In this paper, we study a system of entangled chains that bear reversible cross-links in a melt state. The cross-links are tethered uniformly on the backbone of each chain. A slip-link type model for the system is presented and solved for the relaxation modulus. The effects of entanglements and reversible cross-linkers are modelled as a discrete form of constraints that influence the motion of the primitive path. In contrast to a non-associating entangled system, the model calculations demonstrate that the elastic modulus has a much higher first plateau and a delayed terminal relaxation. These effects are attributed to the evolution of the entangled chains, as influenced by tethered reversible linkers. The model is solved for the case when the linker survival time τ is greater than the entanglement time τ, but less than the Rouse time τ.

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Abstract. Reliable estimates of daily, monthly and seasonal soil moisture are useful in a variety of disciplines. The availability of continuous in situ soil moisture observations in southern Africa barely exists; hence, process-based simulation model outputs are a valuable source of climate information, needed for guiding farming practices and policy interventions at various spatio-temporal scales. The aim of this study is to evaluate soil moisture outputs from simulated and satellite-based soil moisture products, and to compare modelled soil moisture across different landscapes. The simulation model consists of a global circulation model known as the conformal-cubic atmospheric model (CCAM), coupled with the CSIRO Atmosphere Biosphere Land Exchange model (CABLE). The satellite-based soil moisture data products include satellite observations from the European Space Agency (ESA) and satellite-observation-based model estimates from the Global Land Evaporation Amsterdam Model (GLEAM). The evaluation is done for both the surface (0–10 cm) and root zone (10–100 cm) using in situ soil moisture measurements collected from two study sites. The results indicate that both the simulation- and satellite-derived models produce outputs that are higher in magnitude range compared to in situ soil moisture observations at the two study sites, especially at the surface. The correlation coefficient ranges from 0.7 to 0.8 (at the root zone) and 0.7 to 0.9 (at the surface), suggesting that models mostly are in an acceptable phase agreement at the surface than at the root zone, and this was further confirmed by the root mean squared error and the standard deviation values. The models mostly show a bias towards overestimation of the observed soil moisture at both the surface and root zone, with the CCAM-CABLE showing the least bias. An analysis evaluating phase agreement using the cross-wavelet analysis has shown that, despite the models' outputs being in phase with the in situ observations, there are time lags in some instances. An analysis of soil moisture mutual information (MI) between CCAM-CABLE and the GLEAM models has successfully revealed that both the simulation and model estimates have a high MI at the root zone as opposed to the surface. The MI mostly ranges between 0.5 and 1.5 at both the surface and root zone. The MI is predominantly high for low-lying relative to high-lying areas.

The reliable performance of roads is crucial for service delivery, and it is a catalyst for domestic and cross-border spatial development. Paved national roads are expected to carry higher traffic volumes over time as a result of urbanization and to support the economic development in the continent. Increased traffic levels combined with expected increases in air temperatures as a result of global warming highlight the need to appropriately select bituminous road materials for a reliable performance of asphalt roads. The objective of the paper is to present African case studies on the development of temperature maps necessary for performance-graded bitumen selection for road design and construction. A consistent approach, that caters for the variability of geographical, environmental and climatic conditions, does not currently exist within the continent. Therefore, this paper discusses a series of critical components in the development of temperature maps for performance-graded bitumen including (i) pavement temperature models and climatic zones in Africa; (ii) the effect of urban heat islands on pavement temperature; (iii) sources of weather data and (iv) the mapping procedure to produce temperature maps. Characterizing the thermal properties of the pavement was found to be an important factor for reliably calculating expected road temperatures as well as the consideration of the ambient climate for a given location. During this study, the urban heat island effect was found to have little influence on the maximum pavement temperatures but a significant effect on the minimum pavement temperatures. Some areas of the urban district assessed in this investigation were found to increase by two performance grades according to the minimum temperature criteria. The recent observed weather data from weather stations are the most accurate means of measurement of the ambient environmental conditions necessary for performance-based specifications, but they are not always easily accessible, and therefore other sources of data, such as satellite data, may need to be used instead. With the expected temperature increases expected as a result of climate change, the use of Global Climate Models also opens new avenues for performance-based material selection in the African continent for expected climates as an alternative to traditional approaches based on historically observed weather.

Woody plant encroachment (WPE) has been found to alter ecosystem functioning and services in savannas. In rain-limited savannas, increasing woody cover can reduce streamflow and groundwater by altering evapotranspiration rates and rainfall partitioning, but the ecological relevance of this impact is not well known. This study quantified the altered partitioning of rainfall by two woody plant structural types (fine-and broad-leaved trees) across a gradient of encroachment in a semi-arid savanna in South Africa. Averaged across both plant functional types, loss of rainfall through canopy interception and subsequent evaporation roughly doubled (from 20.5% to 43.6% of total rainfall) with a roughly 13-fold increase in woody cover (from 2.4 to 31.4 m 2 /ha tree basal cover). Spatial partitioning changes comprised fourfold increases in stemflow (from 0.8% to 3.9% of total rainfall) and a decline in throughfall proportion of about two-fifths (from 80.2% to 47.3% of total rainfall). Changes in partitioning were dependent on plant functional type; rainfall interception by the fine-leaved multistemmed shrub Dichrostachys cinerea was almost double that of the broad-leaved tree Terminalia sericea at the highest levels of woody encroachment (i.e., 49.7% vs. 29.1% of total rainfall intercepted at tree basal area of 31.4 m 2 /ha). Partitioning was also dependent on rainfall characteristics, with the proportion of rainfall intercepted inversely related to rainfall event size and intensity. Therefore, increasing tree cover in African grassy ecosystems reduces the amount of canopy throughfall, especially beneath canopies of fine-leaved species in smaller rainfall events. Rainfall interception traits may thus confer a selective advantage, especially for fine-leaved woody plant species in semi-arid savannas.