Parameterisation of the ACRU Model for DFE

DECLARATION 2: PUBLICATIONS

3. DEVELOPMENT OF AN IMPROVED COMPREHENSIVE CONTINUOUS

3.2 Parameterisation of the ACRU Model for DFE

ACRU CSM approach in practice. The objective is in line with recommendations from the international literature as reviewed in Chapter 2, e.g. the United Kingdom and Australia, of simplicity and user friendliness, while still providing accurate results. It is hypothesised that a system that incorporates the valuable information calibrated into the CN along with explicit soil water budgeting will provide the most accurate results when simulating flows for different land cover and soil combinations. Additional motivation lies in the realisation that the SCS-CN method is still widely used (Brocca et al., 2011; Grimaldi et al., 2012; Rossman, 2015; USACE, 2016).

Applying a multiple linear regression, a strong relationship between these two ACRU parameters and SCS-SA CN values was obtained and consequently preliminarily rules and equations were developed to represent SCS-SA land cover classes in ACRU. The multiple linear regression, however, was skewed by the results obtained for SCS-SA soil Group C/D, therefore a separate multiple linear regression analysis was performed for soil Group C/D (Rowe et al., 2018).

Equation 3.1 (Rowe et al., 2018) was derived from the multiple linear regression for all SCS- SA land cover classes for all SCS-SA soil groups, excluding SCS-SA soil Group C/D, to estimate “predicted” CN (CNp) values for given QFRESP and SMDDEP combinations as calibrated against actual tabulated SCS-SA CN values.

𝐶𝐶𝐶𝐶𝑝𝑝 = 43.91(𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄)−75.52(𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑄𝑄𝑄𝑄) + 53.78 (3.1)

The CNp values were then compared to the actual tabulated SCS-SA CN values. Based on the good correlation obtained between the CNp values and the actual tabulated SCS-SA CN values, Equation 3.1, was used to develop rules to estimate QFRESP and SMDDEP parameter values for tabulated SCS-SA CN values. These rules, for all SCS-SA soil groups, excluding SCS-SA soil Group C/D, are provided in Table 3.2.

The rules as summarised in Table 3.2 are explained as follows (Rowe et al., 2018). Rules were developed for different CN ranges. The first range of CN values being those ranging from 40 – 48. For this range of CN values, the rules state that a fixed QFRESP value of 0.3 must be used and Equation 3.1 rearranged to solve for SMDDEP. An example is shown in Table 3.2 where an estimated SMDDEP value of 0.28 is calculated for an input CN value of 46, after rearranging Equation 3.1 to solve for SMDDEP. It was recommended by Rowe et al. (2018) that CN values lower than 40 should not be simulated in general, since the SMDDEP ACRU parameter value below a CN value of 40 starts increasing to depths not within the range recommended for use within the ACRU model. The rules in Table 3.2 for the CN range of 40 – 48 may, however, be applied for CN values below 40 for catchments with extremely low stormflow potential.

Extrapolation to CN values below 30, however, is not recommended, and is the absolute minimum threshold. These recommendations are in line with SCS (SCS, 1956) and SCS-SA (Schmidt and Schulze, 1987a) convention, where use of a CN value below 50, particularly for

DFE, is not recommended. Therefore, if a CN value below 40 is identified for a catchment, it is recommended to use a value of 40, unless the catchment has extremely low stormflow potential, where a value between 30 and 40 may be selected by experienced users. For CNs ranging from 48 – 79, the rules state that SMDDEP must remain fixed at a value of 0.25 and Equation 3.1 must be rearranged in order to solve for QFRESP. An example is shown for a CN value of 79, where the QFRESP value is calculated to be 1.00. If a CN value of 48 is identified for a catchment the rules for CN range 40 – 48 or 48 – 79 may be used and will provide the same result, as this is a transition point. For CN values greater than 79, the rules state that QFRESP must remain fixed at 1.00 and Equation 3.1 must be rearranged in order to once again solve for SMDDEP (Rowe et al., 2018).

Table 3.2 Rules developed for all SCS-SA soil groups, excluding SCS-SA soil Group C/D (Rowe et al., 2018)

Rules CN 40 - 48 CN 48 - 79 CN > 79 QFRESP = 0.3 SMDDEP = 0.25 QFRESP = 1

Input CN 46 79 82

Rearrange Equation 3.1 to solve for

SMDDEP or QFRESP SMDDEP QFRESP SMDDEP

Calculated value 0.28 1.00 0.21

Equation 3.2 (Rowe et al., 2018) was derived to estimate CNp values for given QFRESP and SMDDEP combinations for all SCS-SA land cover classes for SCS-SA soil Group C/D:

𝐶𝐶𝐶𝐶𝑝𝑝 = 32.92(𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄𝑄)−48.28(𝑄𝑄𝑆𝑆𝑆𝑆𝑆𝑆𝑄𝑄𝑄𝑄) + 63.91 (3.2)

In addition, the rules presented in Table 3.3 were determined for SCS-SA soil Group C/D and are interpreted in the same manner as the results from Table 3.2 (Rowe et al., 2018). The value of QFRESP cannot be greater than 1, therefore the value of 1.01 in Table 3.3 should be taken as 1. The value of 1.01 in Table 3.3 is an artefact of the regression equation (Equation 3.2).

Table 3.3 Rules developed for SCS-SA soil Group C/D only (Rowe et al., 2018)

Rules CN 57 - 62 CN 62 - 85 CN > 85 QFRESP = 0.3 SMDDEP = 0.25 QFRESP = 1

Input CN 62 85 88

Rearrange Equation 3.2 to solve for

SMDDEP or QFRESP SMDDEP QFRESP SMDDEP

Calculated value 0.24 1.01* 0.18

* Value cannot be greater than 1 therefore if greater than 1 change to 1

The rules defined by Rowe et al. (2018) above were only developed and assessed using design stormflow volumes and not peak discharges. Furthermore, the results were not verified against observed data. Therefore further development and assessment of the approach was highly recommended by Rowe et al. (2018). This included further development of a comprehensive CSM system for DFE in South Africa, and verification of the system performance against observed data in terms of both simulated streamflow volumes and peak discharges. The next section addresses the first recommendation listed above, i.e. further development of a comprehensive CSM system for DFE in South Africa using the ACRU model. This includes defining a complete structure of the system, default datasets and classifications to use with the system, and model options. The performance of the comprehensive CSM system developed is then assessed in subsequent chapters.

3.3 Development of a Comprehensive CSM System for DFE using the ACRU Model