## 2 Materials and Methods  
The general concept for valuation of ecosystem services is based on mapping of different ecosystems and land-cover classes, followed by quantification of ecosystem service values using values (in USD ha\({}^{-1}\) yr\({}^{-1}\)) derived from the literature (Figure 2). MODIS remote sensing data were used in this study, with the time slices of 2001, 2005, 2010, 2014 and 2019. The MODIS data used were the MCD12Q1 MODIS/Terra + Aqua Land Cover product at 500 m spatial resolution (according to the classification of [54]). The MODIS data use 17 classes of land cover that include various natural vegetation types (11 classes), anthropogenically-altered land covers (3 classes) and non-vegetation land covers (3 classes). In this study, 15 classes were used in total. This is because some classes are not present in South Africa. Estimation of overall land degradation was calculated based on changes in NPP between each of the examined time slices (e.g., [55]). The valuation of each land-cover class was estimated based on global published values for ecosystem services (e.g., [56; 2]) as updated and summarized by [3] who integrated data from questionnaires and field workshops in various locations and from different ecosystems globally. Reference [3] (their Table 3) lists unit values in USD ha\({}^{-1}\) yr\({}^{-1}\) for different biome types for the years 1997 and 2011. Here, we used the averaged values for each biome to calculate ecosystem service values for the equivalent land-cover types from the MODIS data (Table 1). Many of these previous studies of land-cover valuation focused in particular on arid and semi-arid ecosystems and are thus relevant to land degradation studies in water-stressed locations such as South Africa. Previous use of MODIS data for  
Figure 2: Schematic diagram for the process of ecosystem services change and degradation (adapted from [11]). calculating NPP shows statistically significant results [57], and this can frame the use of these data in this study as a direct indicator of land degradation. The NPP information was obtained from MODIS product at 500 m pixel resolution. The NPP values (in kg C m\({}^{-2}\)) were calculated based on the summation of the daily gross primary productivity (GPP) after subtracting the annual respirational factors [58]. The respirational factors were defined based on the characteristics of each biome using the Biome Properties Look-Up Table (BPLUT) (e.g., [59]). Four NPP product scenes were required to cover the South African terrestrial area for 2001, 2005, 2010, 2015 and 2019. The scenes were mosaicked and clipped using the national South African boundary layer. Ecosystem degradation and its associated loss in economic value can be evaluated by assessing the net-value changes in various land-cover classes and changes in ecosystem service values from one class to another or degradation by loss of ecosystem service value taking place within the same class. The following equation was developed to estimate the value loss found in different ecosystems between different successive time slices:  
\[LDL_{j}\left(\text{USD ha}^{-1}\text{y}^{-1}\right)=LCEV_{j-1}\left(\text{ USD ha}^{-1}\text{y}^{-1}\right)\times\left(\frac{NPP_{j}-NPP_{j-1}}{NPP_{j-1}}\right) \tag{1}\]  
where \(LDL\) is land degradation economic loss, \(LCEV\) is land-cover economic value, and \(NPP\) is net primary productivity at \(j\) and \(j-1\) as current and previous time periods, respectively. The above equation has two parts: the potential ecosystem value and the degradation ratio. The latter corresponds to the ratio of changes in NPP values between two successive time slices. The equation can be further improved by including the land degradation index reported by [60] as the degradation part of the equation, although this was not done in this study for this first-order analysis.