured water level data to compare the more general seasonal variations of both signals (Fig. 8b).

Streamflow for the sub-catchment shows two distinctively wet periods (1987–1996 and 2008–2017) separated by a dry period (1997–2007) (Fig. 9). Yearly sub-catchment rainfall volumes between 1987 and 1996 were between 288 and 492 mm yr-1, with an average of 426 mm yr-1 and a standard deviation (SD) of 51 mm yr-1. For this period, average yearly streamflow was 1.4 m3 s-1, with an average baseflow contribution of 0.63 m3 s-1. The modelled streamflow reached a maximum of 48 m3 s-1 in 1993, where 5 m3 s-1 of baseflow was generated after 58 mm of rainfall was received. Between 1997 and 2007 (dry period) sub-catchment yearly rainfall was between 222 and 394 mm yr-1 with an average of 326 mm yr-1 and a SD of 69 mm yr-1 (Fig. 9). For this same period, average yearly streamflow was 0.44 m3 s-1, with an average baseflow contribution of 0.18 m3 s-1. The modelled streamflow reached a maximum of 11 m3 s-1 in 2002, with a baseflow contribution of 2.5 m3 s-1 after 28 mm of rainfall was received. During the second wet period between 2008 and 2017 sub-catchment yearly rainfall was between 231 and 582 mm yr-1 with an average of 442 mm yr-1 and a SD of 112 mm yr-1 (Fig. 9). Over this same period, average yearly streamflow was 2.5 m3 s-1 with an average baseflow contribution of 1.3 m3 s-1. The modelled streamflow reached a maximum of 52 m3 s-1 in 2008, with 13 m3 s-1 of baseflow generated after two consecutive rainfall events each of 25 mm.

The four main feeding tributaries (Bergvallei, Kruismans, Hol and Krom Antonies) together contribute 81 % of streamflow for the Verlorenvlei, with the additional 19 % from small tributaries near Redelinghuys (Fig. 10). Kruismans contributes most of the total streamflow at 32 % but only 15 % of the area-weighted contribution, as its sub-catchment is the largest of the four tributaries at 688 km2 (Fig. 10). Bergvallei with a sub-catchment of 320 km2 contributes 29 % of the total flow with an area-weighted contribution of 28 %. Krom Antonies has the largest area-weighted contribution of 30 % due to its small size (140 km2) in comparison to the other tributaries, although Krom Antonies contributes only 13 % of the total flow (Fig. 10). Hol sub-catchment at 126 km2 makes up the smallest contribution to the total flow of only 7 %, but has a weighted contribution of 17 % (Fig. 10).

Streamflow that enters Verlorenvlei has a large daily variability with a CV of 189.90 (Fig. 9). This is mainly due to high streamflow variability from Kruismans (32 %) with a CV of 217.20, which is the major total flow contributor (Fig. 10). Bergvallei and Krom Antonies, which both have high streamflow variability with CV values of 284.54 and 283.00 respectively (Fig. 9), further contribute to the high variability of streamflow that enters the lake. While Hol reduces the overall streamflow variability with a CV of 146.54, it is a minor total flow contributor (7 %) and therefore does not reduce the overall streamflow variability significantly (Fig. 10).

Streamflow that enters Verlorenvlei is dominated by surface runoff which makes up 56 % of total flow, with groundwater and interflow contributing 40 % and 4 % respectively (Fig. 10). The large surface runoff dominance in streamflow entering the lake is due to a high surface runoff contribution from Kruismans and Krom Antonies, which contribute 26 % of total flow from surface runoff. However, for Bergvallei and Hol, surface runoff contributions are less dominant, with 16 % of the total, while the total groundwater contribution is 20 % from these tributaries. Across all four tributaries, the secondary aquifer is the dominant baseflow component, with 28 % of total flow, with the primary aquifer contributing 12 %. Bergvallei and Kruismans contribute the majority of primary aquifer baseflow, with 8 % of the total. The secondary aquifer baseflow is mainly contributed by Kruismans and Bergvallei, where together 18 % of the total is received. Interflow across the four tributaries is uniformly distributed, with 0.3 %–1 % of the total flow being contributed from each tributary.

The flow exceedance probability, which is a measure of how often a given flow is equalled or exceeded, was calculated for each of the tributaries as well as the lake water body. The results for the flow exceedance probabilities include flow volumes which are exceeded 95 %, 75 %, 50 %, 25 % and 5 % of the time. The 95 percentile corresponds to a lake inflow of 0.054 m3 s-1 or 4702 m3 d-1, with between 0.001 and 0.004 m3 s-1 from the feeding tributaries (Fig. 11 and Table 3). The 75-percentile flow, which is exceeded 3/4 of the time, corresponds to an inflow of 0.119 m3 s-1 or 10 303 m3 d-1, with between 0.005 and 0.015 m3 s-1 from the feeding tributaries. Average (50-percentile) streamflow flowing into the Verlorenvlei is 0.237 m3 s-1 or 20 498 m3 d-1, with between 0.010 and 0.035 m3 s-1 from the feeding tributaries. The 25-percentile flow, which is exceeded 1/4 of the time, corresponds to a lake inflow of 1067 m3 s-1 or 92 204 m3 d-1, with between 0.044 and 0.291 m3 s-1 from the feeding tributaries. The lake inflows that are exceeded 5 % of the time correspond to 6.939 m3 s-1 or 599 535 m3 d-1, with between 0.224 and 2.49 m3 s-1 from the feeding tributaries.

A major limitation facing the development and construction of comprehensive modelling systems in sub-Saharan Africa is the availability of appropriate climate and streamflow data. For this study, while there was access to over 20 years of streamflow records, the station was only able to measure a maximum of 3.68 m3 s-1, which hindered calibration of the model for high-flow events. As such, the confidence in the model's ability to simulate high streamflow events using climate records is limited. While the availability of measured data is a limitation that could affect the modelled streamflow, discontinuous climate records also hindered the estimations of long time-series streamflow.

Over the course of the 31-year modelling period, a number of climate stations used for regionalisation were decommissioned and were replaced by stations in different areas. This required adaption of climate regionalisation for simulations over the entire 31-year period to incorporate the measured streamflow from the gauging station. To account for missing streamflow records since 2007, an EMD filtering protocol was applied to the runoff data (Fig. 6). The results from the EMD filtering showed that after removing the first nine IMFs, the local maxima of both signals match the seasonal water level maxima during most of the years. While considerable improvement can be made to the EMD filtering, the results show some agreement which suggested that the simulated runoff was representative of inflows into the lake.

Factors that impact streamflow variability are important for understanding river flow regime dynamics. Previously, factors that affected streamflow variability such as CV and BFI values were used to determine how susceptible particular river systems were to drought (e.g. Hughes and Hannart, 2003). While CV values have been used to account for climatic impacts such as dry and wet cycles, BFI values are associated with runoff generation processes that impact the catchment. For most river systems, BFI values are generally below 1, implying that runoff exceeds baseflow. In comparison, CV values can be in excess of 10, implying high variability in streamflow volumes (Hughes and Hannart, 2003). In this study, these two measurements have been applied to tributaries, as opposed to Quaternary river systems, to understand the streamflow input variability into the Verlorenvlei.

The highest proportion of streamflow needed to sustain the Verlorenvlei lake water level is received from the Bergvallei tributary, although the area-weighted contribution from Krom Antonies is more significant (Fig. 10). However, CV values for the Bergvallei indicate high streamflow variability. This is partially due to the high surface runoff component in modelled streamflow within the Bergvallei in comparison to the minor interflow contribution, suggesting little sub-surface runoff. While streamflow from the Bergvallei tributary is 54 % groundwater, which would suggest a more sustained streamflow, due to the TMG dominance as well as a high primary aquifer contribution, baseflow from the Bergvallei is driven by highly conductive rock and sediment materials. Similarly, CV values for Krom Antonies indicate high streamflow variability due to the presence of a high baseflow contribution from the conductive TMG and primary aquifers. Although Krom Antonies has a larger interflow component, which would reduce streamflow variability, the dominant TMG presence within this tributary partially compensates for the sub-surface flow contributions.

In contrast, Hol has a much smaller daily streamflow variability in comparison to both Bergvallei and Krom Antonies (Fig. 9). While streamflow from Hol tributary is mainly comprised of baseflow (56 %), the dominance of low conductive shale rock formations as well as a large interflow component results in reduced streamflow variability. While the larger shale dominance in this tributary results not only in a more sustained baseflow from the secondary aquifer, it also results in a large interflow component due to the limited conductivity of the shale formations. Compounding the more sustained baseflow from Hol tributary, the reduced extent of the primary aquifer results in a dominance in slow groundwater flow from this tributary. Similarly, Kruismans is dominated by shale formations which result in a larger interflow contribution, although due to the limited baseflow contribution (37 %) the streamflow from this tributary is highly variable, which impacts its susceptibility to drought.

The results from this study have shown that while Krom Antonies was initially believed to be the major flow contributor, Bergvallei is in fact the most significant, although streamflow from the four tributaries is highly variable, with baseflow from Hol tributary the only constant input source. The presence of conductive TMG sandstones and Quaternary sediments in both Krom Antonies and Bergvallei results in quick baseflow responses with little flow attenuation. The potential implication of a constant source of groundwater being provided from Hol tributary is that if the groundwater is of poor quality, this would result in a constant input of saline groundwater, with Krom Antonies and Bergvallei providing freshwater only after sufficient rainfall has been received.

The groundwater components of the J2000 model were adjusted using aquifer hydraulic conductivity from a MODFLOW model of one of the main feeding tributaries of the Verlorenvlei. Krom Antonies was selected as it was previously believed to be the largest input of groundwater to Verlorenvlei (Fig. 2). Baseflow for the Krom Antonies tributary was previously calculated using a MODFLOW model (Watson, 2018) by considering aquifer hydraulic conductivity and average groundwater recharge. As average recharge was used, baseflow estimates from MODFLOW are likely to fall on the upper end of daily baseflow values estimated by the J2000 model. For Krom Antonies sub-catchment, Watson (2018) estimated baseflow between 14 000 and 19 000 m3 d-1 for 2010–2016 using MODFLOW. Similar daily baseflow estimates from J2000 were only exceeded 10 % of the time, with average estimates (50 %) of 1036 m3 d-1 over the course of the modelling period (Fig. 9).

The MODFLOW estimates were applied over the course of a wet cycle (2016). In comparison to the MODFLOW estimates (14 000 to 19 000 m3 d-1) average baseflow from J2000 for 2016 was 8214 m3 d-1. The daily time-step nature of J2000 is likely to result in far lower baseflow estimates, as recharge is only received over a 6-month period as opposed to a yearly average estimate. One possible implication of this is that while common groundwater abstraction scenarios have been based on yearly recharge, abstraction is likely to exceed sustainable volumes during dry months or dry cycles, and this could hinder the ability of the aquifer to supply baseflow. While the groundwater components of J2000 have been distributed to allow for improved baseflow estimates, the groundwater calibration was applied to Krom Antonies. However, this study showed that Bergvallei has been identified as the largest water contributor. In hindsight, the use of geochemistry to identify dominant tributaries could have aided the groundwater model adaption. While it would have been beneficial to adapt the groundwater components of J2000 using the dominant baseflow contributor, considering the geological heterogeneity between tributaries is more important for identifying how to adapt the groundwater components of J2000. While the distribution of aquifer components improved modelled baseflow, including groundwater abstraction scenarios in baseflow modelling in the sub-catchment is important for future water management for this ecologically significant area.

For this study, exceedance probabilities were estimated through rainfall–runoff modelling for the previous 31 years within the Verlorenvlei sub-catchment. The exceedance probabilities were determined for each tributary, as well as the total inflows into the lake. These exceedance probabilities were compared with the evaporative demand of the lake to understand whether inflows are in surplus or whether the evaporation demand exceeds inflow.

From the exceedance probabilities generated in this study, the lake is predominately fed by less frequent large discharge events, where on average the daily inflows to the lake do not sustain the lake water level. This is particularly evident in the measured water level data from station G3T001, where measured water levels have a large daily standard deviation (0.62) (Watson et al., 2018). The daily inflows of water into the Verlorenvlei have also been subject to significant rainfall variability, with yearly rainfall between the second wet cycle (2007–2017) being twice as variable in comparison to the first wet cycle (1987–1996). The change in rainfall variability has had a significant impact on soil moisture conditions, resulting not only in larger peak discharges, but also in lengthened low-flow conditions. With climate change likely to impact the length and severity of dry cycles, it is likely that the lake will dry up more frequently into the future, which could have severe implications for the biodiversity that relies on the lake's habitat for survival. Of importance to the lake's survival is the protection of river inflows during wet cycles, where the lake requires these inflows for regeneration.

While the impact of irrigation could not be incorporated, over-allocation of water resources may potentially have a significant impact on the catchment water balance, especially during wet cycles when ecosystems are recovering from dry conditions. The increased irrigation during wet cycles as a result of agricultural development could be a further impact on the recovery of sensitive ecosystems. This type of issue is not limited to Verlorenvlei, but applies to many wetlands or estuarine lakes around the world; while they have been classified as protected areas, water resources within the catchments are required for food security. As climate change drives increased temperatures and variability in rainfall, the ±10-year cycles of dry and wet conditions may no longer be valid anymore, where these conditions may shorten or lengthen. With the routine breaking of weather records across the world (Bruce, 2018; Davis, 2018), it is becoming increasingly evident that conditions are changing and becoming more variable, which could impact sensitive ecosystems around the world, highlighting the need for effective water management protocols during times of limited rainfall.