Theodore A. Endreny
A DISSERTATION
PRESENTED TO THE FACULTY
OF PRINCETON UNIVERSITY
IN CANDIDACY FOR THE DEGREE
OF DOCTOR OF PHILOSOPHY
RECOMMENDED FOR ACCEPTANCE
BY THE DEPARTMENT OF
CIVIL AND ENVIRONMENTAL ENGINEERING
PROGRAM IN ENVIRONMENTAL ENGINEERING & WATER RESOURCES
© Copyright by Theodore A. Endreny, 1999.
All rights reserved.
Abstract
This dissertation describes the development of bio-geophysical algorithms for the prediction of non-point source (NPS) runoff critical areas, which are the watershed areas generating the greatest share of water pollution. Seven separate research investigations were conducted to examine science questions relating to: 1) how topographic and vegetative watershed features function as predictors of NPS critical areas, and 2) how errors in remotely sensed topographic inputs and overland flow algorithm formulations impact the accuracy of predicted critical area distributions. Initial NPS-based simulations demonstrated that the topographic index, which is a geophysical index unforced by precipitation data, and the much more complex water and energy balance TOPLATS (topographically based land-atmosphere-transfer scheme) model, when fed hourly precipitation data, predicted similar spatial patterns of saturation. Future simulations then documented the extent to which TOPLATS and topographic index predictions were sensitive to topographic data errors, and how these sensitivities changed when predictions were made across a range of statistical and spatial scales. Data analysis techniques were then developed to minimize the observed topographic data error and to identify and construct geophysically based routing algorithms robust to that error yet representative of observed flow dynamics. Ensemble model runs with these overland flow routing algorithms and maps of land cover were then used to predict NPS dispersal areas and rank the likelihood that terrain or land cover caused pollutant trapping. Combination of the topographic index method of predicting saturation runoff with the dispersal area method of predicting pollutant trapping resulted in new bio-geophysical algorithms capable of predicting and ranking the spatial distribution of NPS critical areas.
Chapter 1
Dissertation Summary
NPS Critical Area Problem Statement
In 1972 the U.S. Congress passed the Clean Water Act to address the point and non-point water quality problems keeping 66% of our lakes and rivers unfit for drinking, fishing, and swimming (EPA, 1998). Point sources of pollutants, such as discharge from pipes leaving factories and sewage treatment plants, when controlled by the CWA resulted in 50% of all polluted lakes and rivers qualifying as clean (EPA, 1998). Nearly 20,000 km2 of lakes and 50,000 km of rivers and shoreline remain polluted, however, due to contamination from non-point source (NPS) runoff leaving farms, residential areas, and forests (EPA, 1998; Wald, 1999). These NPS pollutants include disease-causing pathogens from animal manure, reservoir- and river-choking sediment from plowed fields and forest roads, eutrophication-triggering nutrients from agricultural fertilizers, and poisonous chemicals from residentially and agriculturally applied herbicides and pesticides.
NPS pollutants from such land use activities are initially characterized as diffusely distributed across a watershed’s land surface (Figure 1.1). After a precipitation event, however, overland flow processes can carry NPS pollutants to rivers and lakes and result in a degradation of water quality. Landscape features along the flow path, such as filter strips or detention wetlands, can trap entrained pollutants and mitigate the magnitude of pollutants entering a river or lake (Figure 1.2). A challenge in NPS modeling, therefore, is the identification of the areas within a watershed responsible for the disproportionate share of the watershed’s total pollution. These areas are called ‘critical areas’ and are described by the intersection of three land area criteria: 1) presence of a pollutant, 2) presence of runoff entering that land area from upslope, and 3) absence of significant pollutant trapping features within the downslope runoff pathway.
Models that identify NPS critical areas can direct management resources toward the watershed zones offering the greatest water quality improvement per unit land area or management effort. Not only must these models consider the three physical criteria defining critical areas, but they must also consider the temporal needs of land management decisions and the availability of model input data. Land management decisions are typically made at seasonal to yearly time steps while input data is of a spatial and radiometric resolution controlled by operational remote sensing technology. NPS models that utilize remotely sensed bio-geophysical data and provide output that facilitates seasonal to yearly management decisions are needed.
This dissertation addresses these NPS modeling needs through development of algorithms capable of mapping critical pollutant areas using a timestep controlled by changes in land cover and data derived from remotely sensed products. Several existing algorithms were critiqued and modified while additional algorithms were created within this dissertation. The final NPS algorithms are physically based conceptualizations of runoff likelihood and transport fate capable of characterizing the spatial distribution and magnitude of NPS critical areas. A premise of this research is that although NPS runoff is triggered by the short timestep controlling storm dynamics, its fate and transport within the watershed is governed by terrain and land cover features.
Science Questions Addressed by Dissertation Research
This research addresses the following five science questions that originate from efforts to model and manage watershed NPS critical areas.
Chapter 1 developed the framework for using the topographic index and the variable source area (VSA) runoff theory to model the origins of NPS runoff. VSA theory is used together with upslope topographic data to predict the dynamic expansion and contraction of zones of saturation. Hydrologists have known for some time that VSA processes control runoff processes, yet the majority of NPS models do not account for VSA and typically assume spatially homogeneous patterns of runoff across the watershed. Models that lack a VSA hydrology routine are therefore unable to identify spatially dynamic runoff origins. The Topographically based Land Atmosphere Transfer Scheme (TOPLATS) water and energy balance model, although not currently designed for modeling NPS nutrient dynamics, is capable of predicting VSA and non-VSA runoff (e.g. infiltration excess) processes. TOPLATS and the topographic index were each applied in the 17.5-km2 Charlie Creek agricultural watershed in central Oklahoma to examine differences between VSA and non-VSA predicted runoff and determine whether the geophysically based topographic index can predict the majority of TOPLATS-predicted runoff areas.
TOPLATS identified runoff loading zones in a static modeling framework (e.g. topographic index without meteorological data) as a function of pre-storm water table depth and also in a dynamic modeling framework by simulating basin response to 2-, 10-, and 25-yr return period 6-hr design storms. Runoff areas predicted by both frameworks were then intersected with land cover data on pollution likelihood to predict NPS loading areas. VSA expansion occurred throughout the duration of each 6-hr storm and total runoff area increased with design storm intensity while little non-VSA runoff occurred using the hourly precipitation data. Infiltration excess runoff typically occurs during relatively short (e.g. 10’s to 100’s of seconds) bursts of high precipitation rates that is not represented in hourly data. The static model predicted nearly 99% of all saturated runoff areas predicted by the TOPLATS dynamic model, indicating that simple geophysical modeling is a good descriptor of runoff dynamics given hourly precipitation data.
This study, although unique in utilizing upslope-contributing areas to predict runoff likelihood, was incomplete in neglecting the role of downslope dispersal areas on the fate of polluted runoff. This research concluded that 1) VSA concepts of spatial saturation excess runoff modeling should be incorporated into NPS management models, and 2) given hourly precipitation data, runoff predicted using the geophysically based topographic index matches that predicted using a complex meteorologically-driven model.
Chapter 3: Geomorphological Modeling Sensitivity to DEM Accuracy
Chapter 3 departed from NPS runoff research to explore fundamental issues relating to the propagation of elevation errors through topographically based models. TOPLATS, as well as many other topographically based models, use digital elevation model (DEMs) inputs to describe watershed hydro-geomorphologic properties, which are in turn used to predict hydrologic response. DEMs are currently generated using satellite-derived images, but little was known about how errors in satellite-derived DEMs impacted hydro-geomorphologic products such as relief, elevation contours, basin boundaries, and stream networks. Since the research in Chapter 2 indicated that topographic inputs alone could provide reasonable predictions of runoff areas it was obvious that errors in terrain could limit algorithm predictive accuracy.
This study specifically assessed the elevation inaccuracies in a SPOT satellite-derived DEM of the 532 km2 Little Washita River, OK watershed. SPOT-derived DEM errors were identified using a set of ground control points (GCPs) and by comparing the 600,000 pixels comprising the SPOT image of the study area to Level 2 (3-m RMSE) and Level 1 (7-m RMSE) U.S. Geological Survey (USGS) 7.5 minute airborne-derived DEMs. Although SPOT- and USGS-derived topographic relief images had a poor correlation at small spatial scales, at larger hillslope scales nearly 90% of the image pixels overlapped. For basin-scale descriptors, such as catchment area, stream length, stream density, and Horton ratios, SPOT- and USGS-derived estimates differed by no more than 3%. At smaller spatial scales, however, an overlay of SPOT-derived vector images of basin boundaries and stream networks with equivalent higher-accuracy products revealed that the products were incongruent on average 100-m and at most up to distances of 1-km.
This research concluded that differences between micro-scale (30 to 500 m) USGS and SPOT-derived topographic terrain were quickly resolved by aggregation techniques that expanded the analysis to meso (500 to 5000 m) and macro (> 5 km) scales. Hence, losses in horizontal resolution can be exchanged for gains in SPOT-derived product accuracy. In summary, the accuracy of the SPOT-derived DEM was adequate for deriving estimates of basin average hydro-geomorphology but was unable to match equivalent products derived from USGS 7.5 minute DEMs at scales finer than 100-m. This research resulted in the development of an equation to estimate the horizontal extent of hydro-geomorphologic uncertainty based on vertical accuracy measurements.
Chapter 4: Hydrological Modeling Sensitivity to DEM Accuracy
Chapter 4 examined whether vertical errors within a SPOT -derived DEM (used in Chapter 3) for the Little Washita watershed equally impacted TOPLATS predicted catchment average hydrological fluxes, statistically distributed fluxes, and spatially distributed fluxes. Model predictions based on SPOT-derived DEM inputs were compared with USGS 7.5-minute Level 1 (RMSE of 7 m) and Level 2 (RMSE of 3 m) DEM based predictions to determine model sensitivity. These USGS DEMs provided a baseline for model output to which SPOT runs were compared. TOPLATS was modified in this research to include subroutines that predicted changes in temperature and incident short-wave radiation with changing terrain.
Ten year simulation runs using a statistical formulation of TOPLATS indicated that while DEM inaccuracies had little impact on basin-average output, they had significant impact on the upper and lower quartiles of predicted water table depth. These quartiles for water table fluxes were different by nearly 0.5-m from the Level 2 and Level 1 predicted fluxes, causing large discrepancies in predictions of the available storage and saturated volume in the Little Washita during the entire 10-year simulation. In twelve-day simulation runs using a spatially explicit formulation of TOPLATS, which used 30-m grid cells across a 600,000 pixel model domain, elevation errors propagated into model predictions of soil moisture, runoff, evapotranspiration, incoming solar radiation, and surface skin temperature. Aggregation of the 30-m pixel model output to scales of 0.25-km2, however, achieved an r2 of 0.90, representing a good agreement between model predicted vadose zone hydrology that defines NPS areas. Equivalent statistical agreement between model predicted water table hydrology, however, was not achieved until much larger scales of 5-km2.
This error propagation research concluded that differences in how TOPLATS incorporated DEM data into equations for saturated and unsaturated processes caused significant differences in the effectiveness of scaling. Another important finding in this research involved the sensitivity of overland flow paths to DEM errors. In simulations of flow from an agricultural field the SPOT-based TOPLATS overland flow paths diverged significantly from USGS predictions. In NPS management that attempts to target and intercept polluted overland flow, these model differences are troublesome. Additional research is discussed in Chapter 6 that examined the sensitivity of overland flow algorithms to DEM error.
Chapter 5: Techniques for Improving DEM Accuracy
Chapter 5 followed up on an observation regarding the spatial pattern of SPOT-derived DEM errors recorded during research performed in Chapters 3 and 4. In this research of the Little Washita watershed, a 1000 km2 section of the SPOT-derived DEM was observed to contain systematic elevation errors that divided the basin into two distinct areas that were above and below baseline elevations. A technique for minimizing these errors was developed in this chapter.
Error minimization of this systematic SPOT error was achieved by first overlaying the Little Washita section of GTOPO30, the latest DEM providing global land coverage, and then computing GTOPO30 – SPOT elevation residuals. Spatial analysis of these elevation residuals revealed that the systematic elevation error oriented about a single axis, and rotating the SPOT-derived DEM scene about this axis minimized the GTOPO30-SPOT RMSE by nearly 10%. The axis intercept, slope and degree of rotation identified using the relatively coarse 1-km resolution GTOPO30 product were nearly identical to those identified using three separate DEMs of 30 and 90-m resolution. Forty ground control points (GCPs) not used in the original stereocorrelation of the SPOT-derived DEM confirmed that rotation improved the SPOT-derived DEM RMSE by nearly 26%. This research indicated that 60 x 60 km2 SPOT-derived DEM scenes might have interior sub-sections that contain systematic elevation error and that the GTOPO30 data set has an adequate systematic accuracy for identifying and correcting this error.
Chapter 6: Overland Flow Routing: Algorithm Robustness
Chapter 6 examined how inaccuracies in terrain data used by pollutant fate and transport models enter into computations of runoff path to create uncertainties in NPS model predictions of pollutant trapping and subsequent management plans. Along with the use of terrain data for predicting the spatial distribution of saturation, hydrologists use terrain to map likely overland flow pathways. This study examined the sensitivity of the D8, Multiple Flow (MF), DEMON, and D-Infinity runoff routing algorithms, along with two hybrid algorithms, to terrain errors. Overland flow simulations were performed with all six routing algorithms using control terrain data from a SPOT-derived digital elevation model and terrain data that was generated to represent common elevation error types.
Predicted runoff paths were recorded during a simulated storm event and then runoff paths were stored as matrices indicating the presence or absence of flow. Simulations were conducted using terrain inputs from three agricultural fields of high, medium, and low gradient slope with convergent and divergent terrain features. The random elevation errors that were applied to the control SPOT DEM were drawn from a normal distribution with a vertical root mean square error (RMSE) of 0.5, 2, 4, and 6-m each with a spatial correlation that ranged from 0 to 0.99 at lag distances of 180-m. This error structure approximated error fields observed in the SPOT DEM. The ensemble of runoff matrices for each random realization of terrain were compared with the flow networks predicted by the same algorithm during the control runs to identify their fraction of overlap in predicted runoff pathways and thereby rank the robustness of the routing algorithm.
Routing simulations indicated that the MF algorithm was the most robust to terrain uncertainty and possibly overly insensitive to the large 6-m vertical elevation perturbations that warrant a more substantial change in predicted flow path. The DEMON and D-Infinity routing algorithms had comparable overall robustness rankings even though differences were identified for various combinations of terrain type and statistical analysis techniques. All routing algorithms had increased robustness with increases in terrain slope and the presence of terrain convergence, while algorithm robustness decreased with increases in the magnitude of the vertical error perturbations.
An interesting result of this work was the creation of methods for quantifying overland flow uncertainty. A set of NPS modeling tools were created that represent flow path uncertainty by running ensembles of flow path simulation under varying DEM realizations. The runoff matrices from these simulations were then incorporated into frequency diagrams that quantified the likelihood for a watershed area to intercept runoff from agricultural fields. Grid cells with high rates of interception can be used to identify locations for constructing pollutant traps that have a predicted likelihood for pollution interception.
Chapter 7: Overland Flow Routing: Algorithm Accuracy
Chapter 7 examined issues involving overland flow path accuracy. Runoff pathways are fundamental to NPS models for predicting pollutant fate and transport, yet the modeled flow differs significantly from observed runoff pathways. Observed flow is often directed or bifurcated into paths that are transverse to the maximum slope by 0.1 to 1-m scale heterogeneities in topography, soils, or vegetation. Modeled flow, on the other hand, is traditionally dealt with in a raster environment at the 1 to 90-m scale where such heterogeneities are sub-grid scale and flow is simply routed down the steepest slope.
The routing algorithms of D8, DEMON, and D-Infinity direct flow to only one or two lower elevation neighbors, while the Multiple Flow (MF) routing algorithm allows for flow to pass to all neighbors that are lower in elevation. Flow networks predicted by these four algorithms, as well as from seven hybridized algorithms that allow for additional flow options, were compared with flow networks observed in two agricultural hillslopes in Princeton, NJ. Error matrices that identified discrepancies between observed and predicted flow were used to compute errors of omission, errors of commission, and estimate total predictive accuracy using the KAPPA analysis K (hat) statistic.
The D8 algorithm, which constrains flow to a single path, had the highest errors of omission. Three modifications to D8 that increased flow bifurcation significantly decreased these errors while simultaneously increasing errors of commission. MF, which allows flow to divide into all eight neighbors, had the lowest errors of omission but also had the greatest errors of commission. Modifications of MF that limited flow to fewer neighbors increased omission error but greatly reduced errors of commission. DEMON, which divides flow into two adjacent cardinal neighbors had the second lowest errors of omission and had the lowest errors of commission. D-Infinity, which is less dispersive than DEMON and divides flow into adjacent cardinal-diagonal pairs, had larger errors of omission and smaller errors of commission than DEMON. DEMON, D-Infinity and other two-direction flow algorithms, on average, were ranked highest for overall accuracy while individual algorithm rankings varied with the terrain type.
Chapter 7 provided one of the first critical assessments of routing algorithm accuracy for NPS modeling. The research concluded that simulation of overland flow paths in directions other than steepest descent was necessary to represent the observed flow redirection and bifurcation in overland runoff networks. Hence, multiple flow direction algorithms improve model predictive accuracy. Unfortunately, the most accuracy algorithms were the computationally intensive, and it is unlikely that NPS models will be capable of incorporating multi-direction routing at this time.
Chapter 8: Non-point Source Modeling: Algorithm Synthesis
Chapter 8 integrated the work of the previous chapters into the formulation of a conceptually based, spatially distributed NPS critical area model. The topographic index based NPS loading of Chapter 2 was combined with the overland flow modeling of Chapters 6 and 7 to develop a means for predicting the three criteria in critical area modeling. In contrast to widely used lumped model assumptions that pollutant loading is invariant to landscape position, these bio-geophysical models incorporated the influence of contributing area and dispersal area (CADA) features on the distribution of NPS runoff.
This chapter presented the development, calibration, validation, and application of two conceptual NPS runoff models for predicting basin and spatial loading of Total Phosphorous (TP) from land use activities. The first model built upon the Export Coefficient (EC) concept by using spatially distributed CADA weighting functions to emphasize and de-emphasize specific pixel pollutant loads, while preserving the same EC basin average load. The second model was a FErtilizer Release and Trapping (FERT) scheme that used estimates of agricultural management practices and subsequent runoff processes to predict NPS spatial distributions and basin average loading.
Calibration, validation, and management simulations were run for the Delaware River basin in New York in a Monte Carlo framework to ensure that the range of input uncertainty was represented in model predictions. Predictions from both conceptual models matched observations, and the spatially distributed weighting functions directed simulated management actions to the watershed’s most critical NPS areas. Validation of model predicted spatial distributions was limited by the absence of spatially mapped field observations indicating NPS pollutant loading magnitude, however written descriptions of watershed critical areas supported model predictions. In validation studies of lumped basin predictions each model matched observed TP loading at either the median or 75th quartile. Neither model matched the entire observed inter-quartile range, which may reflect errors and bias in limited amount of water quality sampling data rather than the model formulation.
Critical area management simulations demonstrated the model’s capability of guiding spatially distributed management at timesteps controlled by land cover change, not the shorter timestep of precipitation events. Using this procedure both CADA-based models provide a new approach for evaluating relative NPS pollution risk across watershed landscapes. The benefit of using these bio-geophysical-based conceptual models to explore the spatial distribution and behavior of NPS runoff is a reasonable response to issues of data scarcity and management time constraints that prohibit and discourage the parameterization of more complex process based modeling.
Chapter 9: Conclusions and Future Research
This final chapter summarizes of the main dissertation
findings and recommends future investigations to advance the field of bio-geophysical
modeling for the management of NPS pollution.
References