SUMMARYTopology is an important component of tbe arcbitecture of wbole root systems. Unfortunately, most commonly applied indices used for characterizing topology are poorly correlated witb one anotber and thus reflect different aspects of topology. In order to understand better bow different methods of cbaracterizing topology vary, tbis paper presents an exploration of several different methods for assigning order witbin branched root systems on tbe basis of (a) developmental (centrifugal) vs. functional (centripetal) ordering sequences and (b) wbetber orders are assigned to individual links or groups of adjacent links (segments). For eacb ordering system, patterns of scaling in relation to various aspects of link and segment size are explored using regression analyses. Segment-based ordering systems resulted in better fits for simple scaling relationships with size, but these patterns varied between developmental vs. functional ordering as well as tbe different size metrics examined. Tbe functional (centripetal), link-based ordering system sbowed complex, non-linear scaling in relation to numbers of links per order. Using a simple simulation model of root growth, it is demonstrated tbat this metbod of cbaracterizing root topology in relation to root size migbt be a more powerful tool for cbaracterizing root system arcbitecture tban in the use of simple, single-index cbaracterizations of topology.