Application of fixed timestep numerical schemes in engineering has long been criticized for their inaccuracy, inefficiency, and inconsistency across time-scales. Yet, to date, most hydrological models fix their timestep to the input rainfall resolution, instead of using adaptive schemes. Aside from their known maladies, we argue that fixed timestep schemes also suffer from ‘commensurability’ errors: errors that emerge when comparing quantities that are not precisely at the same spatial/temporal scales. At least at <= hourly resolutions, the observed discharge is a set of discrete measurements of an otherwise time-continuous (TC) quantity, but the modelled discharge is time-averaged (TA) across the fixed timestep. Hence the commensurability error when compared against one another during calibration. (In)significance of such errors simultaneously depends on the nonlinearity of the discharge within that timestep, and the timestep size. Consequently, these errors are the largest where they are potentially least acceptable to ignore, i.e., around peaks. Also, they tend to grow with timestep size (data resolution), unless timestep is detached from data resolution using adaptive schemes, which produce a TC solution. Importantly, since modern calibration procedures revolve around ‘fitting’ to observed discharge, such errors are likely undetectable in model’s curve-fitting performance, and instead are to be found in calibrated parameter-sets. Here, in a novel approach within the Generalize Likelihood Uncertainty Estimation (GLUE) framework with Limits of Acceptability (LOA) defined a-priori, and for a micro-catchment case study, we calibrate a TA and a TC version of Dynamic-TOPMODEL to datasets at different resolutions. Through experimentation with the calibrated parameter-sets, we estimate the relative (to TC version) magnitude of the time-commensurability errors resulting from fixing the timestep to input rainfall. Our findings confirm the overall insufficient accuracy, inefficiency of timestepping, and inconsistency across resolution when fixing the timestep. We find that for calibration data resolution >10min, time-commensurability errors become very significant.

Headwater blanket-peat restoration activities, in particular revegetation and gully-blocking, are observed to deliver significant Natural Flood Management (NFM) benefits. A recent Before-After-Control-Intervention (BACI) experiment showed that these interventions reduce flood-peaks and increase lag-times, but the processes controlling these effects remain unclear. We seek to identify these processes at the same BACI sites by inverting the TOPMODEL rainfall-runoff model and linking the response-to-intervention in each catchment to model parameters through rigorous calibration. Through numerical experiments, we infer processes most likely to be driving the BACI observations. Our findings confirm the NFM benefits of these restoration-focused interventions. Independent of storm size/intervention, the increased lag is almost entirely due to surface roughness reducing the floodwave speed. We conceptualise this as a ‘mobile’ surface storage. In flood-relevant storms, at least 90\% of the peak reduction in both interventions is delivered by mobile storage. The additional increase in the mobile storage due to gully-blocking is very significant and comparable to that of revegetation alone. The impact of interventions on ‘immobile’ storage (interception+ponding+evapotranspiration) becomes important for smaller storms, in which revegetation reduces peak discharge by increasing evapotranspiration but the not interception storage. Gully blocking however, increases ponding but reduces evaporation, such that there is no net gain in catchment immobile storage relative to revegetation alone. Although interventions always increase lag-times, they can be less effective in reducing peak magnitude in long duration frontal rainfalls. We propose two approaches to further increase catchment’s surface storage, while adhering to the restoration requirement to keep the water tables high.