This thesis formulates a conceptual framework developed from field observations that describes the influence of surface depressions or potholes on runoff generation in the prairie pothole region of the North American prairies. The fill-and-spill of potholes results in intermittent surface water connectivity between potholes within the basin. The extent of connectivity between potholes is dependent on antecedent water levels. Dynamic connectivity between potholes results in dynamic contributing areas for runoff. The concept of connectivity is manifested in the conceptual curves presented in this thesis. These conceptual curves model the response of runoff events for landscape types found in the prairie pothole region, and capture the influence of the spatial distribution and extent of surface storage on contributing area. The conceptual curves differ due to variations in the spatial distribution and extent of surface storage volume.<p> An algorithm based on the conceptual framework proposed is presented. The algorithm, which uses the the D-8 drainage direction method, automates a methodology for identifying and quantifying runoff contributing area. The algorithm is applied in prairie pothole basins both to demonstrate its efficacy and to test the potential for using conceptual curves to describe the relationship between decreasing potential surface storage in the landscape and contributing area. The algorithm was applied to two digital elevation models (DEM) representative of the prairie pothole region. The first DEM was created using LiDAR elevation points at a 1 m resolution for the St. Denis watershed, and the second was created from orthophotos for the Smith Creek watershed at a 25 m resolution.<p> Fieldwork in the St. Denis watershed was carried out to both provide a basis for the conceptual framework proposed and to validate the results of the algorithm. The fieldwork involved gathering snow survey data, identifying and describing surface water conditions during a snow melt runoff event in 2006, and measuring pond levels from 2004 2007.<p> Results indicate that the proposed conceptual curves represent the non-linear relationship between potential surface storage and contributing area generated by the algorithm in the test basins. To test whether the underlying concepts of the algorithm were valid, the algorithm was used to model pond level depths measured in the St. Denis drainage basin after spring runoff in 2006 and 2007. An r2 value over 0.9 was calculated for the relationship between measured and modeled pond levels in both years. Based on this work, it is clear that any hydrologic study or model applied in the prairie pothole region should consider the effect of dynamic contributing areas on runoff generation.

This thesis formulates a conceptual framework developed from field observations that describes the influence of surface depressions or potholes on runoff generation in the prairie pothole region of the North American prairies. The fill-and-spill of potholes results in intermittent surface water connectivity between potholes within the basin. The extent of connectivity between potholes is dependent on antecedent water levels. Dynamic connectivity between potholes results in dynamic contributing areas for runoff. The concept of connectivity is manifested in the conceptual curves presented in this thesis. These conceptual curves model the response of runoff events for landscape types found in the prairie pothole region, and capture the influence of the spatial distribution and extent of surface storage on contributing area. The conceptual curves differ due to variations in the spatial distribution and extent of surface storage volume.<p> An algorithm based on the conceptual framework proposed is presented. The algorithm, which uses the the D-8 drainage direction method, automates a methodology for identifying and quantifying runoff contributing area. The algorithm is applied in prairie pothole basins both to demonstrate its efficacy and to test the potential for using conceptual curves to describe the relationship between decreasing potential surface storage in the landscape and contributing area. The algorithm was applied to two digital elevation models (DEM) representative of the prairie pothole region. The first DEM was created using LiDAR elevation points at a 1 m resolution for the St. Denis watershed, and the second was created from orthophotos for the Smith Creek watershed at a 25 m resolution.<p> Fieldwork in the St. Denis watershed was carried out to both provide a basis for the conceptual framework proposed and to validate the results of the algorithm. The fieldwork involved gathering snow survey data, identifying and describing surface water conditions during a snow melt runoff event in 2006, and measuring pond levels from 2004 2007.<p> Results indicate that the proposed conceptual curves represent the non-linear relationship between potential surface storage and contributing area generated by the algorithm in the test basins. To test whether the underlying concepts of the algorithm were valid, the algorithm was used to model pond level depths measured in the St. Denis drainage basin after spring runoff in 2006 and 2007. An r2 value over 0.9 was calculated for the relationship between measured and modeled pond levels in both years. Based on this work, it is clear that any hydrologic study or model applied in the prairie pothole region should consider the effect of dynamic contributing areas on runoff generation.

A drainage basins runoff response can be determined by the connectivity of generated runoff to the stream network and the connectivity of the downstream stream network. The connectivity of a drainage basin modulates its ability to produce streamflow and respond to precipitation events and is a function of the complex and variable storage capacities along the drainage network. An improved means to measure and account for the dynamics of hydrological connectivity at the basin scale is needed to improve prediction of basin scale streamflow. The overall goal of this thesis is to improve the understanding of hydrological connectivity at the basin scale by measuring hydrological connectivity at the Baker Creek Research Basin during 2009. To this end, the objectives are to 1) investigate the dynamics of hydrological connectivity during a typical water year, 2) define the relationship between the contributing stream network and contributing area, 3) investigate how hydrological connectivity influences streamflow, and 4) define how hydrological connectivity influences runoff response to rainfall events. At a 150 km2 subarctic Precambrian Shield catchment where the poorly-drained heterogeneous mosaic of lakes, exposed bedrock, and soil filled areas creates variable contributing areas, hydrological connectivity was measured between April and September 2009 in 10 sub-basins with a particular focus on three representative sub-basins. The three sub-basins, although of similar relative size, vary considerably in the dominant typology and topology of their constituent elements. At a 10 m spatial resolution, saturated areas were mapped using both multispectral satellite imagery and in situ measurements of storage according to land cover. To measure basin scale hydrological connectivity, the drainage network was treated as a graph network with stream reaches being the edges that connect sub-catchment nodes. The overall hydrological connectivity of the stream network was described as the ratio of actively flowing relative to potentially flowing stream reaches, and the hydrological connectivity of the stream network to the outlet was described as the ratio of actively flowing stream reaches that were connected to the outlet relative to the potentially flowing stream reaches. Hydrological connectivity was highest during the spring freshet but the stream network began to disintegrate with its passing. In some drainage basins, large gate keepers were able to maintain connectivity of the stream network downstream during dry periods. The length of the longest stream was found to be proportional to contributing area raised to a power of 0.605, similar to that noted in Hacks Law and modified Hacks Law relationships. The length of the contributing stream network was also found to be proportional to contributing area raised to a power of 0.851. In general, higher daily average streamflows were noted for higher states of connectivity to the outlet although preliminary investigations allude to the existence of hysteresis in these relationships. Elevated levels of hydrological connectivity were also found to yield higher basin runoff ratios but the shape of the characteristic curve for each basin was heavily influenced by key traits of its land cover heterogeneity. The implications of these findings are that accurate prediction of streamflow and runoff response in a heterogeneous drainage basin with dynamic connectivity will require both an account of the presence or absence of connections but also a differentiation of connection type and an incorporation of aspects of local function that control the flow through connections themselves. The improved understanding of causal factors for the variable streamflow response to runoff generation in this environment will serve as a first step towards developing improved streamflow prediction methods in formerly glaciated landscapes, especially in small ungauged basins.

A drainage basins runoff response can be determined by the connectivity of generated runoff to the stream network and the connectivity of the downstream stream network. The connectivity of a drainage basin modulates its ability to produce streamflow and respond to precipitation events and is a function of the complex and variable storage capacities along the drainage network. An improved means to measure and account for the dynamics of hydrological connectivity at the basin scale is needed to improve prediction of basin scale streamflow. The overall goal of this thesis is to improve the understanding of hydrological connectivity at the basin scale by measuring hydrological connectivity at the Baker Creek Research Basin during 2009. To this end, the objectives are to 1) investigate the dynamics of hydrological connectivity during a typical water year, 2) define the relationship between the contributing stream network and contributing area, 3) investigate how hydrological connectivity influences streamflow, and 4) define how hydrological connectivity influences runoff response to rainfall events. At a 150 km2 subarctic Precambrian Shield catchment where the poorly-drained heterogeneous mosaic of lakes, exposed bedrock, and soil filled areas creates variable contributing areas, hydrological connectivity was measured between April and September 2009 in 10 sub-basins with a particular focus on three representative sub-basins. The three sub-basins, although of similar relative size, vary considerably in the dominant typology and topology of their constituent elements. At a 10 m spatial resolution, saturated areas were mapped using both multispectral satellite imagery and in situ measurements of storage according to land cover. To measure basin scale hydrological connectivity, the drainage network was treated as a graph network with stream reaches being the edges that connect sub-catchment nodes. The overall hydrological connectivity of the stream network was described as the ratio of actively flowing relative to potentially flowing stream reaches, and the hydrological connectivity of the stream network to the outlet was described as the ratio of actively flowing stream reaches that were connected to the outlet relative to the potentially flowing stream reaches. Hydrological connectivity was highest during the spring freshet but the stream network began to disintegrate with its passing. In some drainage basins, large gate keepers were able to maintain connectivity of the stream network downstream during dry periods. The length of the longest stream was found to be proportional to contributing area raised to a power of 0.605, similar to that noted in Hacks Law and modified Hacks Law relationships. The length of the contributing stream network was also found to be proportional to contributing area raised to a power of 0.851. In general, higher daily average streamflows were noted for higher states of connectivity to the outlet although preliminary investigations allude to the existence of hysteresis in these relationships. Elevated levels of hydrological connectivity were also found to yield higher basin runoff ratios but the shape of the characteristic curve for each basin was heavily influenced by key traits of its land cover heterogeneity. The implications of these findings are that accurate prediction of streamflow and runoff response in a heterogeneous drainage basin with dynamic connectivity will require both an account of the presence or absence of connections but also a differentiation of connection type and an incorporation of aspects of local function that control the flow through connections themselves. The improved understanding of causal factors for the variable streamflow response to runoff generation in this environment will serve as a first step towards developing improved streamflow prediction methods in formerly glaciated landscapes, especially in small ungauged basins.

Surface depressions are important topographic features, which affect overland flow, infiltration, and other hydrologic processes. Specifically, depressions undergo filling-spilling-merging-splitting processes under natural rainfall conditions, featuring discontinuity in hydrologic connectivity and variability in contributing area. However, a constant and time-invariant contributing area is often assumed in traditional hydrologic modeling, and consequently, the real threshold-controlled overland flow dynamics cannot be captured. The overall goal of this dissertation research is to improve hydrologic modeling, especially for depression-dominated areas, by quantifying the hydrologic effects of depressions. The specific objectives are to analyze the hydrotopographic characteristics of depressions and identify the intrinsic relationships of hydrologic variables, develop new modeling methods to simulate the depression-oriented dynamics in overland flow and variations in contributing area, and reveal the influence of spatially distributed depressions on the surface runoff generation and propagation processes. To achieve these objectives, three studies were conducted: (1) the frequency distribution of depression storage capacities was determined and a puddle-based unit (PBU)-probability distribution model (PDM) was developed; (2) the intrinsic changing patterns of contributing area and depression storage were identified, based on which a new depression-oriented variable contributing area (D-VCA) model was developed; and (3) a modified D-VCA (MD-VCA) model was further developed by introducing a depressional time-area zone scheme and a new variable contributing area-based surface runoff routing technique to account for the spatial distribution of depressions. These three models (PBU-PDM, D-VCA, and MD-VCA) were evaluated through the applications to depression-dominated watersheds in North Dakota, and simulation results demonstrated their capabilities in simulating the variations of contributing areas and threshold-controlled overland flow dynamics. In addition, these three studies emphasized the important roles of depressions in the evolution of contributing areas as well as surface runoff generation and propagation. Without considering the spatial distribution of depressions, the formation of contributing area and the timing and quantity of runoff contributions cannot be characterized.