<p>Society-induced changes to the environment are altering the effectiveness of existing management strategies for sustaining natural and agricultural ecosystem productivity. At the watershed scale, natural and agro-ecosystems represent complex spatiotemporal stochastic processes. In time, they respond to random rainfall events, evapotranspiration and other losses that are spatially variable because of heterogeneities in soil properties, root distributions, topography, and other factors. To quantify the environmental impact of anthropogenic activities, it is essential that we characterize the evolution of space and time patterns of ecosystem fluxes (e.g., energy, water, and nutrients). Such a characterization then provides a basis for assessing and managing future anthropogenic risks to the sustainability of ecosystem productivity.</p><p>To characterize the space and time evolution of watershed scale processes, this dissertation introduces a mean field approach to watershed hydrology. Mean field theory (also known as self-consistent field theory) is commonly used in statistical physics when modeling the space-time behavior of complex systems. The mean field theory approximates a complex multi-component system by considering a lumped (or average) effect of all individual components acting on a single component. Thus, the many body problem is reduced to a one body problem. For watershed hydrology, a mean field theory reduces the numerous point component effects to more tractable watershed averages resulting in a consistent method for linking the average watershed fluxes (evapotranspiration, runoff, etc.) to the local fluxes at each point.</p><p>The starting point for this work is a general point description of the soil moisture, rainfall, and runoff system. For this system, we find the joint PDF that describes the temporal variability of the soil water, rainfall, and runoff processes. Since this approach does not account for the spatial variability of runoff, we introduce a probabilistic storage (ProStor) framework for constructing a lumped (unit area) rainfall-runoff response from the spatial distribution of watershed storage. This framework provides a basis for unifying and extending common event-based hydrology models (e.g. Soil Conservation Service curve number (SCS-CN) method) with more modern semi-distributed models (e.g. Variable Infiltration Capacity (VIC) model, the Probability Distributed (PDM) model, and TOPMODEL). In each case, we obtain simple equations for the fractions of the different source areas of runoff, the spatial variability of runoff and soil moisture, and the average runoff value (i.e., the so-called runoff curve). Finally, we link the temporal and spatial descriptions with a mean field approach for watershed hydrology. By applying this mean field approach, we upscale the point description with the spatial distribution of soil moisture and parameterize the numerous local interactions related to lateral fluxes of soil water in terms of its average. With this approach, we then derive PDFs that represent the space and time distribution of soil water and associated watershed fluxes such as evapotranspiration and runoff.</p> / Dissertation

Low relief, heavily human-impacted landscapes like those of the Prairies in south-central Canada have received little attention in previous hydrological research. Here, the rainfall-runoff relationship in the context of both a field-based investigation and an empirical model is examined in an effort to provide insight into Prairie hydrology. Rainfall and water level data were collected for nested sub-watersheds of the Catfish Creek watershed, a 642 km2, near-level, mixed land use and engineered Prairie watershed. First, the dataset is examined for runoff controls. Second, the history of the United States Curve Number Method is reviewed and its initial abstraction ratio examined against collected field data to determine the applicability of a single, constant ratio to Prairie landscapes. Overall, the results indicate that Prairie runoff generation processes differ significantly from those of humid, pristine catchments of higher relief and a conceptual model is proposed with that regards.

Prior to using hydraulic and spatially distributed modelling softwares, the theory of the unit hydrograph was a commonly used tool for modelling of surface and runoff water. While distributed models often provide detailed results from extensive calculation durations, the unit hydrograph have been questioned for simplifying the physical characteristics of the watershed modelled. Typically, the unit hydrograph theory does not explicitly take the flow paths of the watershed in consideration during calculation. With the rise of geographical information systems, methods of deriving spatially distributed unit hydrographs have been developed. The aim of these have commonly been to find a spatially varied form of hydrological modelling, while still keeping the computation times low. The method is commonly built by calculating the travel time to the watershed outlet along the flow path. In this study, spatially distributed unit hydrographs are derived separately for the watershed’s pervious and impervious surfaces in a Python script using map algebra and the Esri’s Python wrapper module Arcpy. The travel times are generated from a velocity field calculated using Maidment and Olivera’s velocity equation. The velocity equation contains three unknown parameters; one for an average velocity and two calibration parameters. The excess precipitation is calculated of a 100 year return period Chicago Design Storm hyetograph using the SCS-CN method. The direct runoff hydrographs are calculated over three semi-urban watersheds in Smedby in southern Sweden, and the results are compared to MIKE 21 hydrograph data of each corresponding watershed and rain input. The result obtained showed to replicate the hydrograph response quite well, but only if the unknown parameters in the velocity equation were calibrated to match the MIKE 21 data. The unknown parameters of the velocity equations produces uncertainties of using the method without calibration data, which implies that the script is not well adapted to use for modelling predictions. It may be of interest to calculate the travel times of the locations within the watershed using a different formula. The script tool could be tested using different design storms as input, and areas of different characteristics compared to Smedby could be tested. / Innan det blev vanligt att använda hydrauliska och rumsliga modellerings- mjukvaror användes ofta teorin bakom enhetshydrografen för modellering av avrinning. Medan de rumsliga mjukvarorna ofta erbjuder detaljerade resultat till priset av långa beräkningstider, har enhetshydrografen ifrågasatts för att förenkla den fysiska karaktären av avrinningsområdet. Typiskt sett tar inte enhetshydrografen avrinningsområdets flödesvägar direkt i hänseende vid beräkning. Utveckling och ökad tillgänglighet av geografiska informations- system förenklade möjligheterna att utveckla beräkning av enhetshydrografer som tar hänsyn till avrinningsområdets karaktär, typiskt sett genom att beräkna rinntiden från varje läge i avrinningsområdet, längs rinnvägarna och till utloppet. I den här studien beräknas spatiala enhetshydrografer separat för avrinningsområdets hårdgjorda och icke hårdgjorda ytor, genom att utveckla ett Python skript med hjälp av karalgebra och Esri’s wrapper modul ArcPy. Rinntiderna från olika lägen i avrinningsområdet beräknas med Maidments och Oliveras formel för hastighet, vilken innehåller okända parametrar för en uppskattad medelhastighet samt två kalibreringsparametrar. Effektivt regn från ett Chicago Design Storm regn med en återkomsttid på 100 år beräknas med hjälp av SCS-CN metoden. Hydrograferna för direkt avrinning faltas för tre semi-urbana avrinningsområden i Smedby i södra Sverige för att sedan jämföras mot MIKE 21 genererad hydrograf data för respektive motsvarade avrinningsområde. Hydrografdata producerat av MIKE 21 har tagits fram med lika CDS-regn data som input. Resultatet visar att hydrografer snarlika MIKE 21 hydrograferna kan tas fram med Maidments spatialt fördelade enhetshydrograf, om de okända parametrarna i Maidments formel kalibrerades mot MIKE 21 data. Utan kalibreringsdata för att bestämma de okända parametrarna kan resultatet anses vara mycket osäkert, vilket antyder att Python skriptet ej bör användas för använda metoden för att förutspå responser av regnevent. Andra beräkningar än Maidments ekvation kan vara av intresse att implementera. Olika typer av regninput samt spatial data över andra platser än Smedby kan vara av intresse att testa Python skriptet för.