Period Covered by Final Report: March 3, 2003 – March 2, 2007
Date of Final Report: June 1, 2007
EPA Cooperative Agreement Number: RD-83059701
Program Name (Title): Watershed Classification System for Tiered Diagnosis of Biological Impairments: A Scalable, Central Plains Focus with National Applicability
Investigators: E. Martinko, J. Thorp, M. Jakubauskas, D. Huggins, J. Whistler, F. deNoyelles, J. Dobson, P. Liechti, and K. Price, University of Kansas, Lawrence, Kansas
Research Category: Development of Watershed Classification Systems for Diagnosis of Biological Impairment in Watersheds and Their Receiving Water Bodies. Sorting Code: 2002-STAR-B1
Institution University of Kansas, Lawrence, Kansas
Project Period: March 3, 2003 - March 2, 2007
Objective of Research: Assessment of time-series satellite data as landscape indicators; development and implementation of classification scheme for watershed condition.
The recommend citation for this report is:
Martinko, E., J. Whistler, D. Peterson, J. Kastens, R. Hagen, D. Huggins, M. Jakubauskas. 2007. A Watershed Classification System for Tiered Diagnosis of Biological Impairments: A Scalable, Central Plains Focus with National Applicability. Final Report to the U.S. Environmental Protection Agency STAR Program, Cooperative Agreement RD-83059701. KBS Report 141. Kansas Biological Survey, University of Kansas Lawrence, 153 pp. Table of Contents Table of Contents...... i List of Figures...... iv List of Tables ...... viii 1.0 Executive Summary...... 1 Abstract...... 1 Data and Methods ...... 1 Results...... 2 Area of Influence ...... 2 Watershed Size...... 3 Regression Tree Analysis and Classification Model Development...... 3 Model Implementation...... 4 Conclusions...... 4 2.0 Introduction...... 5 2.1 Background...... 5 2.1.1 Relationship of landscapes to watershed ecology...... 5 2.1.2 NDVI and phenology metrics as dynamic landscape indicators ...... 6 2.1.3 Traditional geospatial datasets used as static landscape indicators ...... 7 2.1.4 Environmental response indicators...... 8 2.1.5 Spatial and temporal scaling factors ...... 8 2.2 Research Objectives...... 9 2.2.1 Objective 1. Develop and select landscape indicators...... 9 2.2.2 Objective 2. Develop a watershed classification model...... 9 2.2.3 Objective 3. Apply the model for watershed monitoring...... 10 2.3 References...... 11 3.0 Data and Methods ...... 14 3.1 Study area description...... 14 3.2 Stream quality indicators (response/dependent variables)...... 14 3.2.1 Existing data...... 15 3.2.2 New Data ...... 15 3.2.3 Water chemistry...... 16 3.2.4 Benthic macroinvertebrates ...... 16 3.2.5 Fish...... 17 3.2.6 Aggregating and screening sampling events...... 18 3.2.7 Filtering number of response variables...... 18 3.3 Landscape indicators (stressor/predictor variables)...... 20 3.3.1 Static Indicators ...... 20 3.3.2 Dynamic Indicators - NDVI and VPMs...... 21 3.4 Synthetic stream network and automated watershed delineation ...... 23 3.4.1 Procedure used for automated stream and watershed delineation ...... 24 3.4.2 DEM processing and synthetic stream delineation...... 24 3.4.3 Pour point placement and watershed delineation...... 25 3.5 Statistical and spatial processing software...... 25 3.6 References...... 25 4.0 Results - Testing Area of Influence ...... 56 4.1 Introduction...... 56
i 4.2 Data and Methods ...... 56 4.3 Results...... 58 4.3.1 AOI Hypothesis ...... 58 4.3.2 VPM Statistics Breakdown...... 59 4.3.2.1 ‘TotN’ Analysis ...... 60 4.3.2.2 ‘PrpSensF’ Analysis...... 61 4.3.2.3 ‘InvFmRch’ Analysis...... 61 4.3.2.4 Effect of Watershed Size ...... 62 4.4 Conclusions...... 63 4.5 References...... 64 5.0 Results - Testing the Effects of Watershed Size...... 79 5.1 Introduction...... 79 5.2 Data and Methods ...... 79 5.3 Results...... 80 5.3.1 Watershed Size and Ecological Response Values ...... 81 5.3.2 Watershed Size and VPM Performance...... 82 5.3.2.1 ‘TotN’ Analysis ...... 83 5.3.2.2 ‘PrpSensF’ Analysis...... 84 5.3.2.3 ‘InvFmRch’ Analysis...... 84 5.3.2.4 Examining Optimal VPMs for estimation of ‘TotN’ and ‘InvFmRch’ .... 85 5.4 Conclusions...... 86 6.0 Results - Model Development ...... 97 6.1 Introduction...... 97 6.2 Data and Methods ...... 97 6.3 Results...... 99 6.3.1 Landscape Predictors: Static vs. Dynamic...... 99 6.3.1.1 ‘TotN’ RT Models ...... 99 6.3.1.2 ‘PrpSensF’ RT Models ...... 100 6.3.1.3 ‘InvFmRch’ RT Models...... 101 6.3.1.4 ‘PrpFmEPT’ RT Models...... 102 6.3.2 Model Spatial Scale: Global vs. Ecoregion ...... 102 6.3.2.1 ‘TotN’ RT Models ...... 103 6.3.2.2 ‘PrpSensF’ RT Models ...... 103 6.3.2.3 ‘InvFmRch’ RT Models...... 103 6.3.3 Model Temporal Scale: Short-term vs. Long-term...... 104 6.3.3.1 ‘TotN’Models ...... 104 6.3.3.2 ‘PrpSensF’Models...... 104 6.3.3.3 ‘InvFmRch’Models...... 104 6.3.4 Fixed Models ...... 104 6.3.4.1 ‘TotN’Models ...... 105 6.3.4.2 ‘PrpSensF’Models...... 106 6.3.4.3 ‘InvFmRch’Models...... 107 6.4 Conclusions...... 109 6.5 References...... 109 7.0 Results - Implementing a Model: The Stream Trace Map...... 144 7.1 Introduction...... 144
ii 7.2 Study Area ...... 144 7.3 Results...... 144 8.0 Summary...... 150 8.1 Accomplishments...... 150 8.2 Conclusions...... 151 8.3 Research Needs...... 151 8.4 Publications...... 152 8.5 Presentations ...... 152 8.6 Manuscripts in Preparation ...... 152 8.7 Graduate Students Supported...... 153
iii List of Figures
Figure 3 - 1. Location of sample sites for existing chemistry (a), fish (b), and macroinvertebrate (c) data ...... 28 Figure 3 - 2. Location of the 40 non-wadeable sample sites visited during this study in 2003...... 29 Figure 3 - 3. Hypothetical vegetation curve and associated vegetation phenology metrics (VPM) ...... 30 Figure 3 - 4. Map depicting the 15-year average for date of growing season onset...... 31 Figure 3 - 5. Map depicting the 15-year average for NDVI value at growing season onset...... 32 Figure 3 - 6. Map depicting the 15-year average for date of maximum NDVI...... 33 Figure 3 - 7. Map depicting the 15-year average for maximum occurring NDVI value during the growing season ...... 34 Figure 3 - 8. Map depicting the 15-year average for date of dormancy onset...... 35 Figure 3 - 9. Map depicting the 15-year average for NDVI value at dormancy...... 36 Figure 3 - 10. Map depicting the 15-year average for rate of spring greenup ...... 37 Figure 3 - 11. Map depicting the 15-year average for rate of senescence ...... 38 Figure 3 - 12. Map depicting the 15-year average for length of growing season...... 39 Figure 3 - 13. Map depicting the 15-year average for the average NDVI value for the growing season...... 40 Figure 3 - 14. Map depicting the 15-year average for accumulated NDVI for the growing season...... 41 Figure 3 - 15. Map depicting the proportion of cropland per 1-kilometer square area.... 42 Figure 3 - 16. Comparison of stream density depicted for (a) EDNA to NHD, and (b) Synthetic Network to NHD...... 43 Figure 3 - 17. Comparison of positional accuracy of (a) EDNA to NHD and positional accuracy of (b) Synthetic Network to NHD ...... 44 Figure 3 - 18. Examples of inconsistent representation of hydrography in the NHD data ...... 45 Figure 3 - 19. Comparison of automated and manual watershed delineations ...... 46 Figure 3 - 20. Automated pour point creation outcomes ...... 47
Figure 4 - 1. Areas of Influence (AOI) created for two watersheds ...... 65 Figure 4 - 2. Sample distribution, stratified by ecoregion, for (a) ‘TotN’, (b) ‘PrpSensF’, and (c) ‘InvFmRch’ values used in the AOI analysis...... 66 Figure 4 - 3. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the all-ecoregion ‘TotN’ data, by AOI size. 67 Figure 4 - 4. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the ecoregion 27 ‘TotN’ data, by AOI size. 68 Figure 4 - 5. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the all-ecoregion ‘PrpSensF’ data, by AOI size ...... 69
iv Figure 4 - 6. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the ecoregion 27 ‘PrpSensF’ data, by AOI size ...... 70 Figure 4 - 7. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the all-ecoregion ‘InvFmRch’ data, by AOI size ...... 71 Figure 4 - 8. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the ecoregion 27 ‘InvFmRch’ data, by AOI size ...... 72 Figure 4 - 9. General linear statistical correspondence between the top 20% of the VPM statistics and the all-ecoregion ‘TotN’ data, by AOI size...... 73
Figure 5 - 1. Watershed size distributions, stratified by ecoregion, for (a) ‘TotN’, (b) ‘PrpSensF’, and (c) ‘InvFmRch’ samples used in the watershed size analysis...... 88 Figure 5 - 2. Target sample distributions, stratified by ecoregion, for (a) ‘TotN’, (b) ‘PrpSensF’, and (c) ‘InvFmRch’ values used in the watershed size analysis...... 89 Figure 5 - 3. The effects of sample point upstream watershed size on the relationship between ‘TotN’ and VPMs (and between ‘TotN’ and percent cropland) are shown here...... 90 Figure 5 - 4. The effects of sample point upstream watershed size on the relationship between ‘PrpSensF’ and VPMs (and between ‘PrpSensF’ and percent cropland) are shown here ...... 91 Figure 5 - 5. The effects of sample point upstream watershed size on the relationship between ‘InvFmRch’ and VPMs (and between ‘InvFmRch’ and percent cropland) are shown here ...... 92 Figure 5 - 6. The effects of sample point upstream watershed size on the relationship between ‘TotN’ and BD-EX VPMs (and between ‘TotN’ and percent cropland) are shown here, using a 500-point sliding data window...... 93 Figure 5 - 7. The effects of sample point upstream watershed size on the relationship between ‘TotN’ and BD-EX VPMs (and between ‘TotN’ and percent cropland) are shown here, using a 1000-point sliding data window...... 94 Figure 5 - 8. The effects of sample point upstream watershed size on the relationship between ‘InvFmRch’ and AV-EX VPMs (and between ‘InvFmRch’ and percent cropland) are shown here...... 95
Figure 6 - 1. The resubstitution variance explained of ‘TotN’ from RTA for the seven dominant ecoregions in EPA Region 7...... 110 Figure 6 - 2. A regression tree model for predicting ‘TotN’ using the static-dynamic landscape predictor set...... 111 Figure 6 - 3. A regression tree model for predicting ‘TotN’ using the static-dynamic landscape predictor set...... 112 Figure 6 - 4. A regression tree model for predicting ‘TotN’ using the dynamic landscape predictor set...... 113 Figure 6 - 5. The resubstitution variance explained from RTA for ‘PrpSensF’ across the seven dominant ecoregions in EPA Region 7...... 114
v Figure 6 - 6. Areas where KFACT < 0.29 are highlighted in gray...... 115 Figure 6 - 7. A regression tree model predicting ‘PrpSensF’ using the static-dynamic predictor set...... 116 Figure 6 - 8. A regression tree model predicting ‘PrpSensF’ using the dynamic predictor set ...... 117 Figure 6 - 9. The resubstitution variance explained of ‘InvFmRch’ from RTA for the seven dominant ecoregions in EPA Region 7...... 118 Figure 6 - 10. A regression tree model predicting ‘InvFmRch’ using the static-dynamic predictor set...... 119 Figure 6 - 11. A regression tree model predicting ‘InvFmRch’ using the dynamic predictor set...... 120 Figure 6 - 12. The resubstitution variance explained of ‘InvFmEPT’ from RTA for the seven dominant ecoregions in EPA Region 7...... 121 Figure 6 - 13. A regression tree model predicting ‘TotN’ using the 5-year dynamic predictor set...... 122 Figure 6 - 14. A regression tree model predicting ‘PrpSensF’ using the 5-year dynamic predictor set...... 123 Figure 6 - 15. A regression tree model predicting ‘InvFmRch’ using the 5-year dynamic predictor set...... 124 Figure 6 - 16. The final fixed form regression tree model for ‘TotN’ using all sample points...... 125 Figure 6 - 17. The resubstitution proportion of variance explained of ‘TotN’ from RTA using subsets of the dynamic predictors ...... 126 Figure 6 - 18. The regression tree model for ‘TotN’using the top five predictors, all sample points and cost-complexity pruning ...... 127 Figure 6 - 19. A map depicting (a) predicted and (b) observed ‘TotN’ across EPA Region 7 using ‘bda5ex’ and ‘mda1ex’ as predictors ...... 128 Figure 6 - 20. A map illustrating the residuals of the fixed form model used to predict ‘TotN’ ...... 129 Figure 6 - 21. The resubstitution proportion of variance explained of ‘PrpSensF’ from RTA using subsets of the dynamic predictors ...... 130 Figure 6 - 22. A regression tree model predicting ‘PrpSensF’ using the top dynamic predictors and cost-complexity pruning...... 131 Figure 6 - 23. A map depicting (a) predicted and (b) observed ‘PrpSensF’ across EPA Region 7 using ‘ova3ex’ and ‘gua5ex’ as predictors...... 132 Figure 6 - 24. A map illustrating the residuals of the fixed form model used to predict ‘PrpSensF’...... 133 Figure 6 - 25. The final fixed form regression tree model for ‘InvFmRch’ using all sample points ...... 134 Figure 6 - 26. The regression tree model for ‘InvFmRch’ using the top three predictors, all sample points and cost-complexity pruning ...... 135 Figure 6 - 27. The resubstitution proportion of variance explained of ‘InvFmRch’ from RTA using subsets of the dynamic predictors ...... 136 Figure 6 - 28. A map depicting (a) predicted ‘InvFmRch’ and (b) observed ‘InvFmRch’ across EPA Region 7 using ‘mva5ex’, ‘ova1ex’and ‘oda1ex’ as predictors...... 137
vi Figure 6 - 29. A map illustrating the residuals of the regression tree model used to predict ‘InvFmRch’. Point classes are based on the standard deviation of the sample population of ‘InvFmRch’ values (11.13) ...... 138
Figure 7 - 1. Location (in Kansas) of the portion of the Walnut River watershed used to demonstrate the stream trace map ...... 146 Figure 7 - 2. Decision tree model ‘PrpSensF’ predictions for the Walnut River watershed ‘snet1500’ synthetic stream network in (a) 1994 and (b) 2004 ...... 146 Figure 7 - 3. ‘PrpSensF’ change map, comparing predicted values from 1994 and 2004 in the ‘snet1500’ synthetic stream network...... 147 Figure 7 - 4. (a) Density comparison between ‘snet1500’ and ‘snet10000’...... 147 Figure 7 - 5. Decision tree model ‘PrpSensF’ predictions for the Walnut River watershed ‘snet10000’ synthetic stream network in (a) 1994 and (b) 2004 ...... 148 Figure 7 - 6. ‘PrpSensF’ change map, comparing predicted values from 1994 and 2004 in the ‘snet10000’ synthetic stream network ...... 148
vii List of Tables
Table 3 - 1. Summary of response variables stratified by ecoregion...... 48 Table 3 - 2. Summary of response variables stratified by year...... 48 Table 3 - 3. The chemistry, fish and macroinvertebrate databases were primarily compiled from existing data collected by the agencies listed below...... 49 Table 3 - 4. List of the 34 non-wadeable rivers (40 individual sample sites) that were visited in 2003 (see also Figure 3-2)...... 50 Table 3 - 5. Stability of candidate dependent measures. Correlation between values obtained in successive years ...... 50 Table 3 - 6. List of static landscape indicators used to characterize watershed conditions in EPA Region 7 ...... 51 Table 3 - 7. Standardized NDVI biweekly composite periods ...... 52 Table 3 - 8. List of dynamic landscape indicators used to characterize watershed conditions in EPA Region 7...... 53 Table 3 - 9. Correlation matrix #1 for the eleven core VPMs ...... 54 Table 3 - 10. Correlation matrix #2 for the eleven core VPMs ...... 54 Table 3 - 11. Correlations between lagged VPM values ...... 55
Table 4 - 1. Level III Ecoregion names and numbers...... 74 Table 4 - 2. Analysis results for optimal VPM statistics identified during the AOI hypothesis test...... 75 Table 4 - 3. Analysis results for optimal VPM statistics identified during the AOI hypothesis test...... 76 Table 4 - 4. Analysis results for optimal VPM statistics identified during the AOI hypothesis test...... 77 Table 4 - 5. Analysis results for optimal VPM statistics identified during the AOI hypothesis test...... 78
Table 5 - 1. Analysis results for optimal VPM statistics identified during the watershed size test ...... 96
Table 6 - 1. The average R2 across ten random sub-samples using static and dynamic landscape predictors...... 139 Table 6 - 2. Importance values for the static landscape predictor set...... 139 Table 6 - 3. Importance values for the static-dynamic landscape predictor set...... 140 Table 6 - 4. Importance values for the dynamic landscape predictor set...... 141 Table 6 - 5. The average and standard deviation of R2 across ten random 80-20 sub- samples for ecoregion-specific models are shown below...... 142 Table 6 - 6. The average and standard deviation of R2 for global models across ten random sub-samples using three VPM temporal windows as predictor sets...... 142 Table 6 - 7. Importance values for landscape predictor variables using a subset of the dynamic predictor set (VPMs with the sampling year excluded)...... 143 Table 6 - 8. The average R2 across ten random sub-samples using the top VPM predictors...... 143
viii Table 7 - 1. Summary of pixel-level results from application of the ‘PrpSensF’ decision tree model to the Walnut River watershed stream points ...... 149
ix 1.0 Executive Summary
Abstract The goal of this research was to produce an ecoregionally stratified classification system for estimating biological impairment of watersheds. Such a system can be used for ranking watershed vulnerability to impairment and can contribute to developing recommendations for ecosystem rehabilitation. The overarching hypothesis for the research is that landscape-scale surrogates for watershed condition (i.e., stressor indicators) derived from remotely sensed and geospatial data can be used to predict watershed vulnerability and measures of water quality and biological integrity (i.e., response indicators). Unique aspects of this research are (1) the use of time-series satellite data to characterize the dynamic nature of landscapes; (2) the use of classification and regression tree analysis for prediction and classification; (3) the implementation of the model using a trace map; (4) the inclusion of a broad range of watershed sizes, from first order streams to great rivers; (5) the integration of field data from multiple sources to create a large database of response samples; and (6) the large geographic scale of the study. This work was conducted under EPA Cooperative Agreement RD-83059701.
Data and Methods The research project required development of a geographic database to characterize watershed landscape conditions linked to a field sample database containing information on in-stream conditions related to water quality, benthic macroinvertebrates, and fish (Section 3.0). Spatially, the combined database covers the four-state EPA Region 7 (Iowa, Kansas, Missouri, Nebraska). The geographic database consists, for the most part, of data readily available from public sources. These include infrequently updated or functionally invariant datasets such as digital elevation models, transportation networks, soils, hydrography, human population, and land cover (static landscape variables). Time-series data from the Advanced Very High Resolution Radiometer (AVHRR) satellite were used to derive a set of vegetation phenology metrics (VPMs) that express the annually dynamic character of the landscape (dynamic landscape variables). To explore the relationship of short- and long-term landscape trends to field data, two sets of 1- through 5-year VPM temporal averages were calculated; one set using values immediately prior to and including the sampling year and one that excluded the sample year. In total, there are 235 layers in the geographic database (15 static, 220 dynamic). The field sample database was compiled largely from existing datasets collected for wadeable and non-wadeable streams by various groups and agencies from the four states that span a 10-year period (1994-2003). Extensive work went into standardizing and merging these separate datasets and in matching reported locality information to georeferenced stream and river segments. The field sample database was supplemented with additional non-wadeable field sites collected under this grant. The field sample database includes more than 13,000 sampling events representing over 1,300 sites. The original datasets included far more sampling events and sites, but variation in the parameters measured and lack of standardization in field protocols, in addition to uncertainty of sample locations, limited the number that could be
1 included. Measurements of water quality parameters were most numerous. There were far fewer fish and benthic macroinvertebrate samples collected. Unfortunately, very few sample events include all response indicators. After review of available response indicators from each type of sample, one measure was selected from each for analysis: total nitrogen concentration in the water sample (‘TotN’), the proportion of fish species collected in the sample event that are classified as taxa sensitive to water quality impairment (‘PrpSensF’), and the number of macroinvertebrate families collected in the sample event (family-level richness: ‘InvFmRch’). Initially, we proposed to base model development and watershed classification on use of an Index of Biotic Integrity (IBI) representing a composite of multiple measured parameters, standardized by various criteria. During the course of this project, use of an IBI was rejected in favor of using the individual metrics. First, IBIs are specific to ecoregions (or even smaller geographic areas). Development of a region-wide index useful across multiple ecoregions is problematic. Second, the calculation of an IBI reduces all field variable information into a single value, making modeling results difficult to interpret. It was concluded that such a reduction would result in an unwarranted loss of potentially significant information that could only be gleaned through analysis using the metrics individually.
Results The analysis of the field sample data in relation to landscape variables was conducted in three stages. The first two stages focused on issues of spatial scale as they relate to implementing the classification system. In the third stage, regression tree analysis was used to examine temporal and additional spatial issues impacting the relationship between potential landscape stressors and environmental response variables. Results were used to guide development of final classification models. An execution of a model using a trace map concludes the research.
Area of Influence In the first project (Section 4.0), the influence of spatial proximity of landscape stressors to biological and water chemistry response indicators was investigated. Analysis was conducted only on watersheds larger than 1,024 square kilometers. Ten areas of increasing size, or areas of influence (AOIs), immediately upstream of the sample point were delineated and summary statistics extracted from the two 1- through 5- year temporal average VPM datasets. Summary statistics were also extracted for the entire watershed. Bivariate correlation analysis was conducted between the VPMs and three field metrics. For comparison, correlation analysis was also conducted between percent cropland and the three field metrics. The results showed that statistics extracted for the entire watershed correlated better with response variables than statistics extracted from the AOIs. Furthermore, the top performing VPMs explained more variation than did cropland fraction, suggesting that VPMs contain relevant dynamic information related to climate and/or land use management. Optimum VPM predictors for ‘TotN’ were rate of senescence and maximum season NDVI (R2 ~ 0.6, entire watershed), for ‘PrpSensF’ the optimum predictors were rate of greenup and average growing season NDVI (R2 ~ 0.38, entire watershed), and for ‘InvFmRch’ the optimum predictors were average growing season
2 NDVI and peak season NDVI (R2 ~ 0.35, entire watershed). Corresponding R2 values for percent cropland and the three target variables were ~ 0.34 for ‘TotN’, < 0.01 for ‘PrpSensF’, and ~ 0.02 for ‘InvFmRch’.
Watershed Size In the second project (Section 5.0), the effect of watershed size on the relationship between landscape stressors and biological and water chemistry indicators was investigated in depth. Analysis focused on two questions: (1) do the ecological measurements demonstrate dependence on watershed size and, (2) does watershed size affect the relationship between watershed-level VPM statistics and the target values? Statistics were extracted for the entire watershed for all watersheds, and bivariate correlation analysis was conducted between the VPMs and the three field metrics and between percent cropland and the three field metrics. For question one, the results showed that each field metric demonstrated some dependence on watershed size. For question two, the results showed that the strength of relationship for total nitrogen and proportion sensitive fish taxa improved with increasing watershed size, while the strength of relationship for invertebrate family-level richness remained relatively constant across watershed sizes. A secondary analysis found that longer temporal window averages of top predicting VPMs performed better than shorter temporal window averages. Optimum VPM predictors for ‘TotN’ were rate of senescence and date of maximum NDVI (R2 ~ 0. 5); for ‘PrpSensF’ the optimum predictors were average growing season NDVI and rate of green-up (R2 ~ 0.15); and for ‘InvFmRch’ the optimum predictors were average growing season NDVI and peak season NDVI (R2 ~ 0.3). Corresponding R2 values for percent cropland and the three target variables were ~ 0. 4 for ‘TotN’, ~ 0.05 for ‘PrpSensF’, and < 0.04 for ‘InvFmRch’.
Regression Tree Analysis and Classification Model Development The third project (Section 6.0) used classification and regression tree analysis (RTA) to (1) identify landscape predictor variables (static and dynamic stressors) across multiple scales (spatial and temporal) that reliably model aquatic response variables, and (2) develop a classification scheme for watershed vulnerability. To identify suitable landscape predicator variables, regression tree (RT) models were developed to examine (a) only static predictors, (b) a combination of both static and dynamic predictors, and (c) only dynamic predictors. In general, model R2 values were higher using the dynamic predictors than the static predicators. R2 values for models developed using both sets of predictors performed either comparably to or better than those using the dynamic predictor set alone. Examining global model results for ‘TotN’, initial splits using the static predictors most often were based on percent cropland and soil K-factor (R2 ~ 0.39); initial splits using the combined predictors most often were percent cropland and rate of senescence (R2 ~ 0.47); and initial splits using the dynamic predictors most often were rate of senescence and NDVI at green-up onset (R2 ~ 0.48). For ‘PrpSensF’, initial splits using the static predictors most often were based on ecoregion and soil K-factor (R2 ~ 0.57); initial splits using the combined predictors most often were also ecoregion and soil K- factor (R2 ~ 0.62); and initial splits using the dynamic predictors most often were longer
3 temporal window averages for NDVI at greenup onset and rate of greenup (R2 ~ 0.56). For ‘InvFmRch’, initial and secondary splits using the static predictors most often were based on ecoregion (R2 ~ 0.38); initial splits using the combined predictors most often were based on ecoregion, 5-year average maximum NDVI value, and 3-year average date of dormancy (R2 ~ 0.59); and initial splits using the dynamic predictors most often were based on various temporal windows for average growing season NDVI, average NDVI at dormancy onset, and average maximum NDVI (R2 ~ 0.56). Upon examination or random data subsets to assess the robustness of the results, tree topology (structure and composition) varied greatly in many cases due to the large number of predictor variables. Three ecoregions were selected for RT modeling to examine how model results are affected when applied at a different spatial scale. The ecoregions were the Central Irregular Plains, the Western Corn Belt Plains, and the Ozark Highlands. Results generally supported the use of global models, while at the same time indicating the need for more locally determined models in particular situations. Regarding model preference for short-term or long-term average VPM values, results showed that longer temporal window averages produced slightly higher R2 than shorter temporal window averages when ‘TotN’ and ‘PrpSensF’ were considered. For ‘InvFmRch’, there was no clear preference for temporal window size. In an effort to derive a robust model suitable for use in classification, trees were grown using only the top performing dynamic predictors. Using these restricted variable sets, the largest common tree form observed across different data subset evaluations was identified as the final model. In terms of performance, the resultant robust models were 70- 80 percent as effective as their unconstrained counterparts (‘TotN’ R2 ~ 0.42, ‘PrpSensF’ R2 ~ 0.39, ‘InvFmRch’ R2 ~ 0.48).
Model Implementation This work concludes with an application of the ‘PrpSensF’ model to all stream points within a watershed in southeastern Kansas (Section 7.0). The application provides an example of a stream trace map in which each point in the stream network within the watershed is “predicted” using the final model from the regression tree analysis.
Conclusions VPMs are dynamic landscape predictors that explained 30-50% of the variance in the three response variables. VPMs are generally better at predicting the response variables than land use/land cover and other commonly used landscape predictors. Although VPMs are correlated with land cover (e.g., percent cropland), they contain additional information such as vegetation condition and cropping practice. It is this information that may contribute to the stronger predictor/response relationships. The strength of the predictor/response relationship was stronger when the entire watershed was considered. The strength of the relationship was often stronger for larger watersheds. Using regression tree modeling, VPMs can be used to rank order (classify) watershed response conditions.
4 2.0 Introduction The assessment of vulnerability and the establishment of watershed restoration priorities are major goals of ecological risk assessment. Ecological risk assessments employ watershed and landscape classification schemes at different temporal and spatial scales to extrapolate within and among regions and to provide a framework for watershed management. Watershed classification schemes can embody structural and functional characteristics of a classification strategy as well as pragmatic aspects of implementation. It is highly desirable that the classification system is accurate and effective in predicting biological impairment, while providing a basis for recommending rehabilitation. Ideally, the model should be equally applicable for large and small watersheds and for environmentally diverse regions of the country. A “tiered” watershed classification system can provide flexible categories of impairment from less desirable tiers to higher quality tiers. This would enable environmental managers to establish priorities for preventing vulnerable systems from dropping to a lower tier and for selecting watersheds for rehabilitation and transfer to a higher tier. In this report, work is described for the implementation of a geographically independent, tiered classification system capable of predicting biotic impairments and identifying watersheds for rehabilitation. An a posteriori approach was used to empirically develop the system. The classification system was built using current geospatial and remote sensing data to derive landscape indicators. Field survey data for wadeable streams and non-wadeable rivers was used to derive watershed condition indicators. Initial statistical tests examined issues related to spatial and temporal scales. Results from these tests were used to guide classification model development. A decision tree methodology was used to develop the watershed classification model. An application of a final model from the decision tree analysis is demonstrated using a stream trace map, in which each point in the stream network within the watershed is predicted. This work was conducted under EPA Cooperative Agreement RD-83059701.
2.1 Background 2.1.1 Relationship of landscapes to watershed ecology Landscapes play an important role in determining the ecological health of ecosystems. The pattern and composition of elements within the landscape influence important environmental attributes such as water quality. Kepner et al. (1995) summarized potential elements of landscape analyses in the context of integrated ecological assessments and noted the importance of relating individual resources (e.g., biotic condition of streams) to landscape composition and pattern at different scales. Thus, landscape characterization and selection of appropriate landscape indicators becomes an essential component for determining the status and trends in the condition of ecological resources (Norton and Slonecker 1990). Previous work has demonstrated that water quality is influenced by landscape composition and pattern (Sponseller et al. 2001; Herlihy and Johnson 1998; Hunsaker and Levine 1995; Hunsaker et al. 1992). More specifically, landscape indicators have been examined to determine their relative contribution to nonpoint source pollution (Whistler 1996; Haith 1976). Previous work in EPA Region 7 has shown that the total cropland fraction within watersheds is correlated with chemical water quality measurements (Meador 1990) and stream insect diversity (Anderson 1990). Typically,
5 these studies have been limited in scope to small and medium watersheds (<10,000 hectares) and have utilized land use and land cover information derived from aerial photographs or satellite imagery. Recognizing that watersheds possess a “baseline” level of vulnerability as a function of their relatively static characteristics (e.g., basin morphology, geology, and climate), it is dynamic characteristics (e.g., changes in land management, climate, land use/cover, landscape heterogeneity or fragmentation, population density) that present the greatest potential for significant increases or decreases watershed impairment or vulnerability. Changes in dynamic variables are generally poorly modeled, if at all, and often represent no more than a static snapshot in time. Yet they form a key component to water quality when other factors are held constant. Sponseller et al. (2001), Jones et al. (2001) and Detenbeck et al. (2000) identified this issue and recommended that future watershed studies incorporate the unique ability of time series remotely sensed imagery to provide information regarding changes in landscape structure, composition, and land surface condition.
2.1.2 NDVI and phenology metrics as dynamic landscape indicators Vegetation vigor is a reflection of many environmental conditions including soil fertility, nutrient availability, and temperature and precipitation during the growing season. In addition, seasonal vegetation growth patterns (e.g., time and rate of spring green-up) are an indication of plant form (e.g., grass or tree). Growth patterns may also be an indication of plant management (i.e., agriculture). The systematic and frequent acquisition of detailed information reflecting vegetation photosynthetic activity and growth has been possible since 1989 with the advent of the Advanced Very High Resolution Radiometer (AVHRR) carried onboard NOAA satellites. Using the raw AVHRR data, a very useful measure of vegetation can be calculated. The normalized difference vegetation index (NDVI) is a well-established and commonly used vegetation index that is roughly correlated with green plant biomass and vegetation cover (Box et al. 1989; Tucker 1979). The NDVI is based on the relative reflectance values in the red and near infrared (NIR) wavelengths: NDVI = (NIR - Red)/(NIR + Red). The amount of red solar energy reflected by vegetation cover depends primarily and inversely on chlorophyll content, whereas the amount of near infrared energy reflected by vegetation varies with the amount and condition of green biomass, leaf tissue structure, and water content (Jensen 1996). Jones et al. (1996) evaluated the potential of NDVI to assess watershed health and hypothesized that it could indicate losses in productivity, increased erosion, and losses of the buffer capacity along riparian corridors. They suggested examining NDVI patterns and change, as well as comparing observed versus expected NDVI based on soils, topography, vegetation and climate. Whistler (1996) explored NDVI values derived from Landsat Multi-Spectral Scanner (MSS) imagery and hypothesized that average watershed NDVI would have a stronger relationship with water chemistry measures than would watershed cropland proportion derived from the same imagery. He found that relationships between NDVI and selected water quality parameters were stronger than relationships to cropland proportion in most cases. Vegetation phenological metrics (VPMs) are derived from time-series NDVI data. Reed et al. (1994) defined twelve Vegetation Phenological Metrics (VPMs) using
6 AVHRR NDVI bi-weekly composites that can be categorized into three groups: (1) temporal (based on the timing of a phenological event); (2) NDVI-based (the NDVI value at the time of a phenological event); and (3) metrics derived from time-series characteristics. Vegetation phenological events such as emergence, maturity, and senescence are important for assessing the condition of agricultural vegetation (Lee 1999; Samson 1993). Vegetation phenological metrics (VPMs) have been used to assess crop condition and potential yield (Lee 1999), characterize crop phenological variability (Reed et al. 1994), separate grasslands by photosynthetic pathway (C3 or C4) (Tieszen et al. 1997), and map land use/land cover (Loveland et al. 1995). In the EPA Region 7 REMAP (Martinko et al. 2000), correlation and regression analyses were used to find statistical relationships between the field data and the landscape components and NDVI data. Major conclusions derived from this work were (1) NDVI and VPMs better explain variation in stream water quality conditions than either land use/land cover composition or pattern, (2) knowledge of the general land use/land cover setting within the watersheds is necessary to interpret the relationships, (3) stratifying the watersheds by ecoregion yielded stronger relationships between the field data and landscape data (Griffith et al. 2002; Griffith 2000; Whistler 1996). While previous research suggests the potential of NDVI and VPMs as landscape indicators, their application in ecological modeling has not been fully explored. Thus the development of a 15-year (1989-2003) database of NDVI and VPMs is fundamental to this study. Its use in various bivariate analysis and decision tree analysis represents a unique approach to identifying dynamic landscape indicators, modeling watershed impairment, and implementing a watershed classification.
2.1.3 Traditional geospatial datasets used as static landscape indicators Utilizing only watershed vegetation greenness and phenology presents an incomplete representation of factors in the assessment and classification of watershed vulnerability. Numerous contemporary studies have used slow-varying landscape characterizations, such as land cover, landscape heterogeneity/fragmentation, and human population, as predictors of stream/watershed condition. However, because these data are infrequently updated, these landscape predictors present functionally static descriptions. King et al. (2005) examined the linkage of watershed land cover to nitrate-N concentrations and macroinvertebrate-assemblage composition and found the cropland fraction correlated with both response indicators. Mallin et al. (2000) studied the effect of human development on bacteriological water quality and found that fecal coliform abundance was significantly correlated to watershed population, as well as percent watershed impervious surface. The level of land cover fragmentation within a watershed has been linked to water quality measures (Jones et al. 2001; Jones et al. 1996). In the present study, landscape heterogeneity/fragmentation is defined quite differently. Rather than quantifying watershed fragmentation using patch density, diversity, fractal dimension, or shape, watershed fragmentation is quantified using the spatial standard deviation for the NDVI and VPM values. For population density, the study uses the LandScan Dataset (Dobson et al. 2000) as an indicator variable for watershed vulnerability. LandScan represents a significant advance over previous measures of population density computed from census data in that
7 census counts are distributed to cells based on probability coefficients which, in turn, were based on road proximity, slope, land cover, and nighttime lights.
2.1.4 Environmental response indicators An environmental response (ecological) indicator is a numerical value derived from actual measurement that reflects an environmental attribute. It can be a measure, an index, or a model that characterizes an ecosystem or one of its critical components. An indicator may reflect biological, chemical or physical attributes of ecological condition (Jackson et al. 2000). In general, an indicator is selected to meet four criteria: (1) it will relate to an important ecological condition; (2) it will be feasible and practical to collect; (3) it will exhibit a variability linked to environmental stressors with a high signal-to- noise ratio; and (4) it will provide information characterizing relative ecological condition as acceptable, marginal, and unacceptable. As originally proposed, model development and watershed classification was to utilize an Index of Biotic Integrity (IBI) as the primary environmental response indicator. An IBI represents a composite of multiple measured parameters, standardized by various criteria. During the early stages of this project, however, use of an IBI was rejected in favor of using the individual metrics. There were three primary reasons for abandoning development of an IBI. First, IBIs are specific to ecoregions (or even smaller geographic areas). Development of a region-wide index useful across multiple ecoregions is problematic. Second, the calculation of an IBI reduces all field variable information into a single value. Such a reduction results in loss of potentially significant variability that can only be gleaned through analysis of individual metrics. Third, the process of combining, standardizing, and filtering records from the disparate field databases severely narrowed the number variables available to construct an IBI. The response indicators developed in the study were selected based on discussion with regional aquatic experts after the field data had been combined, standardized, and filtered. The indicators represent three categories of ecological response: water chemistry measures, fish population metrics, and benthic macroinvertebrate population metrics.
2.1.5 Spatial and temporal scaling factors Landscapes are spatially heterogeneous areas in which the structure and function of both the stressor and the response indicators are both spatially and temporally scale dependent (Turner et al. 1989; Hunsaker and Levine 1995). Therefore, to quantify either type of indicator requires that scale be considered in their measurement. The response indicators used in this study represent large-scale integrators of ecological condition and point to the development and use of spatially large-scale landscapes, such as the watershed immediately above the sample point. However, a response indicator may exhibit a strong correlation between geographic proximity and landscape conditions. To account for this, studies have employed neighborhood buffers about a stream reach above a sample point or used inverse-distance weighting to represent the decaying effects of spatial proximity (King et al. 2005). This study develops a novel approach to assess the effect of geographic proximity on the stressor/response relationship that utilizes terrain information to delineate areas-of-influence (AOI). Ecological processes are temporally dependent and occur in response to changing environmental conditions over time. Two potential time-dependent complications should
8 be considered when examining the relationships between spatially integrated stressor variables and point-measured response variables. First, an environmental response indicator may not exhibit an immediate response, i.e., it may lag, in reaction to change in a stressor indicator (Kenkel 1996). Such a lag might represent the time needed to transport the stressor effect to the point location of the measured response. Second, and related to lag, there is the possibility that peak manifestation of the stressor effect at the response measurement site is driven by longer-term, cumulative interannual processes rather than by single year events (Kratz et al. 2003). To examine these lag effects, values for candidate VPM stressors are computed that either include or exclude values of the stressor concurrent to the sampling year of the response variable. To examine cumulative interannual effects, 1- to 5-year averages for the VPM stressors (both including and excluding the response variable sampling year) are computed.
2.2 Research Objectives 2.2.1 Objective 1. Develop and select landscape indicators. The fundamental first step in this work is to evaluate the suitability of NDVI and NDVI-derived VPMs as landscape indicators of biological and water quality conditions. Because information represented by NDVI integrates both land cover and biophysical conditions, NDVI can be useful for examining landscape-water quality-biological condition relationships. Of possibly greater utility are the phenological metrics derived from NDVI, which show significant potential as landscape indicators of watershed conditions. Although previous work by Whistler (1996) demonstrated the potential of using NDVI as a landscape indicator of water quality, the use of VPMs for applications in water quality monitoring has yet to be fully explored. The findings of Martinko et al. (2001) and Griffith (2000) support inclusion of VPMs as landscape indicators used for regional and national level monitoring of watershed conditions. To meet Objective 1, the following research questions are addressed:
Research Question 1.1: Are dynamic watershed landscape stressor indicators, such as NDVI and vegetation phenology metrics, strongly related to water quality and biological response indicators?
Research Question 1.2: Are static watershed landscape stressor indicators, such as land cover, human population and landscape heterogeneity/fragmentation, strongly related to water quality and biological response indicators?
2.2.2 Objective 2. Develop a watershed classification model. Using an a posteriori approach to empirically develop a watershed classification scheme involves exploring and testing functional attributes of the classification model. For example, proximity of the landscape indicator to the response sample site can be important to defining the spatial grain needed to detect the stressor/response relationship. Testing the strength of stressor/ response relationships across various geographic extents can help determine the optimal geographic scale to use for model development and application. Examining the strength of stressor/response relationships across various temporal windows can reveal the scale of time-varying ecological processes. To achieve Objective 2, the following research questions are addressed:
9
Research Question 2.1: How does the strength of the stressor/response relationship vary as additional upstream landscape area is included to calculate the landscape indicators?
Research Question 2.2: Do response indicators vary with watershed size?
Research Question 2.3: Does the strength of the stressor/response relationship vary with size of the stream/river watershed?
Research Question 2.4: Does the strength of model prediction for an ecological response favor using (1) only static indicators, (2) only dynamic indicators, or (3) a combination of both?
Research Question 2.5: Are global model predictions stronger, weaker, or comparable to ecoregion-specific model predictions?
2.2.3 Objective 3. Apply the model for watershed monitoring. Because the AVHRR biweekly composite dataset extends from 1989-present in a nearly continuous sequence, estimates of past watershed vulnerability conditions can be modeled using past data, monitored annually, and compared to present-day estimates to determine possible increases or decreases in vulnerability. As a result, the classification model has the potential to reveal to watershed managers areas that are increasing in impairment risk, requiring prioritization for restoration activities or intensive field sampling. Conversely, the model will also identify watersheds with decreasing vulnerability risk that can be assigned or downgraded to a lower priority for restoration and active management. For example, Jones et al. (1997) found that change in NDVI values over a 15-year period in the U.S. Mid-Atlantic states was useful in assessing the relative vulnerability of watersheds to conditions that impact stream water quality. For Objective 3, the following research question is addressed:
Research Question 3.1: Can interannual or directional changes in landscape-scale indicators (e.g., greenness, phenology) reliably forecast degradation of, or improvement in, conditions in the watershed contributing to watershed impairment?
In Results – Section 4.0, the focus is to provide answers to research questions 1.1 and 2.1. Summary statistics are extracted from the VPM dataset using a series of nested and increasingly larger watershed subsets (AOIs) upstream from the sample point. Bivariate correlation is used to (1) identify VPMs suitable for use as landscape indicators, and (2) identify any stressor/response AOI size preference. In Results – Section 5.0, the focus is to provide answers to research questions 1.1, 2.2, and 2.4. Summary statistics are extracted from the VPM dataset for the entire watershed upstream from the sample point. Bivariate analysis is used to (1) determine whether ecological response variables themselves vary by watershed size, (2) identify
10 whether stressor/response relationships vary by watershed size, and (3) identify optimum VPM landscape indicators. In Results – Section 6.0, the focus is to provide answers to research questions 2.4, 2.5, and 3.1. Summary statistics are extracted from both the static and dynamic datasets for the entire watershed upstream from the sample point. Decision tree analysis is used to (1) investigate global and ecoregion model performance, and (2) define a general model for each of the ecological response variables. Finally, in Results – Section 7.0, a general model is applied to an entire stream network within a watershed to demonstrate a broad-scale application of such a model.
2.3 References Anderson, T.M. 1990. The relationship between basin cultivation and stream insect composition in small agricultural streams in Kansas. M.S. Thesis, University of Kansas, Lawrence.
Box, E., B. Holben, and V. Kalb. 1989. Accuracy of the AVHRR vegetation index as a predictor of biomass, primary productivity and net CO2 flux. Vegetatio 80:71-89.
Detenbeck N.E., Batterman S.L., Brady V.J., Brazner J.C., Snarski V.M., Taylor D.L. and Thompson J.A. 2000. A test of watershed classification systems for ecological risk assessment.
Dobson, J. E., E. A. Bright, P. R. Coleman, R.C. Durfee, B. A. Worley. 2000. “LandScan: A Global Population Database for Estimating Populations at Risk,” Photogrammetric Engineering & Remote Sensing (inc. front cover of journal) 66( 7):849- 857.
Griffith, J.A., E.A. Martinko, J.L. Whistler, and K.P. Price. 2002. Preliminary comparison of landscape pattern-Normalized Difference Vegetation Index (NDVI) relationships to Central Plains stream conditions." Journal of Environmental Quality. Vol. 31, No. 3, pp. 846_859.
Griffith, J. 2000. Interrelationships among landscapes, NDVI and stream water quality in the U.S. Central Plains. PhD. Dissertation, Department of Geography. University of Kansas. Lawrence, KS. 222 pp.
Haith, D.A. 1976. Land use and water quality in New York rivers. Journal of Environmental Engineering. ASCE 102:1-15.
Herlihy, A., J. Stoddard and C. Johnson. 1998. The relationship between stream chemistry and watershed land cover data in the Mid-Atlantic Region. Water, Air, and Soil Pollution 105(½):377-386.
Hunsaker, C. T., and D. A. Levine. 1995. Hierarchical approaches to the study of water quality in rivers. BioScience 45: 193–203.
11 Hunsaker, C.T., D.A. Levine, S.P. Timmins, B.L. Jackson, and R.V. O'Neill. 1992. Landscape characterization for assessing regional water quality. In: D.H. McKenzie, D.E. Hyatt, and V.J. McDonald (eds.), Ecological Indicators. Pp. 997-1008. Elsevier Appl. Sci., New York.
Jackson, Laura E., Janis C. Kurtz, and William S. Fisher, eds. 2000. Evaluation Guidelines for Ecological Indicators. EPA/620/R-99/005. U.S. Environmental Protection Agency, Office of Research and Development, Research Triangle Park, NC. 107 p.
Jensen, J. 1996. Introductory Digital Image Processing. Prentice Hall, Englewood Cliffs, NJ. 316 pp.
Jones, K.B., Neale, A.C., Nash, M.S., VanRemortel, R.D., Wickham, J.D., Riitters, K.H., and R.V. O'Neill. 2001. Predicting nutrient and sediment loadings to streams from landscape metrics: a multiple watershed study from the United States mid-Atlantic region. Landscape Ecology. 6:301-312.
Jones, K.B., Riitters, K.H., Wickham, J.D., Tankersley, R.D., O'Neill, R.V., Chaloud, D.J., Smith, E.R., and Neale, A.C. 1997. An Ecological Assessment of the United States Mid-Atlantic Region: A Landscape Atlas. Publication No. EPA/600/R-97/130, Office of Research and Development, US Environmental Protection Agency, Washington, D.C.
Jones, K.B., J. Walker, K. Riitters, J. Wickham, and C. Nicoll. 1996. Indicators of landscape integrity. Pages 155-168. In: J. Walker and D. Reuter, eds. Indicators of Catchment Health. CSIRO Publishing, Melbourne, Australia. 178 pp.
Kenkel, N.C. 1996. Environmental persistence and the structure/composition of northern prairie marshes. Coenoses 11: 137-142.
Kepner, W.G., K.B. Jones, D.J. Chaloud, J.D. Wickham, K.H. Ritters, and R.V. O'Neill. 1995. Mid-Atlantic landscape indicators project plan. EPA/620/R-95/003, U.S. Environmental Protection Agency, Office of Research and Development, Research Triangle Park, NC.
King, R. S., M. E. Baker, D. F. Whigham, D. E. Weller, T. E. Jordan, P. F. Kazyak, and M. K. Hurd. 2005. Spatial considerations for linking watershed land cover to ecological indicators in streams. Ecological Applications 15:137-153.
Kratz T.K.; Deegan L.A.; Harmon M.E.; Lauenroth W.K. 2003. Ecological variability in space and time: Insights gained from the US LTER program. BioScience, Volume 53(1), pp. 57-67.
Lee, R. 1999. Modeling corn yields in Iowa using time-series analysis of AVHRR data and vegetation phenological metrics. PhD. Dissertation. Department of Geography. University of Kansas. 164 pp.
12 Loveland, T.R., Merchant, J.W., Brown, J.F., Ohlen, D.O., Reed, B.C., Olson, P., and Hutchinson, J. 1995, Seasonal land-cover regions of the United States, Annals of the Association of American Geographers, 85(2): 339-355.
Mallin, M. A., K. E. Williams, E. C. Esham, and R. P. Lowe. 2000. Effect of human development on bacteriological water quality in coastal watersheds. Ecological Applications 10 (4): 1047-1056.
Martinko, E.A., J.L. Whistler, F. deNoyelles, Jr., J.A. Griffith, D. Peterson. 2001. EPA Region VII R-EMAP Project: Landscape Analysis and Characterization to Support Regional Environmental Assessment (LACRA). Final Report to US EPA Region VII, EPA Assistance Agreement #CR825877-01-0, Lawrence, KS, 109 pp.
Meador, S.S. 1990. A GIS assessment of landscape/water quality relationships in small Kansas streams impacted by rural nonpoint source pollution. M.S. Thesis, University of Kansas, Lawrence.
Norton, D.J. and E.T. Slonecker. 1990. The ecological geography of EMAP. GeoInfo Systems. 1:33-43.
Reed, B.C., Brown, J.F., VanderZee, D., Loveland, T.R., Merchant, J.W., and Ohlen, D.O. 1994. Measuring phenological variability from satellite imagery. Journal of Vegetation Science 5:703-714.
Samson, S.A. 1993. Two indices to characterize temporal patterns in the spectral response of vegetation. Photogrammetric Engineering and Remote Sensing 59(4):511- 517.
Sponseller, R.A., Benfield, E.F., and Valett, H.M. 2001. Relationships between land use, spatial scale, and stream macroinvertebrate communities. Freshwater Biology 46:1409- 1424.
Tieszen L.L., Reed, B.C., Bliss, N.B., Wylie, B.K., and DeJong, D.D. 1997. NDVI C3 and C4 production and distributions in Great Plains grassland cover classes. Ecological Applications 7:59-78.
Tucker, C.J. 1979. Red and photographic infrared linear combinations for monitoring vegetation. Remote Sensing of Environment 8:127-150.
Turner, M., R. O’Neill, R. Gardner, B. Milne. 1989. Effects of changing spatial scale on the analysis of landscape pattern. Landscape Ecology 3:153-162.
Whistler, J. 1996. A phenological approach to land cover characterization using Landsat MSS data for analysis of nonpoint source pollution. KARS Report No. 96-1. Kansas Applied Remote Sensing Program, University of Kansas, Lawrence, KS. 51 pp.
13
3.0 Data and Methods
3.1 Study area description This study uses existing and new data from field sample collection sites within EPA Region 7; consequently our study area is focused primarily within the states Iowa, Kansas, Missouri and Nebraska. Headwaters for some sample point watersheds stretch to the Rocky Mountains and the continental divide, so landscape datasets include this area as well. In general, the study area straddles two major ecological regions of North America: the Great Plains and the Eastern Temperate Forest. Commonly perceived as a homogenous area, the landscapes of Nebraska, Iowa, Kansas and Missouri are surprisingly varied. Native vegetation consists of shortgrass prairie in westernmost Kansas and Nebraska, tallgrass and mixed-grass prairie in the Nebraska Sand Hills and central Kansas, a mosaic of bluestem prairie and oak-hickory forest in eastern Kansas and northern Missouri, and dense oak-hickory forests in the Ozark Highlands. The central human transformation of the Great Plains region has been conversion of grassland to cropland. Currently, 90% of the area is in farms or ranches and 75% of the land is in cultivation (Riebsame 1990). A large portion of the nation’s wheat belt is located in east-central Kansas and Nebraska and an even larger portion of its’ corn belt spreads through Iowa and eastern Nebraska. Geomorphically, most of the four state region lies within the Interior Plains (Central Lowland and Great Plains province) with much of southern Missouri lying in the Interior Highlands (Ozark Plateau). Area geology consists of limestones and shales in central and eastern Kansas originating from shallow Paleozoic seas. The Nebraskan and Kansan glaciations deposited glacial drift across northern Missouri, eastern Nebraska, and northeastern Kansas. The Precambrian strata of the Ozark Uplands remained a non- glaciated area with steeper and more rugged terrain. Topographically, therefore, much of the region consists of gently rolling hills dissected by the flat floodplains of the Platte, Kansas, and Missouri Rivers, with the major exception being the hilly Ozark Plateau. Two soil orders comprise much of the region; mollisols and ultisols. Mollisols are the result of grassland ecosystems and have a characteristic thick, dark surface horizon. The relatively fertile mollisols occur throughout the region, except for southern Missouri where ultisols are common. Ultisols are leached, acid forest soils with relatively low fertility and are typical for the Ozark Highlands of Missouri. Climatically, the region is typical mid-latitude continental, but has a strong west- to-east precipitation gradient due to the influence of the Gulf of Mexico. Annual precipitation in the semi-arid High Plains of eastern Colorado and western Kansas ranges from 25 – 45 cm. In the Central Plains of Kansas and Nebraska, precipitation ranges from 50 – 75 cm. Across Iowa precipitation ranges 70 – 95 cm, while in Missouri the range is 90 – 125 cm.
3.2 Stream quality indicators (response/dependent variables) The number of sample sites for which stream quality indicator data were collected varied both spatially and temporally across the region (Tables 3-1 and 3-2). Spatially, sample sites were concentrated in ecoregions that are predominant in the EPA Region 7 study area (Figure 3-1). Of the eighteen ecoregions occurring within the study area,
14 seven ecoregions contain the majority of the sample sites (89.6% of chemistry sites; 90% of fish sites; 90% of benthic macroinvertebrate sites). Temporally, data-rich years correspond to the 1994-1995 and 2000-2003 REMAP programs. The 2003 fish and macroinvertebrate data primarily consist of both REMAP and the river site data collected for this study.
3.2.1 Existing data The stream quality indicator database consists of data for water chemistry, benthic macroinvertebrates, and fish. For wadeable streams, data were assembled from a number of independent field datasets provided to the Central Plains Center for BioAssessment by several cooperating agencies and research groups (Table 3-3). The heterogeneity of the data—types of information supplied, methods used to obtain the original data, and data formats—required considerable processing and filtering to yield a usable, standardized compilation. Separate tables were prepared for each response variable because relatively few sites in our region have been assessed for all three data types in the same year (<25% of records).
3.2.2 New Data For larger streams and rivers with little existing data, new data were collected. A sampling campaign was implemented for 40 sample sites on 34 rivers during a 10-12 week period in the spring and summer of 2003 (Table 3-4 and Figure 3-2). Data were sampled in compliance with the American National Standards (ANSI/ASQC E4-2004), Specifications and Guidelines for Environmental Data Collection and Environmental Technology Programs (see Appendix A, Standard Operating Procedure for the Sampling of Water Quality, Benthic Invertebrates, and Fish). Sampling locations were recorded using a Garmin Legend handheld Global Positioning System (GPS) unit. GPS coordinates (latitude and longitude in degree minutes) were recorded at each river launch site. Additional coordinates were obtained if the actual sampling locations were a significant distance (> 1.0 km) from the launch site, or significantly apart from one another. Benthic macroinvertebrate samples were taken from rock substrates, sand/silt, and/or wood snags. Sampling equipment included a mini-Ponar Grab (for muddy, sandy sediments), a Ekman Grab (for silty sediments), a Ellis-Rutter box sampler (for cobble substrates), a Sweep Net (for gravel substrates), and a DTH snag sampler. Samples were preserved in-field using 10% formalin and phloxine-B stain. Fish samples were collected by electroshocking using a Smith-Root 5.0 GPP Electrofisher System and seining. Sampling using electroshocking was performed in a downstream direction at roughly the same velocity as the current, focusing on shorelines, slackwaters, and snag habitats most likely to harbor large concentrations of fish species. Four separate ten-minute sampling runs were conducted along representative reaches above and below a staging point. Seining was used in shallow river reaches where the electroshocking boat could not operate. Four separate seine hauls were conducted along representative reaches above and below a staging point, in a variety of habitats such as pools, riffles, and runs wherever possible. Samples were preserved in-field using 10% formalin.
15 Benthic macroinvertebrate and fish samples were sorted and counted. Macroinvertebrate collection data were identified to family and entered into the database. Fish collection data were identified to species and entered into the database.
3.2.3 Water chemistry The water chemistry dataset is based on 13,404 samples collected from 1,294 sites between 1994 and 2003. In general, the water chemistry data required only simple data manipulations to create a standardized database. For example, values for total-N were reported by some agencies based on direct measurement; others reported values for total- N based on the addition of constitute components. The latter values were summed to report total-N. The following water quality variables were initially compiled for this study.
1) Total Nitrogen 2) Total phosphorous (total-P)* 3) Turbidity*
Variables marked with ‘*’ were dropped from the watershed analysis. See text for explanation.
3.2.4 Benthic macroinvertebrates The macroinvertebrate dataset is based on 1226 sampling events conducted at 709 sites between 1994 and 2003. Macroinvertebrate data required substantial processing to obtain standardized values. Taxonomic identification is one area of difficulty. Names for taxa were matched against the Integrated Taxonomic Information System (ITIS) database of valid names (http://www.itis.gov/). For taxa not yet included in ITIS (many aquatic insect species and some genera), we used a supplemental taxon index maintained by the Central Plains Center for BioAssessment. Variation in field methods and reporting also create problems. Some sources provided data separately for subsamples classified by habitat type (pool, riffle, glide/pool, riffle/pool, and overhanging vegetation), whereas others reported data collected from “multiple habitats,” or gave no information on subsample number or type. For this study, we combined all subsamples collected on the same day to obtain an overall list of (standardized) taxa for each sample event. We then used that list to calculate values for taxon richness and related indices for the sampling event. Because sources differed in taxonomic resolution, we also calculated richness at the family-level, along with richness based on the total number of reported taxa. The following indices were initially calculated for each sampling event.
1) Total Taxa Richness: count of all taxa (Family-level Richness = count of families), found at that site on that date. 2) Proportion EPT*: count of all EPT taxa (Ephemeroptera, Plecoptera, and Trichoptera) found at that site on that date divided by total taxa richness. 3) Proportion Sensitive*: count of all sensitive taxa found at that site on that date divided by total taxa richness.
Variables marked with ‘*’ were dropped from the watershed analysis. See text for explanation.
16 Sensitivity was assigned based on the EPA Rapid BioAssessment Protocols for Use in Wadeable Streams and Rivers Appendix B: Regional Tolerance Values. Based on the five geographic regions, taxa were assigned tolerance values on a scale from 0 (extremely sensitive or not tolerant) to 10 (tolerant). We averaged the scores for each taxon, and placed them in three groups: sensitive (0.0 - 3.67), facultative (3.68 – 7.34), and tolerant (7.35 – 11.0).
3.2.5 Fish The fish dataset is based on 1090 sampling events at 655 sites from 1994-2003. Fish data required less processing than the macroinvertebrate data because there is less variation in sampling methods and far fewer taxa. The ITIS database was used to standardize taxon names. Fish identified only to genus, or identified as hybrids, were excluded. In a few cases, subsamples were recorded separately (e.g., from seining and electroshocking). However, in most cases, only one sampling method was used or only combined totals were reported. For this study, we combined subsamples (collected on the same day), to calculate the following indices:
1) Total Taxa Richness: count of all fish species found at that site on that date. 2) Proportion Sensitive*: count of all sensitive species found at that site on that date divided by total taxa richness. 3) Simpson’s Reciprocal Index*: a measure of species diversity that emphasizes the evenness component of diversity. (For the same total number of species, a sample in which the abundances are more nearly equal will have a higher value of 1/D than a sample dominated by one or a few species.) It is calculated as: 1/ D where D = ∑ n(n −1) / N(N −1) and n = total number of organisms of a particular species N = total number of organisms of all species 4) Fisher’s Alpha*: a measure of diversity that emphasizes the richness component of diversity. It is a sample-size-weighted measure of species richness that is particularly suited for cases when procedures may not ensure that all taxa present in the habitat are included in the sample. It is calculated as: S = α ×ln(1+ n /α) where S = total number of all species n = total number of all individuals α = alpha
Variables marked with ‘*’ were dropped from the watershed analysis. See text for explanation.
Sensitivities for fish species were assigned based on sensitivity lists from two sources. The first was the EPA Rapid BioAssessment Protocols for Use in Wadeable Streams and Rivers Appendix C: Tolerance and Trophic Guilds of Selected Fish Species
17 (Barbour, 1999). In this document, fish taxa were assigned tolerance values of I (intolerant or sensitive), M (intermediate), and T (tolerant). The second source was based on information compiled from Handbook of Fishes of Kansas (Cross, 1967) and The Fishes of Missouri (Phlieger, 1975), updated with more recent information from Goldstein and Simon (1999), Simon (1999), and Goldstein and Meador (2004) that is used in EPA EMAP studies (Peck, 2007). If the two documents differed for a taxon, either the more sensitive category or the category for the "corn belt" region was used.
3.2.6 Aggregating and screening sampling events One criterion for data selection was number of records available. Measures that are known to be useful, but which were infrequently recorded were excluded (e.g., chlorophyll A). A second criterion was consistency. Measures that are subject to large error due to variation in field or lab protocols also were excluded (e.g., dissolved O2). In a second stage of pruning, multiple samples collected from the same site on different dates within the same calendar year were aggregated to yield a single value. For the selected water quality variables (total-N, total-P, and turbidity), the median values were used. Most of the median values are based on more than one sample date (range: 1- 52, mean, 4.7). For fish samples, the mean values for a year were used (species richness, proportion sensitive taxa, and two diversity measures). For benthic macroinvertebrate samples, statistics (total and mean taxon richness, proportion EPT taxa, proportion sensitive taxa) from the sample with the highest total taxon richness were used. After the data tables were compiled they were screened for outliers. There were relatively few outliers, most having been removed in earlier stages. Examples of outliers included (1) high total-N values, with sample comments indicating recent cattle presence; (2) low macroinvertebrate richness value at a site following years of higher values, associated with a change in reporting agency (and presumably, the field protocols used). After aggregation and screening, the water chemistry dataset contained 2,684 annual measures (out of 13,404 sampling events), the macroinvertebrate dataset contained 931 annual measures (out of 1226 sampling events), and the fish dataset contained 969 annual measures (out of 1090 sampling events).
3.2.7 Filtering number of response variables The number of response variables was further reduced to facilitate analysis and interpretation. The goal was to focus on the most informative measures from each dataset. Three strategies were used to guide this process. As a first step, knowledge of regional conditions and statistical properties was used to exclude individual measures expected to be less reliable indicators. For the macroinvertebrate dataset, EPT was excluded because the Central Plains fauna includes a number of highly tolerant taxa that are widely distributed. For the fish dataset, alpha diversity would provide a better measure of “true” species richness if there is a strong correlation between the total number of individuals collected in the sample and the number of species. However, in this case, the correlation was relatively weak (R = 0.4), suggesting that the adjustment is not necessary. Measurements of fish abundance across sites appear to be very unreliable, due to variation in sampling microhabitats, differences in methodology among agencies collecting the data, and fish behavior (schooling). The other measure of diversity (1/D) will be similarly affected.
18 As a second step, we examined between-year correlations for each of the measures. Variables that fluctuate greatly on short time scales may be so dominated by noise as to be unusable for watershed analysis. As a means to identify those, we extracted records from each of the three datasets where samples were obtained from the same site in successive years. From these we constructed sets of independent paired comparisons for each variable (Table 3-5). For each dataset, one measure was notably more consistent than the others: Fish species richness, macroinvertebrate total richness, and (for water quality) log-transformed total N. Finally, the three datasets were queried to extract records from sites sampled for water chemistry, fish, and macroinvertebrates in the same year for use in a factor analysis. Factor analysis of the dependent variables was motivated by two concerns. First, that “impairment” as a stream condition is a latent variable, not directly measured by any single, measurable biotic or water quality variable. Second, that with relatively few sites having all three data types available for the same year, the effective sample size for our study would be greatly increased if measures from all datasets can be interpreted as indicators of the same underlying factor or factors. Ideally, all measured variables would load heavily onto a single latent variable (= “impairment”); in the worst case, there would be three latent variables, uniquely associated with each of the independent datasets. In this case, our factor analysis results appear to be intermediate, and reasonably consistent across different combinations of method, number of factors, and rotations. Two roughly equal factors, and a third accounting for about half as much variation as each of those, explain most of the common correlation matrix. Fish richness, percent sensitive fish species, and percent EPT load strongly (+) onto the first factor. Turbidity, and total-P load (+) onto the second axis, while macroinvertebrate richness and percent sensitive fish species load (-). Total-N is the only variable to load strongly (+) onto the third axis. Because this analysis was conducted with the entire dataset, not partitioned by ecoregion, some of the pattern may be due to regional variation. However, the relatively high correlation between turbidity and total-P, and their low correlation with total-N also appears in other (smaller) studies of Midwestern streams and rivers and fits with known properties (most stream N is transported in solution, whereas most stream P is associated with particulates). Preliminary bivariate tests and regression tree analysis was conducted to identify trends between response variables and static and dynamic (at various temporal windows). Results showed that total-P, turbidity, and proportion EPT taxa had poor response to landscape predictor variables and were dropped from further analysis. Because one potential strategy for conducting the watershed analysis is to partition data between “reference” and non-reference sites, we also compared means and distributions for the dependent variables for these groups. For water quality variables, there was no difference between reference and non-reference sites in mean or shape of the distribution. For fish and macroinvertebrates, reference sites had higher mean values and noticeably different dispersions than the non-reference sites. As in the factor analysis, this comparison was made using the entire datasets, so it is possible that these results may partly reflect geographic (ecoregional) factors as well as differences between reference and non-reference conditions.
19
3.3 Landscape indicators (stressor/predictor variables) Predictor (independent) variables consist of multiple landscape metrics derived from various geospatial data sets and act as surrogates for natural conditions and potential stressors in the watershed environment. A total of 235 landscape related variables were acquired and developed for modeling and represent both static (15 variables) and dynamic (220 variables) characteristics within each watershed. Existing data sources were used when they were available and suitable for analysis.
3.3.1 Static Indicators Static characteristics for which statistics were calculated include both natural and anthropogenic properties (Table 3-6). Natural properties included watershed morphology and soil erodibility. Watershed morphology was described using six variables; watershed area, total length of streams and rivers, drainage density, watershed shape, and slope mean and standard deviation. Taken together, these variables roughly express the capability of a watershed to move water and sediments through it. Soil erodibility, and thus potential sediment load, was described by soil K-factor mean and standard deviation. K-factor is a measure of the susceptibility of entire soil column to erosion and the rate of runoff (Wischmeier and Smith, 1978). For example, soils high in clay have low K values because they resist detachment. Coarse textured soils, such as sandy soils, have low K values, because of their low runoff rates, even though these soils are easily detached. Medium textured soils, such as the silt loam soils, have a moderate K values because they are moderately susceptible to detachment and they produce moderate runoff. Soils having a high silt content are the most erodible of all soils. They are easily detached; tend to crust and produce high rates of runoff. Anthropogenic stressors for which statistics were calculated included population density, total road length and road density, and rural land use/land cover. Although these stressors generally vary slowly over time, they are so infrequently updated that their information content is functionally static. Anthropogenic stressors were chosen for their unique contribution in representing human impact, although there is some redundancy in the type of information being represented (e.g. population density and road density). Source data for population density was the latest version (2003) of the LandScan Dataset (Dobson, 2000). Population density was chosen to reflect the concentrated effects of activities related to urbanized areas, such as fertilizing yards, deicing roads, treating wastewater, and the alteration of natural waterways. The data source for the road network was StreetMap USA 2005 (ESRI, 2005). Road density also reflects the alteration of natural waterways, but in a more direct fashion. It was included, however, because it better reflects alteration of rural waterways than population density. Lastly, three fractions of land use and land cover related to rural, non-urbanized, areas were chosen; percent cropland, percent forest, and percent grassland. Source data for land use/land cover was the National Land Cover Database (NLCD) 2001 (Homer et al., 2004). A final static indicator used as a landscape variable was EPA Ecoregion Level III as derived from Omernik (1987). Although ecoregions are not a direct property of landscapes, they delineate large areas based on similar climate, vegetation, topography, hydrology and land use, among other properties. It’s inclusion served two functions.
20 First, ecoregions were used as a stratifying variable for bivariate analysis and regression modeling. Second, it was used as a categorical predictor variable in regression tree analysis, where it may identify regional splits in the data.
3.3.2 Dynamic Indicators - NDVI and VPMs A 15-year (1989-2003) time series of biweekly composite AVHRR 1-km NDVI data for the study area was analyzed. These data provide a measure of vegetation growth and condition over the conterminous United States. The data were obtained from the U.S. Geological Survey (USGS) National Center for Earth Resources Observation and Science (EROS), where all pre-processing of the raw AVHRR imagery was performed. The value of this data set lies not only in the length of the time series, but also the use of standardized image processing procedures to create science quality data. Data processing steps include (1) radiometric calibration to correct for sensor degradation and account for differences between satellite sensors (AVHRR data contributing to the 15- year database were collected from four satellites), (2) atmospheric correction to correct for water vapor/ozone absorption and Rayleigh scattering, and (3) geometric registration to correct for geometric distortion due to off-nadir viewing angles and to precisely register the imagery to a common map projection (Eidenshink, 2006). An NDVI biweekly (14-day) composite is the result of merging multiple daily observations into a single image to form a nearly cloud-free image. The USGS uses the maximum value composting (MVC) method (Holben, 1986). This approach examines on a pixel-by-pixel basis the NDVI values for all imagery in the time period to determine the maximum value (Eidenshink, 2006). There are 26 biweekly periods compiled during a calendar year. Because the actual start date for the biweekly compilations for a calendar year varies by as much as + 7 days (from December 25 to January 8), a standardized period is used to simplify analysis and facilitate comparison between years. Although standardization results in some loss of temporal detail, the loss is out weighed by the previous considerations. Table 3-7 lists the calendar dates associated with each standardized period. For storage efficiency, NDVI data provided by the USGS are scaled to an integer data range of 0 to 200. For our study, the data were rescaled back to their original range of –1.0 to +1.0. Rare instances of missing, or clearly aberrant, data were replaced with linear interpolated values from neighboring periods if these data were available; otherwise historical average values were used. From this time series, the vegetation phenology metrics (VPMs) were calculated (Figure 3-3). Table 3-8 lists the 11 core VPMs calculated for vegetation characterization in EPA Region 7. Figures 3-4 through 3-14 depict the 15-year average for the 11 core VPMs. (Note: Figure 3-15 depicts the proportion cropland, derived from NLCD, per 1km AVHRR pixel and is provided for reference.) Identification of two phenology events, ‘onset of green-up’ (season start) and ‘onset of dormancy’ (season end), is required for estimation of most of the VPMs (Figure 3-3). To facilitate consistent identification of these onset events, the pixel-level NDVI data were subjected to additional conservative smoothing measures that (1) suppressed post-senescence and wintertime variation occurring during the first and last three biweekly periods of each annual series, and (2) truncated single-period downspikes occurring during the remaining interior periods (Wardlow et al., 2006).
21 Onset of green-up and onset of dormancy events were identified by averaging the outputs from the methods documented in Zhang et al. (2003) and Yu et al. (2004). Due to data characteristics unique to AVHRR NDVI and past experience, specific but functionally minor variations of the methods were employed. The two-method average was used because (1) it consistently produced (more so than either of the two individual methods) season start and season end dates that seemed appropriately placed on the NDVI profiles, and (2) averaging the results from the two methods resulted in more stable (i.e., less variable) calculation of the two onset events. Identification of onset date is made in two steps (Zhang et al., 2003). In step one, sequential six-point running slope values for the NDVI time series are computed and used to isolate the first substantial monotonic data segment (i.e., the green-up phase for green-up onset). In step two, a logistic curve is fit to the segment identified in step 1. From the fitted logistic curve, the point of maximum increase in curvature is calculated (Zhang et al., 2003) as well as the point of maximum concavity (Yu et al., 2004). The ‘onset of green-up’ date is then assigned using the average of these two points. The onset of dormancy date is calculated by simply reversing the time series and running the procedure again. Once these two VPMs have been calculated, calculation of the other VPMs is straightforward. Calculation of the 11 core VPMs for all 15 years of NDVI completed construction of the VPM database. For each sampling location, two watershed-level statistics (the spatial average and standard deviation) were extracted from the 1989-2003 VPM database for each of 11 core VPMs. This resulted in 22 watershed-level VPM statistics, each with a 15-point time series. For each sampling event, two sets of 1- through 5-year VPM temporal averages were calculated using this 15-year dataset; one set with aggregation periods ending with the sampling year and one set with aggregation periods ending with the year just prior to the sampling year. The purpose of considering 1- to 5-year aggregates was to allow examination of a range of potentially useful VPM statistics that reflected various proportions of longer-term stability and shorter-term specificity (i.e., longer- versus shorter-term processes). The purpose of considering one set of aggregates that excluded the sample year was to accommodate the uncertainty of the temporal relation between the VPMs and the sample collection date, a condition often exacerbated by the high variability of within-year sampling dates. Calculating the temporal averages expanded the VPM variable pool by a factor of 10, resulting in 220 VPM variables. To gain some insight on the common variance shared by different VPMs, two correlation exercises involving pairwise comparisons of VPM spatial average variables were conducted. Table 3-9 entries were obtained by averaging 15-year (15-point) correlation values across 2,469 sample locations. Table 3-10 entries were obtained by stacking all of the data and computing 37,035-point correlations (15 * 2,469 = 37,035). To examine the spatial underpinnings of these correlations, visually compare the 15-year average VPM maps displayed in Figures 3-4 to 3-14 to one another. The relationships between VPMs varied markedly, and most were not strongly correlated to one another. Based on values in Table 3-9, VPMs exhibiting the largest average correlation magnitude with other VPMs were the “full season” VPMs of growing season length (GL; mean correlation magnitude = 0.38), accumulated growing season NDVI (AC; 0.36), and average growing season NDVI (AV; 0.34). A similar result is found considering the entries of Table 3-10, though here we also find that start (OV), peak (MV), and end (DV)
22 season NDVI values exhibit mean correlation magnitude comparable to the “full season” VPMs. Table 3-11 shows results from a time-series autocorrelation exercise comparing lagged VPM values using 1- to 5-year lags. Entries were obtained by averaging 2,469- point (one point for each sample location) correlation values over all available lagged- year pairings, so that there are 14 pairings with a 1-year lag (89-90, 90-91,…, 02-03), 13 pairings with a 2-year lag (89-91, 90-92,…, 01-03), and so on, ending with 10 pairings with a 5-year lag (89-94, 90-95,…, 98-03). Though values generally decline with increased lag, most of the VPMs exhibit substantial, persistent autocorrelation. Certainly much of the persistent autocorrelation is attributable to spatial variations in land cover between the different sample sites, which, though largely constant over time, have a strong influence on the general shape of site-specific NDVI profiles.
3.4 Synthetic stream network and automated watershed delineation With over 2400 field sampling locations, the task of manually delineating watersheds was impractical. A more objective, and ideally faster, method of watershed delineation was sought. The automated delineation of watersheds from a DEM is not a new procedure, and initially appeared to be a relatively simple task. The process, however, was rapidly complicated by issues relating to irregularities in an existing digital data set (EDNA) we planned to use. This section describes the procedure developed for automated stream and watershed delineation using as input the field-sampled point locations, the 1:100,000 NHD stream network, and a digital elevation model (DEM). Evaluation of EDNA Our intent was to use the Elevational Derivatives for National Applications (EDNA) database for automated watershed delineation (NHDPlus became available in 2006. This work began in 2004). EDNA is available for the entire nation, but after careful evaluation, we deemed EDNA unsuitable for watershed delineation in our study. Two major issues were identified with the EDNA synthetic network. First, many low order streams not well represented, if at all. EDNA used a relatively large flow accumulation threshold value of 5000 cells to start generation of synthetic stream networks. Figure 3-16a compares the National Hydrologic Database (NHD) stream network to the EDNA synthetic network within an 8-digit hydrologic unit code (HUC8). Because of the large threshold value, many first order, and even some second order, streams are not represented in the EDNA synthetic network. This was a critical omission for EDNA since watershed delineation depends on the accurate placement of a sample point on a stream network. Figure 3-16b depicts the synthetic network generated for this study using a lower flow accumulation value of 1500 cells and more closely matches the stream density of the NHD. Second, the positional accuracy of the EDNA synthetic stream network is poor in some locations due to either DEM encoding errors or precision limitations of the 30- meter DEM data. A close-up of this HUC8 in Figure 3-17a shows how the EDNA synthetic stream deviates significantly from the NHD. In this example, the EDNA synthetic network jumps the 8-digit HUC boundary resulting in a watershed delineated on this stream segment that would be grossly inaccurate. Meanwhile, note how our synthetic stream network for this same area closely follows the NHD (Figure 3-17b).
23 3.4.1 Procedure used for automated stream and watershed delineation The problems identified in the EDNA database are primarily due to the coarse resolution of the source DEMs and subsequent lack of detail in areas of low relief. One approach to overcoming these problems is to modify the DEM with vector stream information. This process is commonly referred to as “stream burning” and essentially modifies the original DEM by lowering elevation values concurrent with, and adjacent to the vector data. A methodology developed by Hellweger (1997) was modified to burn the NHD vector stream information into the original DEM. The methodology employs five steps that were implemented in an ArcInfo AML: (1) convert the hydrography vector layer to a grid representation of the stream network, (2) burn the stream grid cells into the DEM, (3) fill any depressions in the DEM to ensure all cells have a flow direction, (4) calculate flow direction and flow accumulation, and (5) create a synthetic network. Use of the NHD for stream burning is not without problems. The two major problems are illustrated in Figure 3-18. The NHD is a digital representation of 30 x 60 minute 1:100,000 topographic quadrangles that were compiled over time. As such, the quadrangles suffer from inconsistent feature representation, especially the hydrology or stream network. Two factors likely explain these observed inconsistencies. First, most rivers and streams delineated on maps are perennial. The natural variation in precipitation across the study area results in differences in apparent drainage density, i.e., in more arid environments there is less representation of hydrologic features, in more humid environments there is more representation of hydrologic features (Figure 3-18b). Secondly, it is also apparent that some differences are due to either a change in mapping specifications, or perhaps a reflection of the differences and subjectivity of two cartographers interpretating hydrography (Figure 3-18a). As a result of the inconsistencies, it was not possible to have a uniform application of the stream burning algorithm throughout the study area.
3.4.2 DEM processing and synthetic stream delineation The DEMs for the study area were processed using the procedure describe on a HUC-by-HUC basis for the 35 4-digit hydrologic unit code (HUC4) units that were contained within, or immediately proximal to, the four-state Region 7 study area. Stream burning and watershed delineation are computationally intensive tasks that required subdividing the four-state study area into manageable processing units. After initial prototyping, we determined HUC4 units were suitable for processing and maintained hydrologically significant boundaries. Large watersheds extending across multiple HUC4 units were created by adding the upstream area from the appropriate adjacent HUC4(s). HUC4 boundaries, compiled from both 1:24,000 and 1:250,000 topographic data, do not always correspond to the 30-m DEM ridgelines derived from 1:24,000 topographic data (Figure 3-19a). To preserve the topographically more accurate 30-m ridgelines, DEM tiles were merged and then clipped using a buffered (10 km) HUC4 unit. Once preprocessing was completed, derivative data was calculated and included flow direction, flow accumulation, and synthetic stream network. The synthetic stream network, or ‘SNET’, was delineated from the output from the ArcInfo FLOWACCUMULATION function. Flow accumulation is defined as the number of upslope cells that flow into each cell. To define a stream network using the flow accumulation values, an accumulation threshold value is selected to determine the
24 beginning of stream delineation. We selected a threshold value of 1500 pixels (1.35 square kilometers) for stream network delineation. This value produced a uniform stream network density that was similar to NHD tiles located in the eastern part of the study area.
3.4.3 Pour point placement and watershed delineation A pour point is defined as the most downstream point in the watershed, and in this study, is synonymous with the field sampling location. A pour point must fall on the synthetic stream network in order to be used for watershed delineation. Because most field sites did not fall on the synthetic stream network (nor the NHD), converting field sites to pour points required a series of automated and manual steps (Figure 3-20). The steps included: 1) automatically snapping watershed pour points to the synthetic stream network; 2) flagging questionable pour point spatial locations (i.e., points that were greater than 120m from a given stream segment or at a confluence); and 3) manually editing the spatial location of flagged points. Approximately 85% of pour points fell within 120m of the synthetic network and were snapped to the synthetic network using the automated approach. Some sample point could not be manually identified as a pour point because of recording error, recording method, GPS readings taken elsewhere, datum conflicts, and incomplete attribute information. Once all pour points for a HUC4 were placed, the ArcInfo WATERSHED function was used to delineate watersheds. A visual comparison of automated watershed delineations and manual delineations show they were comparable (Figure 3-19a and b). In many cases the automated technique provided more detail, and in all cases there were no overlapping boundaries among adjacent watersheds sharing a common boundary.
3.5 Statistical and spatial processing software Software packages used for statistical analysis and modeling were MATLAB Version 7.4 (The MathWorks, 2006), SPSS for Windows Version 15 (SPSS, 2006) and AnswerTree Version 3.1 (SPSS, 2002). ArcInfo 9.0 and ArcGIS 9.0 were used for both vector and raster processing (ESRI, 2005b). ERDAS Imagine 9.0 was used for image processing (Leica Geosystems, 2005). Microsoft Access 2000 (Microsoft, 1999) was used to build and manage the relational database that contained all field data and spatial attribute values.
3.6 References
Barbour, M.T., J. Gerritsen, B.D. Snyder, and J.B. Stribling. 1999. Rapid bioassessment protocols for use in streams and wadeable rivers: periphyton, benthic macroinvertebrates and fish. Second Edition. EPA 841-B-99-002. U.S. Environmental Protection Agency; Office of Water; Washington, D.C.
Cross, F. B. 1967. Handbook of fishes of Kansas. State Biological Survey and University of Kansas Museum of Natural History, Miscellaneous Publication 45, Topeka, KS.
25 Dobson, J. E., E. A. Bright, P. R. Coleman, R.C. Durfee, B. A. Worley. 2000. "LandScan: a global population database for estimating populations at risk," Photogrammetric Engineering & Remote Sensing, 66(7): 849-857.
Eidenshink, J. 2006. A 16-year time series of 1 km AVHRR satellite data of the conterminous United States and Alaska. Photogrammetric Engineering and Remote Sensing, 72(9):1027-1035.
ESRI. 2005a. ESRI Data & Maps: StreetMap 2005. ESRI. Redlands, CA.
ESRI. 2005b. ArcGIS Version 9.0. ESRI. Redlands, CA.
Goldstein, R.M. and T.P. Simon.1999. Toward a united definition of guild structure for feeding ecology of North American freshwater fishes. pp, 123-139 IN T.P. Simon (ed.), Assessing the sustainability and biological integrity of water resources using fish communities. CRC Press, Boca Raton, FL.
Goldstein, R.M. and M.R. Meador. 2004. Comparisons of fish species traits from small streams to large rivers. Trans. Am. Fish. Soc. 133:971-983.
Hellweger, F.L. 1997. AGREE - DEM Surface Reconditioning System, http://www.ce.utexas.edu/prof/maidment/gishydro/ferdi/research/agree/agree.html as of February 2007.
Holben, B.B. 1986. Characteristics of maximum-value composite images from temporal AVHRR data. International Journal of Remote Sensing, 7:1417-1434.
Homer, C. C. Huang, L. Yang, B. Wylie and M. Coan. 2004. Development of a 2001 national landcover database for the United States. Photogrammetric Engineering and Remote Sensing, 70(7):829-840.
Leica Geosystems. 2005. Erdas Imagine 9.0. Leica Geosystems Geospatial Imaging, LLC. Norcross, GA.
Microsoft. 1999. Microsoft Access 2000. Microsoft Corporation. Redmond, WA.
Omernik, J.M. 1987. Ecoregions of the conterminous United States. Map (scale 1:7,500,000). Annals of the Association of American Geographers 77(1):118-125.
Peck, D.V. 2007. Personal communication. Ecologist, Aquatic Monitoring & Bioassessment Branch, Western Ecology Division, US EPA, Corvallis, OR.
Pflieger, W. L. 1975. The fishes of Missouri. Missouri Department of Conservation, Jefferson City, MO. 343 pp.
26 Riebsame, W. 1990. The United States Great Plains. Pages 561-576. In: B. Turner, and W. Meyer, eds. The Earth as Transformed by Human Action. Cambridge University Press, Cambridge, UK.
Simon, T.P. 1999. Assessment of Balon's reproductive guilds with application to midwestern North American freshwater fishes. pp, 97-121 IN T.P. Simon (ed.), Assessing the sustainability and biological integrity of water resources using fish communities. CRC Press, Boca Raton, FL.
SPSS. 2002. AnswerTree Version 3.1, SPSS Inc. Chicago.
SPSS. 2006. SPSS for Windows, Rel. 15.0.0., SPSS Inc. Chicago.
Wischmeier, W.H., and D.D. Smith. 1978. Predicting rainfal erosion losses- a guide to conservation planning. U.S. Department of Agriculture, Agriculture Handbook No. 537, U.S. Government Printing Office, Washington, D.C., 58pp.
Yu, F., K. P. Price, J. Ellis, and D. Kastens. 2004. Satellite observations of the seasonal vegetation growth in Central Asia: 1982-1990. Photogrammetric Engineering and Remote Sensing, 70(4):461-469.
Zhang, X., M. A. Friedl, C. B. Schaaf, A. H. Strahler, J. C. F. Hodges, F. Gao, B. C. Reed, and A. Huete. 2003. Monitoring vegetation phenology using MODIS. Remote Sensing of Environment, 84(3):471-475.
27
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(b)
(c)
Figure 3 - 1. Location of sample sites for existing chemistry (a), fish (b), and macroinvertebrate (c) data. Sample sites were visited between 1994 and 2003. Shown with state and ecoregion boundaries.
28
Figure 3 - 2. Location of the 40 non-wadeable sample sites visited during this study in 2003. Shown with state and ecoregion boundaries. Selection of sites was affected by river access and depth.
29
Figure 3 - 3. Hypothetical vegetation curve and associated vegetation phenology metrics (VPM).
30
Figure 3 - 4. Map depicting the 15-year average for date of growing season onset. Red tones correspond to areas with an early onset date while green tones correspond to areas with a later onset date. Each period spans 14 days.
31
Figure 3 - 5. Map depicting the 15-year average for NDVI value at growing season onset. Red tones correspond to areas of lower onset values while green tones correspond to areas of higher onset values.
32
Figure 3 - 6. Map depicting the 15-year average for date of maximum NDVI. Red tones correspond to areas with an early maximum date while green tones correspond to areas with a later maximum date. Each period spans 14 days.
33
Figure 3 - 7. Map depicting the 15-year average for maximum occurring NDVI value during the growing season. Red tones correspond to areas of lower maximum value while green tones correspond to areas of higher maximum value.
34
Figure 3 - 8. Map depicting the 15-year average for date of dormancy onset. Red tones correspond to areas with an early onset date while green tones correspond to areas with a later onset date. Each period spans 14 days.
35
Figure 3 - 9. Map depicting the 15-year average for NDVI value at dormancy. Red tones correspond to areas with low NDVI values while green tones correspond to areas with high NDVI values.
36
Figure 3 - 10. Map depicting the 15-year average for rate of spring greenup. Red tones correspond to areas of low rate of greenup while green tones correspond to areas of high rate of greenup. Upper range of data has been clipped to 0.14 for display.
37
Figure 3 - 11. Map depicting the 15-year average for rate of senescence. Red tones correspond to areas of low rate of senescence while green tones correspond to areas of high rate of senescence. Rates of senescence faster than -0.149 have been clipped for this graphic.
38
Figure 3 - 12. Map depicting the 15-year average for length of growing season. Red tones correspond to areas with a shorter growing season while green tones correspond to areas with a longer growing season. Each period corresponds to 14 days.
39
Figure 3 - 13. Map depicting the 15-year average for the average NDVI value for the growing season. Red tones correspond to areas with less average yearly biomass production while green tones correspond to areas with more average yearly biomass production.
40
Figure 3 - 14. Map depicting the 15-year average for accumulated NDVI for the growing season. Red tones correspond to areas with less total annual biomass production while green tones correspond to areas with more total annual biomass production.
41
Figure 3 - 15. Map depicting the proportion of cropland per 1-kilometer square area. Data from the National Land Cover Database (NLCD) was summarized to a 1km grid consistent with the AVHRR data. Red tones correspond to areas with a low proportion of cropland while green tones correspond to areas with a high proportion of cropland.
42
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Figure 3 - 16. Comparison of stream density depicted for (a) EDNA to NHD, and (b) Synthetic Network to NHD.
43
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(b) Figure 3 - 17. Comparison of positional accuracy of (a) EDNA to NHD and positional accuracy of (b) Synthetic Network to NHD.
44
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Reference Map Figure 3 - 18. Examples of inconsistent representation of hydrography in the NHD data. Shown with 1:100,000 topographic quadrangle boundaries.
45
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Figure 3 - 19. Comparison of automated and manual watershed delineations. In (a), note how the manually compiled HUC4 boundary compares to the automated watershed boundaries. Shown with synthetic network.
46 (a) Example of sample points (pour points) successfully snapped to the SNET.
(b) Example of automated flag and manual placement. Buffer containing zero stream arcs indicates the pour point is greater than the 120m from the SNET.
(c) Example of automated flag and manual placement. Buffer containing multiple stream arcs indicates the pour point is near a confluence.
Figure 3 - 20. Automated pour point creation outcomes. In (a), sample points have been successfully snapped to the synthetic network. Unsnapped points are flagged in (b) and ambiguous snapping conditions are flagged in (c) and manually placed on the network.
47 Table 3 - 1. Summary of response variables stratified by ecoregion. Macro- Chemistry Fish invertebrate Sample Sample Sample Ecoregion Sites Events Sites Events Sites Events Boston Mountains 1 3000 0 Central Great Plains 214 451 111 150 84 124 Central Irregular Plains 188 366 74 92 91 153 Central Oklahoma/Texas Plains 4 7343 5 Driftless Area 33 76 26 34 26 35 Flint Hills 89 230 28 42 33 80 Interior River Valleys and Hills 24 34 12 13 13 18 Mississippi Alluvial Plain 5 11 0 0 1 2 Mississippi Valley Loess Plains 2 2000 0 Nebraska Sand Hills 85 129 31 34 18 20 Northern Glaciated Plains 1 5111 1 Northwestern Glaciated Plains 17 32 5 5 2 2 Northwestern Great Plains 7 11 3 3 0 0 Ozark Highlands 131 223 49 55 80 135 Southwestern Tablelands 32 95 15 16 12 17 Western Corn Belt Plains 346 788 294 413 250 324 Western High Plains 107 208 51 63 35 47 Wyoming Basin 8 13 6 6 6 6 Total 1294 2684 709 931 655 969
Table 3 - 2. Summary of response variables stratified by year. Macro- Chemistry Fish invertebrate Year Sample Sample Sample Sampled Sites Events Sites Events Sites Events 1994 130 212 61 139 41 72 1995 131 154 56 81 53 96 1996 5 12 32 53 36 60 1997 32 41 63 75 34 60 1998 32 37 52 62 29 51 1999 63 202 58 67 49 81 2000 224 505 116 144 134 202 2001 244 544 95 121 110 167 2002 277 578 132 139 129 139 2003 156 399 44 50 40 41 Total 1294 2684 709 931 655 969
48 Table 3 - 3. The chemistry, fish and macroinvertebrate databases were primarily compiled from existing data collected by the agencies listed below. The Kansas Biological Survey collected data for forty non-wadeable stream sites in 2003.
Chemistry Data Fish Data Macroinvertebrate Data Dept. of Fisheries & Iowa Department of Iowa Department of Wildlife Sciences, Natural Resources Natural Resources University of Missouri Hygienic Laboratory, Kansas Department of Kansas Biological Survey, University of Iowa Wildlife & Parks University of Kansas
Iowa Department of Kansas Biological Survey, Kansas Department of Natural Resource University of Kansas Health & Environment
Kansas Biological Survey, Missouri Department of Kansas Department of University of Kansas Conservation Wildlife & Parks
Kansas Department of Nebraska Department of Missouri Department. of Health & Environment Environmental Quality Natural Resources
Missouri Department of US Environmental Missouri Department. of Natural Resources Protection Agency Conservation
Nebraska Department of Nebraska Department of
Environmental Quality Environmental Quality
US Environmental US Environmental
Protection Agency Protection Agency
49 Table 3 - 4. List of the 34 non-wadeable rivers (40 individual sample sites) that were visited in 2003 (see also Figure 3-2). Selection of sites was affected by river access and depth. State Drainage Rivers KS Arkansas Arkansas, Neosho Kansas Big Blue, Kansas River (2 sites), Republican IA Mississippi Cedar, Des Moines, Iowa (2 sites), Maquoketa, Wapsinpinicon, Racoon, Skunk Missouri Big Sioux, Little Sioux MO Mississippi Black, Current, Eleven Point, Meramec, Salt, St. Francis Missouri Big, Big Piney, Bourbeuse, Gasconade (2 sites), Grand (2 sites), Lamine, Missouri (2 sites), Niangua, Osage, Platte NE Missouri Elkhorn, Missouri (2 sites), Niobrara Platte Platte
Table 3 - 5. Stability of candidate dependent measures. Correlation between values obtained in successive years. All correlation coefficients were statistically significant (P < 0.001). Between-year Measure Correlation (R) Number of pairs Fish species richness 0.909 125 log(median N) 0.896 968 Macroinvertebrate total richness 0.886 133 % sensitive fish taxa 0.823 125 Fish alpha diversity 0.789 125 log(median P) 0.762 968 log(median Turbidity) 0.658 968 Macroinvertebrate % sensitive taxa 0.604 133 Macroinvertebrate % EPT taxa 0.561 133 Fish diversity (1/D) 0.531 125
50
Table 3 - 6. List of static landscape indicators used to characterize watershed conditions in EPA Region 7.
Variable name Description Source ECO_NUM Predominate Ecoregion for a watershed EPA Level III Ecoregions of the Conterminous United States SHED_AREA Watershed area (square meters) Watersheds derived from processing of USGS 30-m DEMs POPDEN Population density (average number of LandScan 2003 Global Population Database people per square kilometer) RDDEN Road density (average length of road per StreetMap USA 2005 (ESRI) square meter of watershed area) RDLEN Total length of roads in watershed (meters) StreetMap USA 2005 (ESRI) DRDEN Drainage density (average length of stream Synthetic stream network derived from per square meter of watershed area) processing USGS 30-m DEMs DRLEN Total length of streams/rivers in watershed Synthetic stream network derived from (meters) processing USGS 30-m DEMs SHAPE Watershed shape calculated as (basin Watersheds derived from processing of length)2 / basin area USGS 30-m DEMs SLOPEMN Average watershed slope (in degrees Derived from processing of USGS 30-m multiplied by 100) DEMs SLOPESTD Standard deviation of watershed slope Derived from processing of USGS 30-m DEMs KFACTMN Average susceptibility of entire soil column NRCS State Soil Geographic (STATSGO) to erosion and runoff Database KFACTSTD Standard deviation of susceptibility of soil NRCS State Soil Geographic (STATSGO) column to erosion and runoff Database CROP Percent of watershed that has cropland land MRLC National Land Cover Data (NLCD cover 2001) FOREST Percent of watershed that has forest land MRLC National Land Cover Data (NLCD cover 2001) GRASS Percent of watershed that has grassland land MRLC National Land Cover Data (NLCD cover 2001)
51
Table 3 - 7. Standardized NDVI biweekly composite periods. The actual start date for the biweekly compilations for a calendar year varies by as much as + 7 days (from December 25 to January 8).
Julian Biweekly Calendar Start Calendar End JulianStart Day Julian End Day 1 1-Jan 14-Jan 1 14 2 15-Jan 28-Jan 15 28 3 29-Jan 11-Feb 29 42 4 12-Feb 25-Feb 43 56 5 26-Feb 11-Mar 57 70 6 12-Mar 25-Mar 71 84 7 26-Mar 8-Apr 85 98 8 9-Apr 22-Apr 99 112 9 23-Apr 6-May 113 126 10 7-May 20-May 127 140 11 21-May 3-Jun 141 154 12 4-Jun 17-Jun 155 168 13 18-Jun 1-Jul 169 182 14 2-Jul 15-Jul 183 196 15 16-Jul 29-Jul 197 210 16 30-Jul 12-Aug 211 224 17 13-Aug 26-Aug 225 238 18 27-Aug 9-Sep 239 252 19 10-Sep 23-Sep 253 266 20 24-Sep 7-Oct 267 280 21 8-Oct 21-Oct 281 294 22 22-Oct 4-Nov 295 308 23 5-Nov 18-Nov 309 322 24 19-Nov 2-Dec 323 336 25 3-Dec 16-Dec 337 350 26 17-Dec 31-Dec 351 365
52 Table 3 - 8. List of dynamic landscape indicators used to characterize watershed conditions in EPA Region 7. The eleven VPMs below constitute the core dynamic variables. From this core, two sets of 1- through 5- year VPM temporal averages were also calculated; one set that included the sample year in all the aggregates, and one that excluded the sample year. For each temporal average, the spatial average and standard deviation were calculated, resulting in 220 VPM statistics for each watershed.
Variable name Description Source OD Date of spring green-up (bi-weekly period) AVHRR bi-weekly composites OV NDVI value at spring green-up AVHRR bi-weekly composites MD Date of maximum NDVI value during growing AVHRR bi-weekly composites season (bi-weekly period) MV Maximum NDVI value during growing season AVHRR bi-weekly composites DD Date of dormancy (bi-weekly period) AVHRR bi-weekly composites DV NDVI value at dormancy (senescence) AVHRR bi-weekly composites GU Rate of spring green-up AVHRR bi-weekly composites BD Rate of fall senescence (brown down) AVHRR bi-weekly composites GL Length of growing season AVHRR bi-weekly composites AV Average NDVI value during the growing season AVHRR bi-weekly composites (between green-up and dormancy) AC Accumulate NDVI during the growing season AVHRR bi-weekly composites (between green-up and dormancy)
53
Table 3 - 9. Correlation matrix #1 for the eleven core VPMs. Values represent average (across 2,469 sample sites), 15-point (1989-2003) correlation values. Full watershed average VPM values were used in the correlation. Values with magnitudes > 0.5 (accounting for 12 of the 55 entries) are bolded. OV MD MV DD DV GU BD AC AV GL OD 0.278 -0.158 0.088 -0.019 0.114 0.536 0.182 -0.517 0.268 -0.783 OV -0.281 0.310 -0.142 0.212 -0.046 0.161 0.077 0.537 -0.312 MD -0.038 0.285 -0.048 -0.652 -0.668 0.212 -0.073 0.310 MV -0.001 0.460 0.240 -0.081 0.461 0.784 -0.074 DD -0.274 -0.132 0.102 0.506 -0.045 0.606 DV 0.128 0.303 0.266 0.668 -0.237 GU 0.408 -0.332 0.183 -0.511 BD 0.038 0.115 -0.080 AC 0.440 0.719 AV -0.243
Table 3 - 10. Correlation matrix #2 for the eleven core VPMs. Values represent 37,035- point correlations, using stacked data from 2,469 sampling sites and 15 years (1989- 2003). Full watershed average VPM values were used in the correlation. Values with magnitudes > 0.5 (accounting for 15 of the 55 entries) are bolded. OV MD MV DD DV GU BD AC AV GL OD -0.105 0.196 0.037 -0.123 -0.325 0.491 -0.362 -0.486 -0.101 -0.781 OV -0.511 0.415 0.118 0.691 0.215 0.422 0.592 0.724 0.148 MD 0.089 0.200 -0.413 -0.437 -0.729 -0.162 -0.205 -0.012 MV 0.343 0.471 0.416 -0.312 0.684 0.863 0.190 DD 0.208 -0.021 0.194 0.652 0.402 0.716 DV 0.190 0.513 0.745 0.779 0.359 GU 0.034 0.068 0.385 -0.359 BD 0.311 0.128 0.377 AC 0.863 0.752 AV 0.324
54
Table 3 - 11. Correlations between lagged VPM values. Entries represent 2,649-point correlations, averaged across lagged-year pairings occurring in 1989-2003 (i.e., 14 consecutive-year pairings (1-yr), 13 two-year lagged pairings (2-yr), etc.). Values with magnitudes > 0.707 (reflecting at least 50% common variance) are bolded. 1-yr 2-yr 3-yr 4-yr 5-yr OD 0.673 0.558 0.57 0.512 0.467 OV 0.871 0.798 0.763 0.691 0.617 MD 0.644 0.636 0.585 0.515 0.47 MV 0.95 0.882 0.814 0.749 0.683 DD 0.684 0.644 0.565 0.556 0.497 DV 0.853 0.794 0.732 0.666 0.595 GU 0.415 0.388 0.442 0.385 0.314 BD 0.851 0.777 0.724 0.672 0.609 AC 0.94 0.874 0.81 0.742 0.677 AV 0.956 0.879 0.818 0.75 0.685 GL 0.703 0.603 0.605 0.549 0.5
55 4.0 Results - Testing Area of Influence
4.1 Introduction “The spatial scale at which landscape attributes exert a detectable influence on aquatic systems is not well understood” (Gergel, et al., 1999). It is reasonable to hypothesize, however, that for a given a stream sampling location, nearby rather than distal influences provide better indicators of sample values. Thus when landscape statistics are used as predictive/descriptive variables, it may prove beneficial to constrict their calculation to a subset of the watershed that is nearby and upstream from the sampling station. To examine this notion of spatial scale, we extract vegetation phenology metric (VPM) statistics from a series of nested watershed subsets, building upstream from the sample point, basing subset inclusion on mean pixel elevation. The general findings do not support the hypothesis as it pertains to VPM statistics, largely indicating that VPM statistics from the complete reach (i.e., the entire upstream watershed) generally vary with the sample values comparably or better than VPM statistics from reach subsets that are proximal to the sample point.
4.2 Data and Methods Digital elevation models (DEMs) from the 30-m National Elevation Database (NED) were used in this exercise to ascribe an elevation to each 1-km VPM pixel in the watershed for a sample point. To do so, the average NED elevation within the footprint of each 1-km pixel was computed and assigned to it. Pixels were then sorted using these elevation values. Area-of-influence (AOIs) subsets were defined by lowest-elevation pixel subsets that corresponded to a specified set of AOI sizes. The elevation subset method was employed for two reasons, one theoretical and one practical. First, from an ecological perspective, topographically determined buffers arguably should better reflect hydrologic connectivity than, say, fixed-width stream buffers. Second, this intuitive procedure provides a conceptually and computationally simple framework for examining the AOI question. It presumes that the sample point will occur in the 1-km pixel with the lowest average elevation appearing in the sample point’s reach, and that hydrologically proximal pixels will generally have lower elevation values than pixels farther up- and off-stream. The elevation subset method is not free from problems, however. For example, identified subsets may not be fully connected due to potentially high variability in the 30- m elevation values within each 1-km pixel footprint. It is possible that a 1-km pixel beyond the immediate, contiguous sample point neighborhood possesses a lower elevation than some 1-km pixel(s) that intervene. In addition, the 1-km pixel occupied by the sample point may not be the lowest point in the watershed (it was the lowest point in a large majority of cases). Whether calculated as the lowest point or not, in all instances the sample point was identified as the lowest point. In spite of problems such as these, the method still provides a better estimation of hydrologic connectivity than conventional point buffers, such as fixed distance radius, that do not account for topography. Eleven differently sized AOIs were examined in this study. Ten of the AOIs were sized according to powers of two, so that they contained 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024 pixels (square kilometers), respectively. The eleventh AOI comprised the entire watershed, serving as a control and providing a benchmark for
56 comparing results. Figure 4-1 shows two examples of how the AOIs were placed in a sample point watershed. For each sample, 110 AOI-specific VPM statistics were examined for correspondence with the sample data. Eleven core VPMs, concurrent to the sampling year, were considered:
1. Greenup onset date, or season start [OD] 2. Greenup onset NDVI [OV] 3. Peak season date, which is the date of maximum observed NDVI [MD] 4. Peak season NDVI [MV] 5. Dormancy onset date, or season end [DD] 6. Dormancy onset NDVI [DV] 7. Rate of greenup [GU = (MV – OV)/(MD – OD)] 8. Rate of senescence, or “brown down” [BD = (DV – MV)/(DD – MD)] 9. Growing season length [GL = DD – OD] 10. Average growing season NDVI [AV] 11. Accumulated growing season NDVI [AC = AV * (GL + 1)]
The 15-year record of VPM data allowed for investigation into the temporal scale between predictor VPM variables and target nutrient and biological variables in the AOI analyses. Two sets of 1- through 5-year VPM temporal averages were calculated; one set using values immediately prior to and including the sampling year and one that excluded the sample year. The purpose of considering these 1- to 5-year aggregates was to examine a range of potentially useful VPM statistics that reflected various proportions of longer-term stability and shorter-term specificity. The purpose of considering one set of spans that excluded the sample year was to accommodate the uncertainty of the temporal relation between the VPMs and the sample collection date, a condition often exacerbated by the high variability of within-year sample dates. The temporal averages expanded the 11 core VPM statistic pool by a factor of 10, resulting in 110 VPM statistics for each 1- km pixel in a sample’s reach. To obtain single valued, AOI-specific VPM statistics from the 110 VPM pixel maps, the AOI-specific spatial VPM means were calculated. To impose uniformity of sample composition across different AOI evaluations, sampling points considered were screened by watershed size and VPM data availability. First, only sample points with upstream watersheds consisting of at least 1024 1-km pixels were considered to ensure that VPM statistics were available for every AOI. Second, samples from years prior to 1994 were excluded because a complete set of the VPM variables as described above could not be calculated (1989 is the first year of NDVI data availability; a sample collected in 1994 would require VPM data from 1989-1993 to define the 5-year aggregates that exclude the sample year). After screening, 1106 sample points for the target variable ‘total nitrogen’ (denoted by ‘TotN’), 203 sample points for the target variable ‘proportion sensitive fish taxa’ (‘PrpSensF’), and 201 sample points for the target variable ‘invertebrate family-level richness’ (‘InvFmRch’) remained for evaluation. Figure 4-2 shows the distribution of samples by ecoregion for the three target variables (see Table 4-1 for ecoregion ID-to-name lookup). We used the coefficient of determination (R2) statistic, which is the square of the correlation coefficient, to estimate “goodness of fit” of the pairwise relationships between
57 each VPM statistic (denoted by X; AOI dependent) and the target value (denoted by Y; not AOI dependent). R2 provides an estimate for the proportion of variance of Y that can be explained using an optimized linear regression model Y ≈ Ŷ = a + b*X, a contextual 2 2 ˆ 2 notion that leads to the equation R,()X YYYYY=−∑∑( kk) /() −, where summation kk is over the sample points considered, and Y denotes the sample mean for Y. AOI size- specific R2 values were determined and used to compare the different AOI sizes considered.
4.3 Results Results from the bivariate analysis relating VPM statistics and percent cropland to sample site measurement data (‘TotN’, ‘PrpSensF’, and ‘InvFmRch’) are described in this section. First, the AOI hypothesis is stated and examined for merit based on the research findings. Second, VPM statistics that exhibited superior colinearity with the target datasets are described and discussed. Finally, the AOI hypothesis rejection is further scrutinized in an examination of the effect of watershed size on the relationship between AOI-specific VPM statistics and the ‘TotN’ target variable.
4.3.1 AOI Hypothesis The purpose of this exercise was to examine the AOI hypothesis that VPM statistics extracted from pixels hydrologically near (i.e., upstream and within approximately 30 km) the sample point tend to correspond better with sample point measurements than VPM statistics extracted from the entire watershed. Initial bivariate results showed that different target variables (‘TotN’, ‘PrpSensF’, or ‘InvFmRch’) and different sample point sets (e.g., all points, or ecoregion specific sets) demonstrated diverse preferences for different VPM statistics. To account for this observation, we examined the average and median behavior of the top 20% (22 of 110) and top 10% (11 of 110) of VPM variables as indicators of statistical tendency. The choice of these two fractions is largely arbitrary, presenting two possible balances between the optimistic bias expected when considering just the top few optimal variables to determine explanatory potential and the pessimistic bias expected when considering all possible variables without performing any variable selection. Figures 4-3 through 4-8 show results cast in this light, along with results from the optimal VPMs. The R2 for percent cropland, estimated using the National Land Cover Database (NLCD), is shown for comparison and to provide context for discussion. Analyses of ‘TotN’, ‘PrpSensF’, and ‘InvFmRch’ from the all-ecoregion data do not support the AOI hypothesis. In particular, two observations are apparent from Figures 4-3, 4-5, and 4-7: (1) linear statistical relationships between VPM statistics and target values did not degrade (improved in most cases) as AOI size increased, to the point that (2) VPM statistics extracted from the entire watershed demonstrated better linear statistical relationships with each of the three target variables than VPM statistics extracted from AOIs near the sample point. Ecoregion-specific results from EPA Ecoregion 27 (Central Great Plains) are presented in Figures 4-4, 4-6, and 4-8. This ecoregion was selected because it had the best representation in the ‘PrpSensF’ and ‘InvFmRch’ databases and the second best representation in the ‘TotN’ database. ‘TotN’ and ‘InvFmRch’ results do not support the
58 AOI hypothesis. As with the all-ecoregion data, VPM statistics extracted from the entire watershed for these target variables exhibited better linear statistical relationships than VPM statistics extracted from the AOIs. The ‘PrpSensF’ results, on the other hand, do provide some support for the AOI hypothesis for this particular ecoregion and target variable.
4.3.2 VPM Statistics Breakdown In this section we examine the membership and ranking for VPM statistics that appeared in the various top 20% (top 22) and top 10% (top 11) lists identified during the main AOI hypothesis test. Results are shown in Tables 4-2 through 4-5. Regarding the VPM nomenclature used in the table, the first two characters denote the core VPM considered from the list of 11 core VPMs presented above, the third character denotes the number of years used in the temporal average (1-5), and the last two characters denote whether or not the sample year was included in the temporal average (‘in’ = included, ‘ex’ = excluded). For example, the second best ‘PrpSensF’ variable from Table 4-2 is ‘av5in’, which corresponds with the average growing season NDVI (‘av’) and temporal average from the five years (‘5’) just prior to and including the sample year (‘in’). Two performance indicators were calculated: (1) ‘count’, the number of appearances in the top 20/10% (out of 11 opportunities corresponding to the different AOI sizes considered), and (2) cumulative ‘score’ from appearances in the top 20/10%. To compute (2) in the top 20% case, 1st place variables were given 22 points, 2nd place variables were given 21 points, and so on, so that the 22nd place variables received just one point. Consequently, the maximum possible score was 22*11 = 242, and would occur only if a particular variable demonstrated the largest R2 value across all 11 AOI- size trials. To compute (2) in the top 10% case, 1st place variables were given 11 points, 2nd place variables were given 10 points, and so on, so that the 11th place variables received just one point. For the top 10% case, the maximum possible score is 11*11 = 121. To assist interpretation of the VPM results, recall that results for percent cropland are also presented in Figures 4-3 through 4-8. It is useful to track percent cropland because annual, 1-km NDVI profiles are shaped heavily by the cropland fraction due to pronounced phenology differences between cultivated cropland and natural vegetation such as grasslands and forests. In addition, these broadly defined cover classes account for most of the signal from 1-km pixels in the Region 7 study area. Thus cropland must be considered in order to evaluate whether the information contained in the VPM statistics derived from the NDVI profiles was predominantly static, and therefore redundant with NLCD-based percent cropland values. In general, the results indicate that VPM statistics do indeed possess information relevant to sample site measurements that goes beyond their role as proxy for NLCD cropland fraction. We surmise that this additional information is dynamic, largely attributable to annual or interannual variance of the VPMs, reflecting recent climate conditions as well as recent land use information. This observation lends support to the notion that the VPMs have potential actionable utility with respect to predicting sample measurements. The following sections highlight some “points of interest” regarding the AOI/VPM assessment.
59 4.3.2.1 ‘TotN’ Analysis As somewhat anticipated based on past research and the direct connection to cropland management (in particular, extensive nitrogen fertilizer application), NLCD- derived percent cropland was found to possess correlation with ‘TotN’ data comparable to that of the top VPM statistics for the entire watershed in both the all-ecoregion and the Ecoregion 27 analyses. However, unlike with the VPMs in the all-ecoregion assessment, this relationship deteriorated greatly as AOI size decreased. This drop-off is likely a reflection of the cumulative contributions of nitrogen from all cropland in the watershed overriding and dominating any local effects. In the all-ecoregion analysis, at the two largest AOI sizes (1024 sq. km and entire watershed), the median performance of the top 20% strongest correlating VPMs is indistinguishable from the performance of the percent cropland variable. This occurrence possibly undermines the dynamic utility of using the VPMs for ‘TotN’ prediction. On the other hand, unlike the quickly waning performance of the percent cropland variable, VPM performance declined somewhat slowly as AOI size decreased, suggesting perhaps that dynamic aspects (climate in particular) of the VPMs play an increasing role driving the relationship with the ‘TotN’ data as smaller AOIs are considered. In the all-ecoregion analysis, 10 of the 15 variables appearing in all 11 top 20% lists from the ‘TotN’ data were BD (rate of senescence) variables. MV (peak NDVI) variables provided the other 5. All 27 unique variables appearing in the 11 top 20% lists were representatives of three core VPMs. Based on score, the 10 BD variables comprised the top 10. The 10 MV variables comprised positions 11-20. MD (date of peak NDVI) variables filled the remaining 7 positions (21-27). BD variables negatively correlated with the ‘TotN’ data. This indicates that a more rapid senescence of regional vegetation corresponded with increased total nitrogen at the sample point. Cultivated cropland tends to senesce more rapidly than natural vegetation and perhaps provides a partial explanation for this outcome (correlations between ‘TotN’ data and cropland fraction were all positive). These results illustrate that the information content of the VPMs includes implicit description of land cover. Since VPM variables are timely and easily computed as compared to the creation of land cover maps, the value in using them becomes apparent. In addition to cropland senescence, or perhaps alternatively, a rationale for this outcome may be associated with climatic aspects of BD. For example, late growing seasoning stress (heat, lack of moisture, or both) can produce a more rapid rate of senescence resulting in less uptake/utilization (or more release) by regional vegetation of available nitrogen during fruiting or seed set. This could result in a greater amount of unbound nitrogen in the landscape that is free to enter into streams and rivers and is subsequently measured at the sample site. MV and MD variables demonstrated positive correlation with ‘TotN’ data, though with a substantial drop-off in strength of relationship compared to BD. To see this, compare Figures 4-3a and 4-3b. About 45% of the top 20% results reflect BD relationships, whereas about 90% of the top 10% results reflect BD relationships. Regarding MV and MD results, increased maximum NDVI corresponded with increased ‘TotN’ values, and later occurring maximum NDVI also corresponded with increased ‘TotN’ values. One might expect these relationships to be tied to the implicit land cover information reflected in these VPMs and the association between cultivated
60 crops and applied nitrogen fertilizer, but this is not entirely clear. Commonly occurring summer crops like corn, soybeans (which do not require nitrogen application), and sorghum typically realize a later MD than natural vegetation from the study area, but a similarly clear ordering is not ascribable to MV since cultivated cropland MV values are frequently straddled by MV values from grasslands (lower) and forest (similar or higher).
4.3.2.2 ‘PrpSensF’ Analysis Unlike the VPMs, percent cropland exhibited marginal linear correspondence with ‘PrpSensF’ data (R2 < 0.03 for all AOIs; see Figures 4-5 and 4-6). In the all- ecoregion analysis, the 32 unique VPM variables appearing in the various top 20% sets demonstrated positive correlation with ‘PrpSensF’ values. In the Ecoregion 27 analysis, 29 of the 38 VPM variables exhibited positive correlation with ‘PrpSensF’ values (Table 4-4). The nine variables demonstrating negative correlation with the ‘PrpSensF’ data scored in the bottom half of the top 20%. In the all-ecoregion analysis, eight of the 13 variables appearing in all 11 top 20% lists from the ‘PrpSensF’ data were AV (average growing season NDVI) variables (Table 4-2). Three were AC (accumulated growing season NDVI) variables, and 2 were GU (rate of greenup) variables. Based on score, 8 of the top 14 variables were AV variables, and 6 of the top 14 variables were GU variables. Thus more rapid green-up of regional vegetation and higher average NDVI corresponded with increased percentage of sensitive fish species at the sample point. From the land cover perspective, cultivated cropland tends to be associated with more rapid green-up than natural vegetation. However, the relationship between ‘PrpSensF’ measurements and percent cropland were all poor and negative, suggesting no static influence. It then follows that the land cover aspect of the VPMs was not responsible for their correspondence with the ‘PrpSensF’ data. From the dynamic perspective, higher GU and AV values are generally associated with increased plant biomass that is, in turn, likely due to more favorable growing conditions. These conditions may include increased rainfall and more available soil moisture to facilitate plant growth. Such circumstances would also promote higher stream flow levels and thus an increase in potential fish habitat. Alternatively, more nutrients useful for plant growth, but potentially harmful to sensitive fish species, may be sequestered in greater quantities by more lush vegetation, leaving less of such material available for transport to the sampling site.
4.3.2.3 ‘InvFmRch’ Analysis Unlike the VPMs, percent cropland exhibited mostly marginal linear correspondence with ‘InvFmRch’ data (R2 < 0.06 for all AOIs; see Figures 4-7 and 4-8). In the all-ecoregion analysis, the 24 unique VPM variables appearing in the various top 20% sets demonstrated positive correlation with ‘InvFmRch’ values. In the Ecoregion 27 analysis, 26 of the 35 VPM variables exhibited positive correlation with ‘InvFmRch’ (Table 4-4). Eight of the nine variables demonstrating negative correlation with the ‘InvFmRch’ data scored in the bottom half of the top 20%. In the all-ecoregion analysis, the top 20% variable lists were highly consistent across the different AOI sizes; only 24 unique variables were encountered, with the minimum possible value of 22 if all lists consisted of the same variable set. Nineteen of
61 the 24 variables appeared in all 11 lists. Just 2 of the 24 appeared in fewer than 9 lists. Also of note is that in Table 4-3, where top 10% results are presented from the all- ecoregion analysis, the top 5 variables were the same (even in ordering) in all examined AOIs (note the maximum possible scores associated with these variables). Based on “Score,” the top 6 variables were AV (average growing season NDVI) variables (Table 4-2). All 10 of the AV variables ranked in the top 14. The other 9 of the top 19 were MV (peak NDVI) variables, with the tenth MV variable ranked 22. Higher AV and MV are generally associated with increased plant biomass due to favorable growing conditions. These conditions, in turn, possibly reflect an increased availability of sustenance material and habitat for macroinvertebrate populations, which have both static properties based on the long-term biomass gradient across the study area (largely shaped by soils composition and historical temperature and precipitation gradients) and dynamic characteristics reflecting recent climatic conditions.
4.3.2.4 Effect of Watershed Size To provide additional support for the all-ecoregion ‘TotN’ data AOI hypothesis rejection, we investigated a simple conclusion expected to follow from the observed results. Specifically, if VPM statistics from the entire watershed are more indicative of ‘TotN’ values than VPM statistics from AOIs localized to the sample point, then this effect should become more pronounced as watershed size increases. To evaluate this claim, the ‘TotN’ samples were sorted by watershed size, and the analysis was repeated for the smallest 200 and largest 200 sample points. The decision to use “200” (which is ~18% of the total ‘TotN’ sample) was somewhat arbitrary, dictated by the dual constraints of choosing a sub-sample that is as large as possible but small enough to be collectively representative of an extreme (relative to the total sample) in watershed size. Unfortunately, the ‘PrpSensF’ and ‘InvFmRch’ datasets lacked sufficient sample sizes to perform this sub-sample assessment with any reasonable degree of confidence. Results from this sub-sample analysis are shown in Figure 4-8. The 200 small watershed samples considered in Figure 4-8(a) ranged in watershed size from 1025 – 1523 sq. km, with an average size of 1238 sq. km (recall that 1 AVHRR pixel = 1 sq. km). Performance across the localized AOIs was fairly stable and generally comparable to entire watershed performance for these cases. The 200 large watershed samples considered in Figure 4-8(b) ranged in watershed size from 21,398 – 203,916 sq. km, with an average size of 80,469 sq. km. Performance across the localized AOIs was fairly stable but substantially diminished relative to entire watershed performance for these cases. These observations support the conclusion reached in the AOI hypothesis test in the case of the all-ecoregion ‘TotN’ data, namely that it is generally advisable to use VPM statistics extracted from the entire watershed when using such information to estimate ‘TotN’ values from a broad, geographically diverse study area such as that examined in this research. An additional noteworthy outcome was that VPMs extracted for entire watersheds performed consistently across the two extreme subsets, with respect to both accuracy and which VPMs were optimal. In the entire watershed case, the average R2 between the mean and median performance of the top 20% of VPM statistics was 0.319 for the small watershed sub-sample and 0.325 for the large watershed sub-sample (R2 = 0.388 in the analogous full sample result). The top 10 VPM statistics in both the small and large
62 watershed subsets consisted of the 10 BD variables in the entire watershed case, just like the full sample analysis. However, there was one major distinction when considering results tabulated across all AOIs (analogous to results presented in Tables 4-2 through 4- 5) for the large watershed sub-sample, where it was observed that MV and AV variables comprised the top 10, with MV variables filling 8 of the top 9 positions. This distinction is insignificant due to the greatly diminished linear correspondence between VPMs from the localized AOIs (relative to the entire watershed AOI) and ‘TotN’ values in the large watershed sub-sample. The same assessment for the small watershed sub-sample, on the other hand, still produced a top 10 list consisting solely of the 10 BD variables, which was consistent with the full sample analysis.
4.4 Conclusions The primary goal of the analysis described in this section was to evaluate the AOI hypothesis, which posits that VPM statistics based on 1-km AVHRR NDVI data extracted from a region hydrologically near and upstream from the sample site should better correspond to sample site measurements than VPM statistics extracted from the entire upstream watershed from the sample site. Analysis of the ‘TotN’, ‘PrpSensF’, and ‘InvFmRch’ data is largely suggestive that the AOI hypothesis should be rejected, even so much as to provide evidence that VPM statistics extracted from the entire watershed is generally preferable to using a localized AOI for VPM extraction. To further assess the robustness of this last claim as it pertains to across-ecoregion ‘TotN’ data, the ‘TotN’ samples were stratified by size, and two subsets were examined corresponding to watershed size extremes. Results were in accord with the entire watershed VPM extraction preference. Performance across the localized AOIs was comparable to entire watershed performance in the small watershed sub-sample, whereas performance across the localized AOIs was substantially diminished relative to entire watershed performance in the large watershed sub-sample. Additionally, performance using entire watershed VPMs was fairly consistent across the full sample and the two watershed size extreme sub-samples in terms of accuracy and VPM variable selection. We close this section with a general observation regarding an important difference between across-ecoregion results and ecoregion-specific results that became rather apparent in the course of this analysis but is not readily discernible from the “scale free” R2 results that have been presented. Measured by R2, all-ecoregion VPMs generally performed better than ecoregion-specific VPMs (e.g., see Figures 4-3 through 4-8). This can be explained thusly, though this explanation has not been verified. Sample data from different ecoregions often exhibit substantially different central tendencies (see Figure 4- 9), enough so that the mean sample values from different ecoregions demonstrate variation comparable to that of observations from within a single ecoregion. Consequently, variation in the VPMs in the all-ecoregion sample might be useful for ascribing an appropriate, general level, whereas variation in the VPMs from a particular ecoregion does not generally capture as well the variational subtleties of the ecoregion- specific samples. This does not necessarily preclude the findings presented here, but this effect may need to be considered in future research and application designs.
63 4.5 References
Gergel, S, M. Turner, and T. Kratz. 1999. Dissolved organic carbon as an indicator of the scale of watershed influence on streams and rivers. Ecological Applications. 9(4), pp. 1377-1390.
64
Figure 4 - 1. Areas of Influence (AOI) created for two watersheds. Shown with synthetic stream network superimposed.
65 (a)
(b)
(c)
Figure 4 - 2. Sample distribution, stratified by ecoregion, for (a) ‘TotN’, (b) ‘PrpSensF’, and (c) ‘InvFmRch’ values used in the AOI analysis. Black dots demark the sample means.
66
(a)
(b)
Figure 4 - 3. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the all-ecoregion ‘TotN’ data, by AOI size. No sub-watershed AOI preference is indicated, so that the AOI hypothesis is not supported by t his analysis. The relationship between percent cropland and the ‘TotN’ data is also shown for comparison.
67 (a)
(b)
Figure 4 - 4. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the ecoregion 27 ‘TotN’ data, by AOI size. No sub-watershed AOI preference is indicated, so that the AOI hypothesis is not supported by this analysis. The relationship between percent cropland and the ‘TotN’ data is also shown for comparison.
68 (a)
(b)
Figure 4 - 5. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the all-ecoregion ‘PrpSensF’ data, by AOI size. No sub-watershed AOI preference is indicated, so that the AOI hypothesis is not supported by this analysis. The relationship between percent cropland and the ‘PrpSensF’ data is also shown for comparison.
69 (a)
(b)
Figure 4 - 6. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the ecoregion 27 ‘PrpSensF’ data, by AOI size. The AOI hypothesis is supported by this analysis. The relationship between percent cropland and the ‘PrpSensF’ data is also shown for comparison.
70 (a)
(b)
Figure 4 - 7. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the all-ecoregion ‘InvFmRch’ data, by AOI size. No sub-watershed AOI preference is indicated, so that the AOI hypothesis is not supported by this analysis. The relationship between percent cropland and the ‘InvFmRch’ data is also shown for comparison.
71 (a)
(b)
Figure 4 - 8. General linear statistical correspondence between (a) the top 20% and (b) the top 10% of the VPM statistics and the ecoregion 27 ‘InvFmRch’ data, by AOI size. No sub-watershed AOI preference is indicated, so that the AOI hypothesis is not supported by this analysis. The relationship between percent cropland and the ‘InvFmRch’ data is also shown for comparison.
72 (a)
(b)
Figure 4 - 9. General linear statistical correspondence between the top 20% of the VPM statistics and the all-ecoregion ‘TotN’ data, by AOI size. Results from the 200 sample points with the smallest (a) and largest (b) upstream watersheds are shown. As expected, the AOI hypothesis is more clearly rejected when sample points with larger watersheds are considered. The relationship between percent cropland and the ‘TotN’ data is also shown for comparison.
73
Table 4 - 1. Level III Ecoregion names and numbers.
Level III Ecoregion Name Level III Ecoregion Number Wyoming Basin 18 Western High Plains 25 Southwestern Tablelands 26 Central Great Plains 27 Flint Hills 28 Central Oklahoma/Texas Plains 29 Boston Mountains 38 Ozark Highlands 39 Central Irregular Plains 40 Northwestern Glaciated Plains 42 Northwestern Great Plains 43 Nebraska Sand Hills 44 Northern Glaciated Plains 46 Western Corn Belt Plains 47 Driftless Area 52 Interior River Valleys and Hills 72 Mississippi Alluvial Plain 73 Mississippi Valley Loess Plains 74
74 Table 4 - 2. Analysis results for optimal VPM statistics identified during the AOI hypothesis test. This table gives results considering data from all ecoregions and the top 20% (22 of 110) of VPM statistics. TotN PrpSensF InvFmRch Count (type of Count (type of Count (type of VPM Score* relationship)** VPM Score* relationship)** VPM Score* relationship)** bd3in 235 11 (-) gu3ex 217 11 (+) av5ex 242 11 (+) bd4in 226 11 (-) av5in 198 11 (+) av4ex 231 11 (+) bd2in 226 11 (-) gu4ex 196 11 (+) av5in 220 11 (+) bd5in 210 11 (-) av1in 182 11 (+) av3ex 209 11 (+) bd2ex 186 11 (-) av5ex 179 11 (+) av4in 198 11 (+) bd3ex 185 11 (-) gu5in 167 9 (+) av3in 183 11 (+) bd5ex 181 11 (-) av4ex 163 11 (+) mv5ex 171 11 (+) bd1ex 172 11 (-) gu5ex 160 9 (+) av2ex 166 11 (+) bd4ex 161 11 (-) av4in 144 11 (+) mv4ex 152 11 (+) bd1in 143 11 (-) gu4in 135 9 (+) av2in 145 11 (+) mv4ex 128 11 (+) gu2ex 134 9 (+) mv3ex 121 11 (+) mv5ex 116 11 (+) av3in 111 11 (+) av1ex 118 11 (+) mv5in 110 11 (+) av2in 108 11 (+) mv5in 118 11 (+) mv4in 94 11 (+) av3ex 87 11 (+) av1in 106 11 (+) mv3ex 87 11 (+) ac1in 84 11 (+) mv4in 93 11 (+) mv3in 70 10 (+) mv5ex 83 10 (+) mv2ex 75 11 (+) mv2ex 60 10 (+) gu3in 78 7 (+) mv1ex 59 10 (+) mv2in 50 10 (+) ac3in 73 11 (+) mv3in 56 11 (+) mv1ex 40 10 (+) ac2in 72 11 (+) mv2in 43 11 (+) mv1in 30 10 (+) mv4ex 51 9 (+) dv5ex 38 11 (+) md3in 28 10 (+) mv5in 48 9 (+) ac5ex 19 10 (+) md4in 20 7 (+) ac5in 31 8 (+) mv1in 15 9 (+) md5in 11 2 (+) av2ex 15 4 (+) dv5in 3 3 (+) md2in 7 5 (+) ac4in 13 4 (+) gu2in 2 1 (+) md3ex 4 1 (+) mv4in 13 2 (+) ------md5ex 2 1 (+) mv3ex 11 2 (+) ------md4ex 1 1 (+) ac5ex 10 2 (+) ------mv3in 8 1 (+) ------mv2ex 6 1 (+) ------gu2in 3 1 (+) ------ac4ex 2 2 (+) ------mv2in 1 1 (+) ------*Score = sum of AOI-specific scores defined by (23 – rank in top 22); max score is 11*22 = 242 **Count = number of appearance in top 20% (out of 11 opportunities); +/- indicates positive/negative correlation
75 Table 4 - 3. Analysis results for optimal VPM statistics identified during the AOI hypothesis test. This table gives results considering data from all ecoregions and the top 10% (11 of 110) of VPM statistics. TotN PrpSensF InvFmRch Count (type of Count (type of Count (type of VPM Score* relationship)** VPM Score* relationship)** VPM Score* relationship)** bd3in 114 11 (-) gu3ex 98 9 (+) av5ex 121 11 (+) bd4in 105 11 (-) gu4ex 90 9 (+) av4ex 110 11 (+) bd2in 105 11 (-) av5in 77 11 (+) av5in 99 11 (+) bd5in 89 11 (-) gu5in 68 9 (+) av3ex 88 11 (+) bd2ex 65 11 (-) av1in 61 11 (+) av4in 77 11 (+) bd3ex 64 11 (-) gu5ex 61 9 (+) av3in 62 11 (+) bd5ex 60 11 (-) av5ex 58 11 (+) mv5ex 50 11 (+) bd1ex 51 11 (-) gu4in 46 7 (+) av2ex 45 11 (+) bd4ex 40 11 (-) av4ex 42 10 (+) mv4ex 31 11 (+) bd1in 22 11 (-) gu2ex 36 7 (+) av2in 26 10 (+) mv4ex 10 10 (+) av4in 25 7 (+) av1ex 7 6 (+) md4in 1 1 (+) mv5ex 13 2 (+) mv3ex 6 5 (+) ------gu3in 12 4 (+) mv5in 4 1 (+) ------ac1in 9 3 (+) ------av2in 6 3 (+) ------av3in 5 3 (+) ------ac3in 5 2 (+) ------mv4ex 5 1 (+) ------ac2in 4 1 (+) ------mv5in 4 1 (+) ------av3ex 1 1 (+) ------*Score = sum of AOI-specific scores defined by (12 – rank in top 11); max score is 11*11 = 121 **Count = number of appearance in top 10% (out of 11 opportunities); +/- indicates positive/negative correlation
76 Table 4 - 4. Analysis results for optimal VPM statistics identified during the AOI hypothesis test. This table gives results considering data from ecoregion 27 and the top 20% (22 of 110) of VPM statistics. TotN PrpSensF InvFmRch Count (type of Count (type of Count (type of VPM Score* relationship)** VPM Score* relationship)** VPM Score* relationship)** bd4ex 231 11 (-) mv5ex 228 11 (+) av5ex 231 11 (+) bd5in 226 11 (-) mv5in 221 11 (+) dv5ex 228 11 (+) bd5ex 206 11 (-) mv4ex 204 11 (+) av4ex 210 11 (+) bd3ex 173 11 (-) mv4in 189 10 (+) dv4ex 209 11 (+) mv2ex 167 11 (+) av5in 178 11 (+) av3ex 180 11 (+) bd4in 163 11 (-) mv3ex 166 10 (+) ov3ex 174 11 (+) bd2ex 145 10 (-) av5ex 163 11 (+) ov4ex 170 11 (+) mv3in 144 11 (+) mv1in 158 11 (+) dv5in 162 11 (+) mv3ex 123 11 (+) mv3in 149 10 (+) ov5ex 154 11 (+) bd3in 119 9 (-) av4ex 140 11 (+) av5in 139 11 (+) md3in 118 10 (+) av4in 110 10 (+) dv3ex 113 10 (+) md1in 118 8 (+) mv2ex 96 10 (+) mv5ex 106 11 (+) mv4ex 108 11 (+) av1in 90 10 (+) gl3ex 99 11 (-) mv5in 99 11 (+) mv2in 87 10 (+) av4in 93 10 (+) mv4in 99 10 (+) gu4in 75 10 (+) gu2in 70 10 (+) md4in 83 10 (+) av3in 73 10 (+) mv4ex 65 10 (+) mv5ex 68 8 (+) av3ex 72 10 (+) dv4in 56 9 (+) md5in 50 10 (+) gu3in 47 9 (+) av2ex 52 8 (+) mv2in 49 8 (+) av2in 40 8 (+) mv3ex 41 7 (+) md2ex 47 10 (+) dv1in 36 6 (+) gl4in 37 4 (-) md2in 47 7 (+) bd5ex 32 7 (-) gl4ex 36 3 (-) bd2in 37 3 (-) bd4ex 30 8 (-) gl2ex 35 6 (-) mv1ex 28 7 (+) av2ex 27 6 (+) gl5in 26 3 (-) md3ex 27 6 (+) gu3ex 27 3 (+) gl3in 19 2 (-) bd1in 24 2 (-) gu5in 27 2 (+) ov2ex 19 6 (+) gu5ex 19 1 (+) gu4ex 18 1 (+) ov5in 19 7 (+) gu5in 18 1 (+) gu5ex 17 1 (+) gu3in 11 4 (+) md5ex 18 5 (+) gu2ex 16 1 (+) gu1ex 9 3 (+) bd1ex 13 2 (-) gl4ex 15 1 (-) gl5ex 8 1 (-) gu4ex 8 1 (+) gl5ex 12 1 (-) gl1ex 3 1 (-) md4ex 5 2 (+) gl3ex 11 1 (-) gu4in 3 2 (+) gu4in 2 1 (+) gl5in 8 1 (-) gl2in 2 1 (-) gu3ex 1 1 (+) bd5in 7 4 (-) od2in 2 1 (+) ------gl2ex 5 1 (-) ov4in 1 1 (+) ------gl4in 3 1 (-) od3in 1 1 (+) ------dv2in 3 1 (+) ------od2ex 2 1 (+) ------mv1ex 1 1 (+) ------*Score = sum of AOI-specific scores defined by (23 – rank in top 22); max score is 11*22 = 242 **Count = number of appearance in top 20% (out of 11 opportunities); +/- indicates positive/negative correlation
77 Table 4 - 5. Analysis results for optimal VPM statistics identified during the AOI hypothesis test. This table gives results considering data from ecoregion 27 and the 10% (11 of 110) of VPM statistics. TotN PrpSensF InvFmRch Count (type of Count (type of Count (type of VPM Score* relationship)** VPM Score* relationship)** VPM Score* relationship)** bd4ex 110 11 (-) mv5ex 107 11 (+) av5ex 110 11 (+) bd5in 105 11 (-) mv5in 105 10 (+) dv5ex 107 11 (+) bd5ex 85 11 (-) mv4ex 90 10 (+) av4ex 89 11 (+) bd3ex 59 10 (-) mv4in 79 10 (+) dv4ex 88 11 (+) mv2ex 57 7 (+) av5in 58 10 (+) av3ex 65 10 (+) bd4in 51 9 (-) mv3ex 57 9 (+) ov3ex 55 10 (+) bd2ex 39 7 (-) mv1in 47 10 (+) ov4ex 49 10 (+) mv3in 36 8 (+) av5ex 42 11 (+) dv5in 42 10 (+) md1in 36 6 (+) mv3in 39 9 (+) ov5ex 33 11 (+) bd3in 30 5 (-) av4ex 23 10 (+) av5in 23 9 (+) mv3ex 30 6 (+) gu4in 14 2 (+) gl3ex 16 2 (-) mv4ex 22 5 (+) gu3in 10 1 (+) gl4ex 10 1 (-) md3in 18 7 (+) gu5in 9 1 (+) gl4in 9 1 (-) mv4in 9 4 (+) gu3ex 8 1 (+) gl5in 8 1 (-) gu5ex 8 1 (+) gu4ex 7 1 (+) gl2ex 7 1 (-) mv5in 8 4 (+) gu5ex 6 1 (+) dv3ex 7 6 (+) gu5in 7 1 (+) gu2ex 5 1 (+) gl3in 4 1 (-) bd2in 6 2 (-) mv2ex 5 4 (+) mv5ex 3 3 (+) bd1in 3 1 (-) gl4ex 4 1 (-) av4in 1 1 (+) md4in 3 2 (+) dv1in 4 1 (+) ------mv5ex 2 1 (+) av4in 3 3 (+) ------bd1ex 1 1 (-) av1in 3 3 (+) ------md2in 1 1 (+) gl5ex 1 1 (-) ------*Score = sum of AOI-specific scores defined by (12 – rank in top 11); max score is 11*11 = 121 **Count = number of appearance in top 10% (out of 11 opportunities); +/- indicates positive/negative correlation
78 5.0 Results - Testing the Effects of Watershed Size
5.1 Introduction In the previous section of this report, Testing Area of Influence (Spatial Scale), strong evidence emerged that vegetation phenology metric (VPM) statistics extracted for the entire watershed exhibited better linear correspondence with ecological response variable measurements than VPM statistics extracted from pixels hydrologically near and upstream from the sample point. This result indicates that VPM extractions should be made for the entire watershed when used for the purpose of estimating particular ecological response values, namely, ‘total nitrogen’ (denoted by ‘TotN’), ‘proportion sensitive fish taxa’ (‘PrpSensF’), and ‘invertebrate family-level richness’ (‘InvFmRch’). The analysis in this section builds from this premise, with the focus now turning to the impact of watershed size on target response variables and VPM-indicator relationships. When relating watershed-level spatial VPM data to ecological response measurements taken at the sample point, two basic questions emerge regarding the effect of watershed size on the relationship: (1) Do the ecological measurements themselves demonstrate dependence on watershed size and, (2) How does watershed size affect the relationship between watershed-level VPM statistics and the target values? These two questions are investigated in this section, with results presented and discussed.
5.2 Data and Methods The 110 VPM statistics described and used in the previous section on “area of influence” (AOI) are also used in this section. These consist of two sets of 1- through 5- year VPM temporal averages created from the 11 core VPMs, one set calculated using values immediately prior to and including the sampling year and one calculated excluding the sample year. Samples are ordered by watershed size, and sample subsets are determined using a moving window. The use of a moving data window provides an indicator of the generality of the relationship while also preserving watershed size- specific detail. While there is some variation in watershed size between ecoregions, most watersheds are smaller than 10,000 square kilometers (Figure 5-1). In general, the larger watersheds are located predominately in the western, more arid ecoregions. In the western most ecoregions such as the Western High Plains and Southwestern Tablelands, persistent stream flow needed for reliable field sampling can only be maintained far downstream from the top of the watershed. Scatter plots for watershed size distribution for the three target variables, stratified by ecoregion, are shown in Figure 5-1. To obtain the sample subsets used in this watershed size analysis, sampling points considered were screened by VPM data availability. As discussed in the AOI section, samples from years prior to 1994 were excluded because a complete set of the VPM variables could not be calculated. After screening, 2684 sample points (from 1368 unique sampling locations) for the target variable ‘TotN’, 932 sample points (from 766 unique sampling locations) for the target variable ‘PrpSensF’, and 969 sample points (from 661 unique sampling locations) for the target variable ‘InvFmRch’ remained for evaluation. Scatter plots for these distributions, stratified by ecoregion, are shown in Figure 5-2.
79 Given a target variable, associated samples were sorted by watershed size. Then, using a data subset window consisting of the 500 samples associated with the smallest watersheds, a bivariate analysis was performed by which VPM statistics and percent cropland information were related to target values. The window was then iterated one sample, so that the sample with the smallest watershed dropped out of consideration and the sample with smallest watershed not previously appearing in the window was included. Due to presence of multiple observations associated with some sample sites, sample year was used as a secondary ordering statistic. The choice of “500” for the window size was largely arbitrary, chosen fairly large to promote robustness and continuity of results. This design resulted in 2185 window iterations for the ‘TotN’ data, 433 window iterations for the ‘PrpSensF’ data, and 470 window iterations for the ‘InvFmRch’ data. We used the coefficient of determination (R2) statistic, which is the square of the correlation coefficient, to estimate “goodness of fit” of the pairwise relationships between each VPM statistic (denoted by X) and the target value (denoted by Y). R2 provides an estimate for the proportion of variance of Y that can be explained using an optimized linear regression model Y ≈ Ŷ = a + b*X, a contextual notion that leads to the equation 2 2 ˆ 2 R,()X YYYYY=−∑∑()kk /() −, where summation is over the sample points kk considered, and Y denotes the sample mean for Y. Window-specific R2 values were determined and charted to examine effects of watershed size.
5.3 Results Results from the bivariate analysis relating VPM statistics and percent cropland to sample site measurement data (‘TotN’, ‘PrpSensF’, and ‘InvFmRch’) are described in this section. First, the question “Do the ecological measurements themselves demonstrate dependence on watershed size?” is examined. Second, VPM statistics that exhibited superior colinearity with the target datasets are described and discussed that address question (2). With respect to ‘TotN’ and ‘InvFmRich’ target variables, one unique VPM (though not the same one) emerged as providing a clearly superior indicator of the respective target values compared to other VPMs. Consequently, we present additional results that examine this outcome in more detail. Initial bivariate results showed that the individual response target variables (‘TotN’, ‘PrpSensF’, or ‘InvFmRch’) demonstrated diverse preferences for different VPM statistics. To account for this observation, we examined the mean and median behavior of the top 20% (22 of 110) of VPM variables as indicators of statistical tendency. The choice of this fraction is largely arbitrary, presenting one possible balance between the optimistic bias expected when considering just the top few optimal variables to determine explanatory potential and the pessimistic bias expected when considering all possible variables without performing any variable selection. Figures 5-2 through 5-7 show results cast in this light, along with the corresponding mean target values. Results comparing target values to percent cropland, estimated using the NLCD, are shown for comparison and to provide context for discussion. Results for each target variable are presented using three distinct x-axis scalings in Figures 5-2 through 5-7. Specifically, square root of window mean watershed size is used in the (a) plots, square root of window median watershed size is used in the (b)
80 plots, and window iteration number is used in the (c) plots. “Square roots” are used to enhance detail among smaller watershed windows (where most of the results reside) and to facilitate interpretation (e.g., an x-value of “12” in an (a) or (b) plot can be thought of as reflecting watersheds approximately 12 km by 12 km in size). The window iteration plots further enhance detail among smaller watershed windows.
5.3.1 Watershed Size and Ecological Response Values Beginning with data windows (sub-samples) associated with the smallest watersheds, mean ‘TotN’ values begin at a maximal level (~4.2 mg/L) that decreases steadily as the data window is iterated (see Figure 5-3). This holds until the mean/median watershed size is ~400 sq. km (square root ≈ 20 km), after which window-averaged ‘TotN’ values partially rebound and then settle into a more confined range (~2.3-3.2 mg/L) as window iterations continue and mean/median watershed size increases. These observations suggest that ‘TotN’ values from watersheds less than approximately 100 sq. km in size (where ‘TotN’ values first enter the range just described) exhibit a substantial inverse dependence on watershed size. This dependence appears to dissipate among watersheds approximately 100-400 sq. km in size, eventually vanishing toward the upper end of this range. This relationship is explained by examining the fate of nitrogen (N) in stream/river networks. In general, field sampling events occurred during normal and base flow conditions when the source of most in-stream N was from subsurface water flow (soluble nitrate-N). Under such conditions, headwater streams typically experience an initial high loading and concentration of N. This is primarily a function of the relatively high ratio of terrestrial/aquatic contact area to stream water volume. As N is transported through the stream/river network, it is removed due to denitrification, organic matter buried in sediments, sediment sorption, plant and microbial uptake as a function of time in-stream. This removal results in a reduction in N concentration as one moves downstream and sample points represent pour points for increasingly large watersheds. Using a much smaller sample, Seitzerger et al. (2002) noted a watershed size dependency similar to that we observed, namely, N concentration decreases as watershed size increases until equilibrium is reached between N input and N removal. Beginning with data windows (sub-samples) associated with the smallest watersheds, mean ‘PrpSensF’ values begin at a minimal level (~9.6%) that increases steadily as the data window is iterated (see Figure 5-4). This holds until the mean watershed size is ~250 sq. km (square root ≈ 16 km) or the median watershed size is ~170 sq. km (square root ≈ 13 km), after which window-averaged ‘PrpSensF’ values settle into a more confined range (~13.6-14.8%) as window iterations continue and mean/median watershed size increases. These observations suggest that ‘PrpSensF’ values exhibit an appreciable direct dependence on watershed size when watershed size is below roughly 200 sq. km, after which point this dependence appears to abate substantially. This relationship likely reflects limited available fish habitat found in smaller watersheds, a condition exacerbated as watershed size decreases. This assertion assumes that stable stream flow becomes less certain and available in-stream habitat decreases in watersheds smaller than 200 sq. km, a threshold expected to depend on sample-specific hydrology and precipitation characteristics that dictate stream flow. Under such conditions, the opportunity for sensitive fish species to establish populations will decrease more quickly than for non-sensitive fish species.
81 Beginning with data windows (sub-samples) associated with the smallest watersheds, mean ‘InvFmRch’ values begin at a minimal level (~26 families) that increases steadily as the data window is iterated (see Figure 5-5). This holds until the mean watershed size is ~180 sq. km (square root ≈ 13.5 km) or the median watershed size is ~150 sq. km (square root ≈ 12.5 km). Then, for windows with mean watershed size in the range ~180-380 sq. km (or median watershed size in the range ~150-270 sq. km), window-averaged ‘InvFmRch’ values appear to stabilize around a maximal level (~29.15 families, with a range of ~29-29.3). Once beyond this watershed size range, however, ‘InvFmRch’ values begin to steadily decline until bottoming out at ~26.3 when the window of samples with the largest watersheds is considered. These observations suggest that for watersheds similar to those we are investigating, there is an optimal watershed size range with respect to maximizing the number of invertebrate families represented at a sample site. Within this size range, there does not appear to be a dependence of ‘InvFmRch’ on watershed size, but values from watersheds outside of this size range do appear to be markedly influenced by watershed size. This result potentially reflects an optimization of invertebrate habitat associated with moderately-sized watersheds, where the in-stream environment may exhibit maximal ecological complexity/heterogeneity due to the lack of domination by either terrestrial influences (as would be observed in smaller watersheds) or aquatic influences (as would be observed in larger watersheds). In summary, all three ecological target variables demonstrated some regular variation (trending) that is apparently dependent on watershed size. ‘InvFmRch’ exhibited a two-sided dependency on watershed size, whereas ‘TotN’ and ‘PrpSensF’ values appeared to depend on watershed size only at the smaller end of the size range. ‘TotN’ values monotonically declined in value level as watershed size increased, eventually rebounding a bit and leveling off (stabilizing) after reaching a particular size threshold. ‘PrpSensF’ monotonically increased in value level as watershed size increased, eventually leveling off after reaching a particular size threshold. ‘InvFmRch’ demonstrated uptrending and saturating behavior similar to ‘PrpSensF’, but with a roughly symmetric (when plotted against window iteration) downtrending regime observed at the upper extreme in watershed size, resulting in a quasi-inverse parabolic relationship between ‘InvFmRch’ and watershed size.
5.3.2 Watershed Size and VPM Performance To economize the discussion in this section, we use the following definitions:
• r2med = median R2 of top 20% VPMs • r2avg = mean R2 of top 20% VPMs • r2cp = cropland density R2
Also, given two n-point value series denoted by X and Y, define the “generic” (or “symmetric”, or “commutative”) version of mean absolute percent error (MAPE):
n 200 • MAPE[X,Y] = 100*mean(|X – Y|/mean[X,Y]) = n ∑ X jj−+YXY/ () jj j=1
82 In the traditional definition for MAPE, either X or Y values are used in the denominator to make the output scale-free but relative to that one particular input. In the variant defined above, the roles of X and Y are interchangeable, which is useful when there is no preference regarding which of the inputs is used for descaling.
5.3.2.1 ‘TotN’ Analysis The sub-sample window relationships between mean and median of the top 20% (top 22) of R2 values comparing VPM statistics to ‘TotN’ values are shown in Figure 5-3. Also depicted is the sub-sample window relationship between percent cropland and ‘TotN’, as well as window-averaged ‘TotN’ values (using a secondary y-axis). Among the three distinct ecological response variables under consideration in this section, the strongest linear correspondences with VPM statistics were observed when analyzing ‘TotN’ values. In particular, the relationship between the top 20% of VPM statistics and ‘TotN’ values was maximized when mean/median watershed size exceeded ~3600 sq. km (square root ≈ 60 km). Data windows with central watershed size values beyond this point frequently exhibited top 20% median R2 values greater than 0.4 and mean R2 values greater than 0.5. One obvious observation from Figure 5-3 involves the exceptional correspondence between ‘r2med’ and ‘r2cp’. Specifically, we have R2[r2med,r2cp] = 0.965 and MAPE[r2med,r2cp] = 8.65%. This extreme similarity between ‘r2med’ and ‘r2cp’ strongly suggests that the largely static, land cover aspect of VPM information content (specifically, its reflection of cropland fraction) is a major component driving the relationship between VPMs and ‘TotN’. The advantage in using the VPMs remains because they are much easier to compute, and can be computed with greater objectivity, than cropland fraction. VPMs also have the advantage of being current. But the fact that NLCD cropland fraction based on data from the early to mid 1990s performed so comparably raises questions about the advantage of VPM “timeliness” with respect to the prediction of ‘TotN’ values. Consistent with the results obtained in the AOI analysis, BD (rate of senescence) variables dominated the other VPMs and were the only variables in the top 20% for every sample window (see the “Count” column in the ‘TotN’ section of Table 5-1). This performance was underscored by the stark contrast between BD variable and the other VPMs in ranking (see the corresponding “Score” column in Table 5-1). The latter property is also evident in the fact that the ‘r2avg’ profile in Figure 5-3 is substantially greater than ‘r2med’ profile, suggesting a high-value skew (caused by the BD results) among the top 20% (top 22) of the highest correlating VPMs. Further inspection of the results presented in Table 5-1 provides additional perspective regarding the dominance of the BD variables in this examination. The sum of the scores from the ten BD variables is 382,283. The maximum possible score sum is 382,375 (=2185*sum(13:22)), indicating that these 10 variables left only 92 “points” unaccounted for; i.e., BD variables accounted for 99.976% of the maximum possible cumulative top 10 score. This means that at most 7 of 21,850 possible top 10 opportunities were filled by non-BD variables.
83 5.3.2.2 ‘PrpSensF’ Analysis The sub-sample window relationships between mean and median of the top 20% (top 22) of R2 values comparing VPM statistics to ‘PrpSensF’ values are shown in Figure 5-4. Also depicted is the sub-sample window relationship between percent cropland and ‘PrpSensF’, as well as window-averaged ‘PrpSensF’ values (using a secondary y-axis). An interesting observation involves the moderate correspondence between ‘r2med’ and ‘r2cp’. Specifically, we have R2[r2med,r2cp] = 0.294, with a negative underlying correlation (-0.542). We presently do not have a hypothesis explaining this relationship. Regardless of this assessment, the relationship between ‘PrpSensF’ and percent cropland is quite weak (maximum R2 < 0.063) and of no practical value. Pragmatically speaking, the situation with the VPMs is not greatly improved compared to the percent cropland results, with only four of the 433 top 20% median R2 values exceeding 0.2 (none of the top 20% mean R2 values exceeded this threshold). In spite of these generally weak relationships, one observation that can be made is that VPM relationships to ‘PrpSensF’ values improved as the direct dependency of ‘PrpSensF’ on watershed size abated. The relationships continued to improve even after ‘PrpSensF’ values stabilized, with optimal results observed when data windows associated with the largest watershed sizes were considered. As in the AOI analysis, AV (growing season average NDVI) and GU (rate of green-up) variables were dominant in the ‘PrpSensF’ assessment. All 12 of the variables appearing in the top 20% for every sample window (see the “Count” column in the ‘PrpSensF’ section of Table 5-1) are AV or GU variables, which actually comprise the top 16 most frequently appearing variables. In terms of “Score”, AV and GU variables comprise the top 18 performers. All other variables appearing at least once in a top 20% list were either MV (maximum NDVI) or AC (accumulated growing season NDVI) variables. In this watershed size study, the worst general relationship between VPMs and the three target variables was observed when ‘PrpSensF’ values were considered. Interestingly, this assessment also produced the least diverse set of VPM statistics (34 in total) that comprised all of the top 22 lists across the different data windows.
5.3.2.3 ‘InvFmRch’ Analysis The sub-sample window relationships between mean and median of the top 20% (top 22) of R2 values comparing VPM statistics to ‘InvFmRch’ values are shown in Figure 5-5. Also depicted is the sub-sample window relationship between percent cropland and ‘InvFmRch’, as well as window-averaged ‘InvFmRch’ values (using a secondary y-axis). Generally speaking, the linear correspondence between percent cropland and ‘InvFmRch’ values was worse than for the other two target variables, with no data window producing an R2 value greater than 0.05. Among the three distinct ecological response variables under consideration in this section, the most consistent linear correspondences with VPM statistics across different watershed sizes were observed when analyzing ‘InvFmRch’ values. In particular, the relationship between the mean R2 values from the top 20% of VPM statistics and ‘InvFmRch’ values from the different data windows all occurred in the range [0.26,0.34] (the range for corresponding median R2 values was [0.23,0.32]). R2 values generally increased until the reaching the watershed size range corresponding with maximum
84 ‘InvFmRch’ values, after which they remained fairly level across the remaining data windows. As observed in the AOI analysis, only more so, AV (growing season average NDVI) variables were dominant and were the only variables appearing in the top 20% for every sample window (see the “Count” column in the ‘InvFmRch’ section of Table 5-1). They also performed markedly better than the other VPMs in ranking (see the corresponding “Score” column in Table 5-1). This property is also evident in the fact that ‘r2avg’ profile in Figure 5-5 is notably greater than ‘r2med’ profile, suggesting a high- value skew (caused by the AV results) among the top 20% (top 22) of the highest correlating VPMs. Further inspection of the results presented in Table 5-1 provides additional perspective regarding the dominance of the AV variables in this examination. The sum of the scores from the ten AV variables is 82,250 (=470*sum(13:22), which is the maximum possible), indicating that these 10 variables comprised the top 10 list from all 470 window iterations.
5.3.2.4 Examining Optimal VPMs for estimation of ‘TotN’ and ‘InvFmRch’ The obvious superiority of the BD variables in the ‘TotN’ analysis and the AV variables in the ‘InvFmRch’ analysis warranted more specific assessment. Given that these two core VPMs cannot be calculated until the end of the growing season, in addition to the uncertainty of collection date for the sampled target values, the analysis in this section is restricted to just the five “EX” (sample year excluded) VPM statistics. This restriction assures that results are free from any data anachronisms. The larger sample associated with the ‘TotN’ data set (n = 2684) allowed for the use of a larger data window in the watershed size examination. Generally speaking, larger data windows provide better indicators of the generality of the relationships at the expense of losing watershed size-specific detail. Results from the BD-‘TotN’ assessment using a 500-point window are shown in Figure 5-6, and results using a 1000-point window are shown in Figure 5-7. Several observations can be made from the results shown in Figures 5-5 and 5-6. Foremost among these is the obvious parallel behavior between percent cropland R2 values and BD R2 values, which suggests that an appreciable component of the BD- ‘TotN’ relationship is attributable to the cropland density information implicit in the BD summary statistics. However, BD R2 values are substantially greater than percent cropland R2 values, indicating that the BD statistics harbor additional useful information with respect to predicting ‘TotN’ values. The relationship between BD and ‘TotN’ values is roughly flat (fluctuating around R2 ≈ 0.33 in Figure 5-6, or R2 ≈ 0.36 in Figure 5-7) throughout the portion of the data where watershed size apparently has an inverse influence on ‘TotN’ values. Once this influence abates, then the relationship steadily improves until R2 values in the range ~0.6-0.68 are achieved when 500-point data windows associated with the largest watersheds are considered (see Figure 5-6; in Figure 5-7, where 1000-point data windows are used, this range is approximately ~0.55-0.6). Another observation associated with the behavior of the R2 results is the convergence of the R2 series from the five individual BD variables as watershed size increases. When 500-point windows are considered, the five series initially span an R2
85 range about ~0.1 in width (range width is ~0.06 when 1000-point windows are used), and this spread tapers until nearly vanishing approximately where the watershed size influence on ‘TotN’ values disappears and BD-‘TotN’ R2 values begin increasing. The disappearance of the spread in this exercise indicates that it may not matter which of the five temporal BD aggregates one uses once watersheds exceed a particular size threshold. Though this distinction cannot be ascertained from the plots, among the smaller watershed data windows where performance varied among the different BD variables, the better performers corresponded with the longer-span aggregates. For the AV-‘InvFmRch’ assessment (n = 969), the window size was kept at 500. The general improvement observed when focusing exclusively on the five AV-EX variables compared to the top 20% results was approximately 0.05 R2 “units” (compare Figure 5-8 to Figure 5-5). As observed in the top 20% assessment, the relationship between the investigated VPMs and ‘InvFmRch’ data appeared to depend little on watershed size, increasing slightly until the range of maximum ‘InvFmRch’ values was encountered, and then remaining fairly stable across the remainder of the window evaluations. The mean AV-EX performance (in terms of R2) varied from ~0.32 to ~0.38. R2 values among the unique AV variables maintained their spread across all of the data windows. Though this distinction cannot be ascertained from Figure 5-8, as observed in the BD-‘TotN’ analysis, the better performers corresponded with the longer- span aggregates. In particular, the distinct lowest R2 profile in Figure 5-8 corresponds to the ‘av1ex’ variable, and the next one up with the ‘av2ex’ variable. Performances of ‘av3ex’, ‘av4ex’, and ‘av5ex’ were very similar with no clear preference indicated, as each of these three variables produced some of the largest R2 values observed when the five AV-EX variables were considered.
5.4 Conclusions The primary goals of the analysis described in this section were to evaluate the effect of watershed size on (1) sample site ecological response values, and (2) the relationship between these values and VPM statistics. Regarding (1), analysis of data sub-samples stratified by watershed size revealed that ‘TotN’, ‘PrpSensF’, and ‘InvFmRch’ data each demonstrated some dependence on watershed size. In particular, mean behavior of ‘TotN’ and ‘PrpSensF’ values from samples associated with smaller watersheds (relative to each respective total sample) appeared to trend with watershed size, inversely for ‘TotN’ and directly for ‘PrpSensF’. Mean ‘InvFmRch’ values demonstrated a two-sided dependence on watershed size. Specifically, values from samples associated with smaller watersheds (relative to the total sample) appeared to trend upward with increasing watershed size, then stabilize in level for a non-negligible interval of sizes, and finally trend downward as increasingly larger watersheds were considered. Regarding (2), relationships between VPM statistics and ‘TotN’ and ‘PrpSensF’ values were clearly strongest among the sub-samples associated with larger watersheds. The same was true when ‘InvFmRch’ values were examined, but with notably less performance decline observed as sub-samples associated with smaller watersheds were considered. Among the three target variables, the strongest relationships were observed between VPM statistics and ‘TotN’ values, where mean and median top 20% R2 values were attained that were approximately 0.5. However, this relationship degraded heavily
86 as watershed size decreased, with R2 values eventually fluctuating ~0.23 once watershed size effects began to exert notable influence on ‘TotN’ values. Relationships between the top 20% VPM statistics and ‘PrpSensF’ values varied with watershed size in a manner similar to ‘TotN’ values, albeit with R2 values at approximately half the magnitude of those observed in the ‘TotN’ analysis. Relationships between the top 20% VPM statistics and ‘InvFmRch’ data did not vary greatly with watershed size, perhaps indicating a more general relationship between VPM statistics and this quantity than between VPM statistics and the other two target variables. Most R2 values between mean and median top 20% VPM statistics and ‘InvFmRch’ data were in the range ~0.2-0.33. VPM variable preferences observed during this watershed size evaluation exercise were consistent with the preferences observed in the AOI analysis. Specifically, BD (rate of senescence) variables were optimal in the ‘TotN’ assessment, AV (growing season average NDVI) and GU (rate of green-up) variables were optimal when ‘PrpSensF’ values were considered, and AV variables were superior to other VPMs when correlated with ‘InvFmRch’ values. Due to the clear distinction of just one preferred VPM statistic when examining either ‘TotN’ or ‘InvFmRch’ values, in addition to the generally higher R2 values observed when considering these two target variables than ‘PrpSensF’, the BD-‘TotN’ and AV-‘InvFmRch’ relationships were the subject of additional analysis. The BD- ‘TotN’ examination used two different window sizes (500 and 1000) and the five BD-EX variables. In this exercise, R2 values were observed to vary near 0.35 across the range of sub-sample watershed sizes where watershed size apparently influenced ‘TotN’ values, eventually reaching levels ~0.6 after the ‘TotN’-watershed size relationship abated and sub-samples associated with larger watersheds were inspected. The AV-‘InvFmRch’ examination used just a 500-point window (due to the smaller total sample size compared to the ‘TotN’ sample) and the five AV-EX variables. In this exercise, most R2 values exceeded 0.35. Those that fell below this value occurred exclusively during the regime of apparent ‘InvFmRch’ dependence on watershed size that was observed for the smaller watershed data windows. In summary, some clear dependencies of ‘TotN’, ‘PrpSensF’, and ‘InvFmRch’ values on watershed size were observed across certain (relative to the respective total sample) watershed size ranges. All three target variables exhibited a watershed size dependency when sample points associated with smaller watersheds were considered, and ‘InvFmRch’ values also demonstrated a watershed size dependency when sample points associated with larger watersheds were examined. Analysis of linear correspondences between VPM statistics and ‘TotN’ and ‘PrpSensF’ values found the relationships to improve as the dependency of target values on watershed size degraded. Interestingly, watershed size had notably less effect on the ‘InvFmRch’-VPM relationships in spite of the apparent greater dependence of ‘InvFmRch’ values on watershed size than either of the other two target quantities.
87 (a)
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Figure 5 - 1. Watershed size distributions, stratified by ecoregion, for (a) ‘TotN’, (b) ‘PrpSensF’, and (c) ‘InvFmRch’ samples used in the watershed size analysis. Black dots demark the sample means.
88 (a)
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Figure 5 - 2. Target sample distributions, stratified by ecoregion, for (a) ‘TotN’, (b) ‘PrpSensF’, and (c) ‘InvFmRch’ values used in the watershed size analysis. Black dots demark the sample means.
89
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Figure 5 - 3. The effects of sample point upstream watershed size on the relationship between ‘TotN’ and VPMs (and between ‘TotN’ and percent cropland) are shown here. The same data are depicted using three different x-axis scalings characterizing the data windows: (a) square root of mean watershed size, (b) square root of median watershed size, and (c) window iteration number.
90
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Figure 5 - 4. The effects of sample point upstream watershed size on the relationship between ‘PrpSensF’ and VPMs (and between ‘PrpSensF’ and percent cropland) are shown here. The same data are depicted using three different x-axis scalings characterizing the data windows: (a) square root of mean watershed size, (b) square root of median watershed size, and (c) window iteration number.
91
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Figure 5 - 5. The effects of sample point upstream watershed size on the relationship between ‘InvFmRch’ and VPMs (and between ‘InvFmRch’ and percent cropland) are shown here. The same data are depicted using three different x-axis scalings characterizing the data windows: (a) square root of mean watershed size, (b) square root of median watershed size, and (c) window iteration number.
92
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Figure 5 - 6. The effects of sample point upstream watershed size on the relationship between ‘TotN’ and BD-EX VPMs (and between ‘TotN’ and percent cropland) are shown here, using a 500-point sliding data window. The same data are depicted using three different x-axis scalings characterizing the data windows: (a) square root of mean watershed size, (b) square root of median watershed size, and (c) window iteration number.
93
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Figure 5 - 7. The effects of sample point upstream watershed size on the relationship between ‘TotN’ and BD-EX VPMs (and between ‘TotN’ and percent cropland) are shown here, using a 1000-point sliding data window. The same data are depicted using three different x-axis scalings characterizing the data windows: (a) square root of mean watershed size, (b) square root of median watershed size, and (c) window iteration number.
94
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Figure 5 - 8. The effects of sample point upstream watershed size on the relationship between ‘InvFmRch’ and AV-EX VPMs (and between ‘InvFmRch’ and percent cropland) are shown here. The same data are depicted using three different x-axis scalings characterizing the data windows: (a) square root of mean watershed size, (b) square root of median watershed size, and (c) window iteration number.
95 Table 5 - 1. Analysis results for optimal VPM statistics identified during the watershed size test. This table gives results from the top 20% (22 of 110) of VPM statistics across all data windows. TotN PctSensF InvFmRch Count (type of Count (type of Count (type of VPM Score* relationship)** VPM Score* relationship)** VPM Score* relationship)** bd4in 43534 2185 (-) av5ex 8376 433 (+) av4in 9578 470 (+) bd3in 43140 2185 (-) av5in 7834 433 (+) av3ex 9515 470 (+) bd2in 41961 2185 (-) gu5in 7815 433 (+) av4ex 9411 470 (+) bd5in 40674 2185 (-) gu4in 7468 433 (+) av5in 9361 470 (+) bd3ex 39407 2185 (-) av4ex 7225 433 (+) av5ex 9119 470 (+) bd4ex 37695 2185 (-) av4in 6745 433 (+) av3in 7987 470 (+) bd5ex 36863 2185 (-) gu3in 5872 433 (+) av2ex 7539 470 (+) bd1ex 35306 2185 (-) gu1in 5824 320 (+) av2in 7050 470 (+) bd2ex 35025 2185 (-) av3ex 5729 433 (+) av1ex 6575 470 (+) bd1in 28678 2185 (-) av3in 5682 433 (+) av1in 6115 470 (+) md3in 17123 2040 (+) gu2in 5298 433 (+) ac4ex 3693 350 (+) md4in 16950 2006 (+) gu4ex 4815 377 (+) ac5ex 3367 339 (+) md2in 15153 1623 (+) av2in 4810 433 (+) ov2ex 2845 354 (+) md5in 12481 1875 (+) av1in 4496 394 (+) ac5in 2766 332 (+) mv5ex 9850 1120 (+) av2ex 4256 433 (+) ac3ex 2406 306 (+) mv4ex 8476 1113 (+) gu3ex 4010 373 (+) dv4in 2278 424 (+) md3ex 7890 1443 (+) av1ex 2422 390 (+) ov3ex 2202 321 (+) mv5in 7536 877 (+) gu5ex 2044 288 (+) mv5ex 1795 231 (+) md1in 6082 882 (+) mv5ex 1981 321 (+) ac4in 1781 259 (+) mv4in 5985 811 (+) mv5in 1263 326 (+) mv4ex 1473 222 (+) md2ex 5919 924 (+) mv4ex 1120 232 (+) ac2ex 1130 186 (+) ov2in 5913 565 (-) ac1in 821 113 (+) mv5in 1129 146 (+) mv3ex 5175 799 (+) mv4in 659 267 (+) ov4ex 1091 245 (+) ov3in 5086 535 (-) mv3ex 636 165 (+) dv3ex 1027 193 (+) md4ex 5069 1108 (+) mv1in 527 134 (+) mv3ex 1001 146 (+) md1ex 4592 713 (+) ac2in 521 113 (+) ov5ex 918 224 (+) ov4in 4206 552 (-) gu2ex 383 67 (+) ac3in 871 160 (+) mv3in 3717 731 (+) ac3in 324 107 (+) mv4in 821 109 (+) dv3in 3086 669 (-) ac5in 199 107 (+) ov3in 780 192 (+) mv2ex 2750 737 (+) mv3in 113 61 (+) mv2ex 653 108 (+) md5ex 2691 860 (+) ac5ex 99 46 (+) mv3in 589 103 (+) ov5in 2509 491 (-) mv2ex 94 53 (+) ac1ex 567 138 (+) gu5ex 2276 350 (+) mv2in 50 38 (+) ov4in 429 199 (+) dv2in 2163 571 (-) ac4in 38 38 (+) ac2in 246 92 (+) mv2in 1824 569 (+) ------mv2in 241 62 (+) dv4in 1376 414 (-) ------mv1in 221 55 (+) gu5in 1103 278 (+) ------mv1ex 95 36 (+) ov1ex 976 368 (-) ------ov5in 84 32 (+) dv1in 707 244 (-) ------dv5in 76 27 (+) ov3ex 466 211 (-) ------dv3in 66 32 (+) gu4in 405 214 (+) ------ov1ex 12 11 (+) dv2ex 294 130 (-) ------dv5ex 7 6 (+) ov4ex 175 92 (-) ------dv5in 160 68 (-) ------dv3ex 120 84 (-) ------mv1in 83 65 (+) ------dv5ex 67 28 (-) ------gu4ex 37 21 (+) ------mv1ex 32 20 (+) ------ov2ex 11 11 (-) ------gu3in 8 8 (+) ------*Score = sum of AOI-specific scores defined by (23 – rank in top 22); max score for ‘TotN’ is 2185*22 = 48070; 433*22 = 9526 for ‘PctSensF’; and 470*22 = 10340 for ‘InvFmRch’ **Count = number of appearance in top 20%, out of 2185 opportunities for ‘TotN’, 433 for ‘PctSensF’, and 470 for ‘InvFmRch’; +/- indicates positive/negative correlation
96 6.0 Results - Model Development
6.1 Introduction The purpose of this analysis is to produce a classification scheme to assess watershed vulnerability using regression tree analysis (RTA). The analysis in this section focuses on evaluating the utility of static and dynamic predictors to estimate total nitrogen (‘TotN’), proportion sensitive fish taxa (‘PrpSensF’), and invertebrate family- level richness (‘InvFmRch’). Aspects of spatial and temporal scales are also incorporated into the modeling endeavor to identify the most appropriate modeling approach for EPA Region 7. To examine whether ecoregion-specific or global modeling is better suited, ecoregion-specific models for three ecoregions are built and compared to global models. To assess whether shorter or longer temporal VPM averages better predict response variables, RT models are built and compared using 1-year and 5-year aggregates of the VPM variables.
6.2 Data and Methods RTA was used in this modeling exercise for two purposes. First, RTA is used as a data-mining tool to identify landscape predictor variables (static and dynamic stressors) across multiple scales (spatial and temporal) that accurately and reliably model the chemistry and biological response variables. Second, RTA is used in the development of a classification scheme for watershed vulnerability. RTA is a non-parametric statistical method that allows a target or response variable to be modeled by continuous and categorical predictor variables. It is a recursive, binary tree-growing algorithm based on minimizing impurity using the least- squared deviation measure R(t). For split s at node t, the least-squared deviation criterion (Ф(s,t) = R(t) – pLR(tL)-pRR(tR), where pL and pR are the proportions of observations sent to the left (tL) and right (tR) nodes, respectively) identifies the predictor variable that maximizes Ф(s,t). When weighted, Ф(s,t) represents the reduction of impurity and is identified at each split as the “improvement” value. Tree growth or splitting of the response variable continues until either a user-specified minimum homogeneity or maximum complexity stopping criterion is met. Regression trees (RTs) were generated for ten sub-samples for each response variable using a random 80%-20% partition of the data for model training and validation, respectively. Training sets were used for RT construction, and validation sets were used to assess “out of sample” accuracy of the tree model. An eleventh tree was generated using all sample points. To avoid overfitting the model, cost-complexity pruning (using the one standard error risk rule) was used to identify optimal tree size (Breiman 1984). Cost-complexity pruning calculates the linear combination of the tree’s misclassification risk and complexity (the number of terminal nodes). A series of successively pruned trees are built and evaluated to find the smallest subtree whose risk is within one standard error of the tree with the minimum risk (i.e., the largest tree where each terminal node is perfectly homogeneous, containing only samples with identical response variable values). Each terminal node in the pruned tree is assigned the mean value of the response variable samples that are assigned to the node. This value is used as a prediction for future observations landing in the terminal node. The proportion of variance in the response variable explained by the tree model, or the “R2 equivalent” (R2-E), is equal to 1
97 - {the risk estimate}, where the risk estimate equals the remaining fraction of unexplained variance in the response variable. A tree with no growth, or only a root node, would have a risk estimate equal to one and thus R2-E = 0. For simplicity, since calculation of R2-E is identical to that of the standard coefficient of determination, these values will be referred to using the conventional “R2” notation. Variable importance is calculated by weighting the average improvement values across the models generated from the ten sub-samples by variable frequency. Initial RTA was essentially a data mining exercise to identify (1) the utility of dynamic landscape predictors as compared to traditionally used static predictors, (2) the appropriate modeling spatial scale (global or all ecoregions vs. ecoregion-specific models), and (3) the appropriate modeling temporal scale for dynamic landscape predictors (1-year or longer term average). Regression trees were generated using the following criteria: maximum tree depth = 10 levels; parent nodes have a minimum of n = 5; and child nodes have a minimum of n = 1; and a minimum impurity measure (change in within-node variance) of 1%. Traditionally, land use/land cover (especially cropland fraction) estimates in conjunction with soil characteristics, watershed morphology and other static measures of anthropogenic stress have been used to model or predict aquatic response variables. To determine the utility of both the static predictors and the dynamic VPM predictors, three sets of predictors were entered into separate RTAs (Data & Methods: Table 2). These are:
1. Static-only 2. Static-Dynamic 3. Dynamic-only
To examine whether ecoregion-specific or global modeling was better suited for EPA Region 7, ecoregion-specific models for three ecoregions (Central Irregular Plains, Ozark Highlands, and Western Corn Belt Plains) were generated and compared against global model results. Ecoregions were selected based on sample size and, secondarily, contrasting land use/land cover. To examine temporal scale, three VPM temporal windows were subjected to RTA to determine (1) how a reduced set of dynamic landscape predictors could predict response variables while maintaining model generalization accuracy, and (2) whether shorter or longer temporal windows yield landscape variables that better predict response variables. The three temporal windows compared are:
1. a 5-year window including the sample year 2. a 1-year window corresponding to the sample year 3. a 1-year window prior to the sample year
For the temporal window examination exercise, regression tree models were generated using the following criteria: maximum tree depth = 4 levels; parent nodes have a minimum of n = 5; and child nodes have a minimum of n = 1; and a minimum impurity measure (change of within-node variance) of 1%.
98 Lastly, the top VPM predictors, identified by variable importance from a reduced dynamic predictor set, were subjected to RTA. For each response variable, the largest common tree form, in terms of structure and composition, across the ten sub-samples was identified as the “fixed model”. In some cases, branches were pruned or grown to obtain the fixed model tree structure. A final model, with the structure and composition of the “fixed model”, for each response variable was generated using all data points (i.e., no points withheld for model validation). R2 values were calculated for cost-complexity pruned and fixed models. The final model was applied to landscape metrics for each watershed to identify terminal node membership. Maps of predicted values were created for watershed pour points for each response variable to illustrate regional variation in each predicted response variable. In RTA, sample sites were restricted to the seven dominant ecoregions in EPA Region 7 (Central Great Plains, Central Irregular, Plains, Flint Hills, Nebraska Sand Hills, Ozark Highlands, Western Corn Belt Plains, and Western High Plains). Sites sampled prior to 1994 were excluded in RTA since 5-year aggregates of the VPM statistics could not be calculated for those sites. Sample size varied by response variable. For ‘TotN’, n = 1158; for ‘PrpSensF’, n = 638; and for ‘InvFmRch’, n = 591.
6.3 Results 6.3.1 Landscape Predictors: Static vs. Dynamic Land Use/Land Cover (LULC) statistics are traditionally used to estimate expected watershed water quality characteristics. While LULC maps provide useful landscape information (e.g., percent cropland), they only represent a snapshot in time, are time-consuming and costly to produce, and vary in development methodologies, classification schemes, and spatial resolution. Furthermore, because a LULC map is static or infrequently updated, it is unable to reflect temporal changes in land cover, land management practices and climatic conditions. These limitations generally characterize the other static landscape predictors as well. Results from RTAs using the static-only, static-dynamic, and dynamic-only predictor datasets for ‘TotN’, ‘PrpSensF’, and ‘InvFmRch’ are described in this section.
6.3.1.1 ‘TotN’ RT Models For ‘TotN’, the static predictor set averaged a resubstitution R2 of 0.39 (± 0.03) for the ten sub-samples (Table 1). Percent cropland and soil K-factor (KFACT) were the only two static landscape predictors entering regression tree models and therefore the only two with variable importance (Table 2). All ten trees initially split on percent cropland, four trees had secondary splits on KFACT, and one tree had secondary splits on both percent cropland and KFACT. Across the ten sub-samples, the static-dynamic predictor set and dynamic predictor set explained more variation in ‘TotN’ than the static predictor set (Table 1; Figure 6-1). The average resubstitution R2 across the ten validation sets increased to 0.47 (± 0.09) and 0.48 (± 0.10) for the static-dynamic predictor set and dynamic predictor set, respectively. When combining static and dynamic landscape predictors, longer temporal windows for average brown down rate (BDA 3-5 years) made initial splits in eight of the ten training sub-sample tree models, while percent cropland made initial splits in two tree
99 models. Both BDA and percent cropland split the training data similarly into approximately 80/20% subsets. The models predicted higher ‘TotN’ for watersheds with BDA less than approximately –0.069 (e.g., Figure 6-2). The models also predicted higher ‘TotN’ for watersheds that are at least 83.6% cultivated (e.g., Figure 6-3). ‘Bda5in’ had the highest variable importance followed by percent cropland, ‘bda3in’, and ‘ova3in’ (Table 3). When dynamic landscape predictors were used exclusively, longer temporal windows of BDA and average NDVI at greenup onset (OVA) were the most frequently occurring dynamic predictors and had the highest variable importance across the ten tree models (Table 4). The dynamic predictor set averaged higher R2 than the static predictor set. However, tree topology (structure and composition) varied appreciably among the ten trees. Four trees consisted of a single split on BDA, while the other six also initially split on BDA but grew complex trees with only a second split on OVA in common. Again, steeper (i.e., more negative, indicating relatively rapid senescence) BDA values predicted higher ‘TotN’ (Figure 6-4), and when the node split at the second level on OVA, lower OVA predicted higher ‘TotN’. To some degree, BDA provides a surrogate for percent cropland in the regression tree models. Annual agricultural crops generally senesce more rapidly than natural vegetation, so a faster mean rate of senescence can reflect a greater cropland fraction within a watershed. Comparing maps of the fifteen-year average rate of senescence and percent cropland within 1-km AVHRR pixels shows some correspondence exists between the two landscape predictors (Figure 3-9 and Figure 3-13). However, BDA values less than approximately –0.069 do not represent all cropland types and only largely characterizes regions of homogenous crop types (i.e., the corn belt in the Western Corn Belt Plains and Central Great Plains, the wheat belt in the Central Great Plains, and several smaller agricultural areas in the Western High Plains and Central Irregular Plains). Other agricultural areas in the Central Great Plains and Western High Plains not corresponding with steep BDA are more heterogeneous, and in these locations BDA reflects a blend of crop types (which often have distinctive phenologies) characterizing many of the 1-km AVHRR pixel footprints. This result suggests that BDA provides additional information beyond percent cropland and may identify types of agricultural landscapes with different loading capacities to streams. In separating homogenous and heterogeneous crop regions, BDA identified a region (the homogenous corn belt region) that, due to land management practices, tends to have greater potential loading capacities than regions of mixed crop types and of natural vegetation (e.g.,forests of the Ozark Highlands and grasslands in the Flint Hills and Nebraska Sand Hills) that have lower or more diffuse potential loading capacities.
6.3.1.2 ‘PrpSensF’ RT Models For ‘PrpSensF’, the static predictor set averaged a resubstitution R2 of 0.57 (± 0.05) across the ten sub-samples (Table 1; Figure 6-5). Ecoregion was the first split in the ten tree models, with the second split often based on average watershed KFACT. These two variables distinctly had the highest variable importance followed by nine other static variables (Table 2). The first split separated the Ozark Highlands from the other ecoregions, and regression tree models indicated this node to have the highest ‘PrpSensF’ (~0.38). On secondary splits for the remaining six ecoregions, soil KFACT values less
100 than approximately 0.29 predicted ‘PrpSensF’ ~ 0.18 and correspond to areas in the Nebraska Sand Hills and portions of the Western Corn Belt Plains, Central Great Plains and Western High Plains, while KFACT > 0.29 predicted ‘PrpSensF’ ~ 0.07 (Figure 6-6). Beyond the secondary split, tree topology varied. Even so, model validation results remained consistently high across the ten trials, and most splits and predicted values were easily interpreted for the static predictors (e.g., higher population density (POPDEN) and higher percent cropland predicted lower ‘PrpSensF’ values). The addition of dynamic landscape predictors increased the average resubstitution R2 from 0.57 (± 0.05) to 0.62 (± 0.07) (Table 1; Figure 6-5). Ecoregion and KFACT typically entered as the first and second splitting predictors, respectively, and produced similar tree topology as the static predictor set (Figure 6-7). Ecoregion and KFACT had the highest variable importance followed by the 4-year average standard deviation for date of dormancy (‘dds4ex’) and ‘POPDEN’ (Table 3). Tree topology varied and trees typically grew large. The dynamic predictor set averaged a resubstitution R2 of 0.56 (± 0.06) across the ten sub-samples. However, validation accuracies decreased considerably more for the dynamic predictor set than the static and static-dynamic predictor sets (Table 1). Longer temporal windows for OVA (3- to 5-year) were the first splitting predictors in eight of ten models. A 5-year temporal window for average rate of greenup (‘gua5ex’) was consistently the second splitting predictor. Longer temporal windows of DVS were a third splitting predictor in nine of ten models. Longer temporal windows of OVA, DVS, and GUA were the most frequently occurring dynamic predictors and had the highest importance values across the ten models (Table 4). OVA values greater than approximately 0.44 predicted the highest ‘PrpSensF’, and OVA < 0.44 and GUA values > 0.057 predicted moderate ‘PrpSensF’ (Figure 6-8). A map of the fifteen-year average NDVI value at greenup onset shows that OVA > 0.44 corresponds to the Ozark Highlands and small portions of the wheat belt (Figure 3-3). Meanwhile, OVA < 0.44 and GUA > 0.057 correspond to grasslands in the Flint Hills and Sand Hills as well as agriculture in the Western Corn Belt Plains and Central Great Plains (Figure 3-3 and Figure 3-8).
6.3.1.3 ‘InvFmRch’ RT Models The static predictor set for ‘InvFmRch’ had an average resubstitution R2 of 0.38 (± 0.03) for the ten sub-samples (Table 1; Figure 6-9). Ecoregion entered as the first, and often the second, splitting predictor. The first level split separated the Ozark Highlands from other ecoregions, with the Ozark Highlands node having the highest predicted ‘InvFmRch’ values. The second level split separated the Central Great Plains, Western High Plains, and Flint Hills from the Central Irregular Plains, Western Corn Belt Plains, and Nebraska Sand Hills, with the latter group having higher predicted ‘InvFmRch’ values. We speculate that higher stream flows associated with groundwater (Nebraska Sand Hills) and increased precipitation (Central Irregular Plains and Western Corn Belt Plains) account for increased potential for habitat necessary to support macroinvertebrate communities. Seven of the ten models stopped tree growth after the two splits on ecoregion. In these cases, the three resultant nodes (representing ecoregion groups) are similar to Level II Ecoregions. KFACT and watershed area (SHED_AREA) also provided splitting variables for trees grown beyond the second level.
101 The addition of dynamic landscape predictors to the static landscape predictor set increased the average resubstitution R2 for the ten sub-samples from 0.38 (± 0.03) to 0.59 (± 0.07) (Table 1; Figure 6-9). Ecoregion was typically the first split, followed by second level splits on the 5-year average NDVI at season maximum (‘mva5ex’) and 3-year average date of dormancy (‘dda3ex’) (e.g., Figure 6-10). Once again, the Ozark Highlands was split from the other ecoregions. For the remaining six ecoregions, nodes with MVA values greater than approximately 0.71 were predicted as having higher ‘InvFmRch’ (Figure 6-10). A map of the fifteen-year average maximum NDVI value shows MVA > 0.71 corresponds to landscapes dominated either by natural vegetation (grasslands eastward from central Kansas and Nebraska) or by cropland, except for non- irrigated crops in western Kansas and Nebraska (Figure 3-5). Dynamic landscape predictors outperformed static predictors, with an average resubstitution R2 of 0.56 (± 0.07) across the ten sub-samples (Table 1; Figure 6-9). Various temporal windows for the average growing season NDVI (AVA), average NDVI at dormancy (DVA), and average NDVI at season maximum (MVA) were the initial splitting predictors, where nodes with (approximately) AVA > 0.63, DVA > 0.49, or MVA > 0.73 were linked with higher ‘InvFmRch’ (e.g., Figure 6-11). Maps of these VPMs show these values correspond generally to forested regions in the Ozark Highlands (Figure 3-5, Figure 3-7, and Figure 3-11). ‘Mva5ex’, ‘ova1ex’, and ‘oda2in’ were the most important variables in the models (Table 4). While tree topology between sub- samples varied, validation accuracies were relatively high and fairly stable (Table 1).
6.3.1.4 ‘PrpFmEPT’ RT Models The proportion of variance explained of ‘PrpFmEPT’ by static and dynamic landscape predictors was relatively inconsistent and even null in multiple models (Table 1; Figure 6-12). Instances where R2 for training samples was relatively high (0.4-0.5), model validation was poor with substantially lower R2 (Table 1). Due to poor results, this variable was dropped from further analyses.
6.3.2 Model Spatial Scale: Global vs. Ecoregion As noted in the previous section, ecoregion was the first split in the majority of global regression tree models for ‘PrpSensF’ and ‘InvFmRch’ when both the static and static-dynamic predictor sets were used. This result suggests that ecoregion-specific models might be developed to better predict biological response variables. This section tests this idea by developing regression tree models for the three response variables (‘TotN’, ‘PrpSensF’, and ‘InvFmRch’) in three ecoregions: the Central Irregular Plains (CIP), the Ozark Highlands (OH), and the Western Corn Belt Plains (WCBP). Static and dynamic predictors were used in the analysis. Performance of ecoregion-specific models was compared to global models. Ten ecoregion models were trained and validated using ten runs of the 80-20 data splitting procedure, limited to just samples from the ecoregion of interest. Tree form was determined using standard cost-complexity pruning methods. For simplicity, a single global tree model was determined for each response variable using all data points and standard cost-complexity pruning. As a consequence of not cross-validating the global trees, resulting R2 values likely appear more favorable than they should be. However, due to the large sample sizes used for global model development, the magnitude of this
102 bias is not expected to overwhelm the presented results. Accuracy values shown in Table 5 for global models were evaluated using 500,000 ecoregion-specific, random 80-20 data splits and simple resubstitution.
6.3.2.1 ‘TotN’ RT Models Results from the OH and WCBP ecoregions exhibited no advantage in using ecoregion-specific models rather than a global model (Table 5). Across the 20% subsets (validation sets for ecoregion-specific models, resubstitution sets for global models), similar variability in the R2 measure was observed between the ecoregion-specific and global model evaluations. However, in the WCBP, notably higher accuracies were observed for the global model (R2 = 0.60) than for the ecoregion-specific model (validation R2 = 0.38), though the global results are likely somewhat inflated due to disproportionate influence of the relatively large WCBP sample on global model development. In contrast, results from ecoregion-specific models from the CIP ecoregion did show a clear advantage over the global model (Table 5). Variability of ‘TotN’ values from the CIP ecoregion simply was not captured by the global model (R2 = 0.06 for 20% subsets). This outcome exemplifies a danger to global model development, in that errors will not necessarily be distributed randomly and uniformly across the region of study, with entire sub-regions possibly not receiving any significant representation in the model. Additionally, this effect was exacerbated in the CIP-‘TotN’ scenario, as mean CIP validation accuracy was the highest among the three ecoregion-specific evaluations with R2 = 0.46.
6.3.2.2 ‘PrpSensF’ RT Models Results from the ‘PrpSensF’ assessment were similar to those from the ‘TotN’ assessment, but with smaller discrepancies (Table 5). Across the 20% subsets, ecoregion-specific and global models performed comparably in the OH ecoregion (R2 = 0.41 and R2 = 0.40, respectively). In the CIP ecoregion, like in the ‘TotN’ analysis, ecoregion-specific models outperformed the global model, but to a lesser degree of difference (R2 = 0.41 and R2 = 0.31, respectively). In the WCBP ecoregion, also like in the ‘TotN’ analysis, the global model outperformed the ecoregion-specific models, but again to a lesser degree of difference (R2 = 0.54 and R2 = 0.45, respectively).
6.3.2.3 ‘InvFmRch’ RT Models Specific results for ‘InvFmRch’ differed somewhat from the ‘TotN’ and ‘PrpSensF’ evaluations, though not with respect to the general relationship between global and ecoregion-specific model performance (Table 5). Across the 20% subsets, the global models performed comparably or better than the ecoregion-specific models for the OH ecoregion (R2 = 0.61 and R2 = 0.42, respectively) and the CIP ecoregion (R2 = 0.46 and R2 = 0.40, respectively). Performance across different 20% subsets was also more stable in these two ecoregions for the global models than for the ecoregion-specific models. However, for the WCBP ecoregion, the ecoregion-specific models outperformed the global model (R2 = 0.43 and R2 = 0.30, respectively) despite this ecoregion accounting for 42% of the total global sample.
103 6.3.3 Model Temporal Scale: Short-term vs. Long-term For ‘TotN’ and ‘PrpSensF’, the 5-year temporal window average produced generally higher R2 for the response variables than either 1-year temporal window (Table 6). For ‘InvFmRch’, there was no clear preference for temporal window size. Regardless of the temporal window, tree topology varied significantly more for the biological response variables than for ‘TotN’.
6.3.3.1 ‘TotN’Models For ‘TotN’, average resubstitution R2 values across the ten sub-samples were slightly higher for the 5-year window than the 1-year windows (Table 6). BDA was consistently the first split across the ten sub-samples, with only one regression tree growing beyond the first level split. Similar to previous model results, steeper BDA rates (approximately less than –0.067) predicted higher ‘TotN’ (e.g., Figure 6-13).
6.3.3.2 ‘PrpSensF’Models For ‘PrpSensF’, the 5-year window produced higher R2 than either 1-year window (Table 6). Using the 5-year window, five different trees emerged from the ten replicates for ‘PrpSensF’, although most variation occurred at the third or fourth tree level. Generally, OVA or AVA were the first splitting predictors, followed by GUA at the second level (e.g., Figure 6-14). Five of the tree models grew to a third or fourth level while the other five stopped at the second split on GUA. The first split on OVA and AVA separated watersheds with OVA values greater than approximately 0.43 or AVA > 0.64, which were associated with higher ‘PrpSensF’ values. The second level split down the lower value path predicted higher ‘PrpSensF’ for watersheds with GUA > 0.057 (Figure 6-14). Tree topology and dominant predictors (particularly OVA and GUA) were similar to regression tree results when all temporal windows were used.
6.3.3.3 ‘InvFmRch’Models Average resubstitution R2 values across the ten sub-samples were similar for all three temporal windows (Table 6). MVA, OVA, ODA, and AVA were reoccurring predictors in the regression trees, though tree composition and structure varied greatly. As described previously, MVA, OVA, and ODA were also reoccurring predictors when the entire dynamic predictor set was used. Figure 6-15 shows one of the ten RT models generated for ‘InvFmRch’.
6.3.4 Fixed Models Correlation among the 220 dynamic landscape predictors likely is contributing to the observed variations in model form for the two biological response variables. In an effort to develop general, robust models, we reduced the number of dynamic predictors to use for the final RTA of this section. Because VPMs prior to and within the sampling year were highly correlated, the dynamic predictor set was first reduced to half its size half by eliminating all VPM predictors that were calculated using the sampling year (i.e., retaining only the ‘ex’ VPM variables). This decision also precludes any potential anachronistic problems between sampling events and corresponding VPMs, in reference to situations where a sample is collected before a VPM can be determined. Based on improvement values from preliminary RTA applied to this reduced variable set, top
104 dynamic predictors were selected and used as input for a final RTA to determine if a robust, useful model could be developed for each of the response variables. As an additional constraint, since pairwise correlation was typically high among the different temporal window averages for each VPM, only one temporal window average for each optimal VPM type was used in the final RTA. Once trees were grown using the top dynamic predictors and cost-complexity pruning, commonalities in tree form were identified across the ten sub-samples models. The largest common tree form across the ten sub-samples was termed the “fixed model”. In cases where the common form was not obtained using cost-complexity pruning, branches were manually grown or pruned to the fixed model form, and the resulting set of fixed-form models were further analyzed. Resubstitution and validation accuracies were calculated for both model sets (cost-complexity pruned and fixed model). To produce a “final model”, a tree was first developed using all data points, the top dynamic predictors, and cost-complexity pruning, and then was further grown or pruned to obtain the selected fixed model form. Comparisons are made between RTs developed using all ‘ex’ VPM variables and cost-complexity pruning (figure label ‘VPM ex’), top VPM predictors and cost-complexity pruning (‘Top VPM ex’), and top VPM predictors with trees forced to the fixed model form (‘VPM Fixed Form’). Resubstitution accuracy for the final model can be ascertained from the ‘All sites’ point of the ‘VPM Fixed Form’ line plot found in various figures.
6.3.4.1 ‘TotN’Models The reduction of dynamic predictors to VPMs prior to the sampling year did not greatly impact tree topology for the ‘TotN’ model. Results were similar to previous regression tree results with longer temporal windows of BDA having the highest variable importance (Table 7), appearing as the initial splitting variable in all ten trees. Tree growth stopped in seven of the ten trees after splitting on BDA. Two of the remaining three trees had second level splits on ‘mva1ex’ and ‘oda5ex’. The final set of predictors was reduced to ‘bda5ex’, ‘mda1ex’, ‘oda5ex’ and ‘dva1ex’. Restricting the predictors to four variables did not greately affect tree topology compared to previous evaluations. Three trees grew to two levels with three terminal nodes, the tree form selected as the fixed model (Figure 6-16). Seven of the cost- complexity pruned trees were grown to a second level to produce the fixed model form. Model accuracies were comparable between cost-complexity pruned and fixed form regression tree models (Figure 6-17; Table 8), though the latter produced slightly higher R2 values. The tree generated using all sample points and cost-complexity pruning (i.e., the preliminary final model) grew to a fourth level and required pruning to produce the fixed model tree topology (Figure 6-18). The final model had resubstitution R2 = 0.41 (Figure 6-17), similar to the average resubstitution and validation R2 values for the cost- complexity pruned and fixed model subset evaluations using just the top predictors (Table 8). Consistent with previous RTA results, watersheds with ‘bda5ex’ < –0.067 in Node 1 had higher predicted ‘TotN’ (6.4 ± 3.9) and correspond to homogenous agricultural regions such as the corn belt and the wheat belt (Figure 6-16 and Figure 3-9). Watersheds with ‘bda5ex’ > –0.067 in Node 2 had lower predicted ‘TotN’ (1.8 ± 1.9) and correspond to landscapes dominated by homogenous natural vegetation or heterogeneous
105 agriculture. The 248 watersheds with steep ‘bda5ex’ in Node 1 were then split on ‘mda1ex’. Watersheds with ‘mda1ex’ < 16.9 (Node 3) had relatively moderate ‘TotN’ (5.8 ± 3.6). Forty-three watersheds with ‘mda1ex’ > 16.9 (Node 4) had the highest ‘TotN’ (9.6 ± 3.6). A map of predicted ‘TotN’ (Figure 6-19(a)) reveals the watersheds with the highest ‘TotN’ are concentrated in central Iowa. Comparing maps of predicted and observed ‘TotN’ show that the RT model captured regional variation in ‘TotN’ (Figure 6-19). A map of model residuals (= predicted – observed) (Figure 6-20) show the model predicted ‘TotN’ relatively well in a large portion of the study area. For example, error magnitude from 1009 of 1158 samples (87%) was less than the ‘TotN’ sample standard deviation. The largest residuals were concentrated in the Western Corn Belt Plains, where there is more subregional variation in observed ‘TotN’.
6.3.4.2 ‘PrpSensF’Models For ‘PrpSensF’, the reduction of dynamic predictors to VPMs prior to the sampling year reduced variations in tree form (after cost-complexity pruning) and produced an average resubstitution R2 of 0.40 (± 0.06) (Figure 6-21). Eight of the ten trees split on a longer temporal window of OVA (3- 5yr). The other two trees initially split on the three-year temporal window of average NDVI (‘ava3ex’). All eight trees had a second split on longer temporal windows of GUA, consistent with modeling results discussed in previous ‘PrpSensF’ sections. Only two of the ten trees grew beyond a second level. ‘Gua5ex’ and ‘ova3ex’ had the highest weighted variable importance and were the only predictors retained for a final set of RTA (Table 7). As expected, limiting the dynamic predictors to ‘gua5ex’ and ‘ova3ex’ further reduced variations in tree topology across the ten sub-samples. A fixed tree form was readily identified among the ten trees. The fixed model for ‘PrpSensF’ produced a two level tree containing three terminal nodes (Figure 6-22). Six of the cost-complexity pruned trees were manually grown to a second level and one tree was manually pruned to obtain the fixed model form for the ten trees. Model accuracies were comparable between cost-complexity pruned and fixed form regression tree models (Figure 6-21; Table 8), though the latter produced slightly higher R2 values. The final model had resubstitution R2 = 0.39 (Figure 6-22), slightly greater than the average resubstitution and validation R2 values for the cost-complexity pruned and fixed model subset evaluations using just the top predictors (Table 8). A map of predicted ‘PrpSensF’ (Figure 6-23(a)) shows some distinct regional variation. Forty-six watersheds defined Node 2. These watersheds had ‘ova3ex’ > 0.429 and were predicted to have high ‘PrpSensF’ (0.378 ± 0.104). With the exception of two watersheds in the Central Great Plains, watersheds in this node are located in the Ozark Highlands. The map depicting the fifteen-year average greenup onset NDVI value illustrates the regional variation in this statistic, with the Ozark Highlands having the highest values (Figure 3-3). Compared to the other six ecoregions, the Ozark Highlands is a relatively undisturbed landscape with distinct physiographic characteristics. Perennial streams with ample flow dominate the Ozark Highlands and often produce a habitat structure that supports a large variety of fish species. Observed ‘PrpSensF’ values are shown in Figure 6-23(b).
106 Watersheds with ‘ova3ex’ < 0.429 had a secondary split on ‘gua5ex’. This split divided the remaining watersheds into an approximate 50-50 split. Watersheds with ‘ova3ex’ < 0.429 and ‘gua5ex’ > 0.057 were predicted to have relatively moderate ‘PrpSensF’ (0.143 ± 0.114). A map of the fifteen-year average of rate of greenup shows relatively moderate to high GUA (excluding the Ozark Highlands) correspond to grasslands in the Flint Hills and Nebraska Sand Hills as well as cropland in the Central Great Plains and Western Corn Belt Plains (Figure 3-3 and Figure 3-8). The commonality between these grassland and cropland regions is that they represent homogenous landscapes. This characteristic supports higher pixel-level AVHRR NDVI greenup rates than found in mixed landscapes, where pixel-level AVHRR NDVI profiles more frequently reflect the smearing together of distinctive component phenology signals. Watersheds with ‘ova3ex’ < 0.429 and ‘gua5ex’ < 0.057 were predicted to have relatively low ‘PrpSensF’ (0.066 ± 0.083) and correspond to more heterogeneous agricultural landscapes in the Central Great Plains, Central Irregular Plains, Western High Plains, and southwest portions of the Western Corn Belt Plains. Reasonable overall model performance was observed, as the magnitude of most model residuals (493 of 638, or 77%) was less than the ‘PrpSensF’ sample standard deviation (Figure 6-24). The residual map indicates the largest concentrations of underestimated ‘PrpSensF’ are located in the Iowan Surface region (situated in the northeastern part of the Western Corn Belt Plains) and Nebraska Sand Hills. The distribution of observed ‘PrpSensF’ was highly skewed as relatively few watersheds had high observed ‘PrpSensF’, while 222 watersheds had ‘PrpSensF’ = 0. Furthermore, the majority of high ‘PrpSensF’ are concentrated in the Ozark Highlands. Since a stratified random sample was not used for model training, the Ozark Highlands was likely more represented in model training than smaller regions with high ‘PrpSensF’. ‘PrpSensF’ was overestimated in multiple watersheds in central Kansas and Nebraska and eastward.
6.3.4.3 ‘InvFmRch’Models The subset of VPMs for predicting ‘InvFmRch’ produced an average R2 of 0.51 (± 0.04). Six of the ten trees used ‘mva5ex’ as the initial splitting variable. Three of the trees used a shorter temporal window of OVA, and one tree used ‘ava3ex’ as the initial splitting variable. Even though there were three initial splitting variables across the ten sub-samples, the subset of VPMs produced more consistency in the first split than previous runs. Shorter temporal windows of OVA and ODA were commonly the second splitting variables in the tree models. Watersheds with ‘mva5ex’ > ~ 0.73 were then generally split by ‘ova1ex’, and watersheds with ‘ova1ex’ > ~ 0.38 had the highest predicted ‘PrpSensF’ (~ 0.40). Watersheds with ‘mva5ex’< ~ 0.73 were typically split by ‘oda1ex’, and watersheds with ‘oda1ex’ < ~ 8.2 were predicted with the lowest ‘PrpSensF’ (~ 0.16). ‘Mva5ex’, ‘oda1ex’, and ‘ova1ex’ had the highest variable importance and were used as predictors for the final RTA (Table 7). As anticipated, using just three dynamic predictors reduced variations in tree form across the ten sub-samples. The ten sub-samples had average resubstitution R2 of 0.48 (± 0.02). Nine of ten trees initially split on ‘mva5ex’, and the common tree structure among these nine trees was identified as the fixed form. The fixed model for ‘InvFmRch’ produced a three level tree (including the root node) containing five terminal nodes (Figure 6-25). Six of the cost-complexity pruned trees had additional branches that had
107 to be manually pruned, three trees had to have branches grown, and one tree had a branch grown and another pruned to obtain the fixed model form. Model performance and stability between the cost-complexity pruned and fixed form regression tree models were comparable (Table 8). The model developed using all data points and cost-complexity pruning (i.e., the preliminary final model) grew to the fourth level (Figure 6-26), with two nodes that had to be manually pruned to obtain the fixed form. The final model had a resubstitution R2 = 0.47 (Figure 6-27), a value comparable to the average resubstitution and validation R2 values for the cost-complexity pruned and fixed model subset evaluations using just the top predictors (Table 8). Thirty-six watersheds in Node 6, characterized by ‘mva5ex’ > 0.735 and ‘ova1ex’ > 0.441 (Figure 6-25), had the highest predicted ‘InvFmRch’ (46.8 ± 6.9). As with ‘PrpSensF’, watersheds with the highest predicted ‘InvFmRch’ are concentrated in the Ozark Highlands (Figure 6-28(a)). A map of the fifteen-year average maximum NDVI shows the northern portion of the Western Corn Belt Plains and approximately one third of the Ozark Highlands have the highest MVA (> 0.81; Figure 3-5), but only portions of the Ozark Highlands have a fifteen-year average greenup onset NDVI value > 0.44 (Figure 3-3). Watersheds with ‘mva5ex’ > 0.735 and ‘ova1ex’ <= 0.44 (Node 5) had predicted ‘InvFmRch’ = 27.9 (± 7.3). These 317 watersheds are concentrated in the Western Corn Belt Plains and the Ozark Highlands (Figure 6-28(a); Figure 3-3 and Figure 3-5). Watersheds in Node 1 (n = 238) with ‘mva5ex’ < 0.74 (Figure 6-25) were split by ‘oda1ex’. Watersheds with ‘oda1ex’ > 8.21 (Node 4) also had relatively high predicted ‘InvFmRch’ (27.9 ± 10.3) and correspond to grasslands in the Nebraska Sand Hills, small portions in the northern Flint Hills, and remaining Kansas and Nebraska grassland remnants in the Western High Plains (Figure 3-2 and Figure 3-5). These regions are typically used as rangeland. Relatively high predicted ‘InvFmRch’ suggest the land use and management practices in these grasslands have less impact on macroinvertebrate species richness than other types of land cover and land use in the surrounding area. The remaining 205 watersheds (characterized by ‘oda1ex’ < 8.21) were further split, where watersheds with ‘mva5ex’ < 0.619 had the lowest predicted ‘InvFmRch’ (12.74 ± 6.64). These watersheds correspond to non-irrigated agricultural areas in Central Great Plains and Western High Plains (Figure 6-28(a); Figure 3-5). ‘Oda1ex’ < 8.21 and ‘mva5ex’ > 0.619 resulted in a predicted ‘InvFmRch’ value of 19.6 (± 10.0) (Node 8). Node 8 consists of watersheds in central and eastern Kansas where streams experience fewer drought disturbances and are able to support and maintain a more diverse macroinvertebrate community (compared to watersheds occupying Node 7). The map of predicted values shows a general west-east trend of low-high ‘InvFmRch’ that resembles the low-high precipitation gradient in the study area. Comparing predicted and observed values shows the model captured regional variability in ‘InvFmRch’ but less so subregional or localized variability (Figure 6-28). The magnitude of most model residuals (507 of 591, or 86%) was less than the ‘InvFmRch’ sample standard deviation (Figure 6-29), indicating relatively good overall model performance. The largest concentration of overestimated ‘InvFmRch’ is located in northeastern Kansas. Observed ‘InvFmRch’ was not skewed like ‘PrpSensF’, but had a fairly symmetric distribution. However, closer examination of the observed ‘InvFmRch’ map (Figure 6-28(b)) reveals an interesting artifact in the data that may help explain the
108 area with overestimated ‘InvFmRch’. The map shows that most low ‘InvFmRch’ sample sites occur in Kansas and almost abruptly change character at the state border. While the data could be indicative of ‘InvFmRch’ in Kansas streams, we also recognize the limitations and biases inherent in existing databases. The stream samples represented in this database are a compilation from multiple agencies collecting field data with specific objectives in mind, and thus samples are not always perfectly compatible.
6.4 Conclusions The goal of the RTA exercise was to develop robust and reasonably precise models for predicting three aquatic response variables that in turn could be used in a classification scheme for watershed vulnerability. Dynamic predictors used in conjunction with or instead of static landscape predictors frequently improved model performance. Unique sets of VPMs were determined to be optimal for modeling each response variable. This research also demonstrates the dynamic ability of VPMs to capture landscape processes operating at various temporal scales. A comparison of regression tree models specifically comparing short and long-term dynamic predictors suggested that ‘InvFmRch’ had no temporal scale preference. However, using all VPM temporal windows, the top predictors for ‘InvFmRch’ in fact were a combination of long and short-term VPMs, suggesting that macroinvertebrate richness may respond to a combination of short and long-term landscape processes within a watershed. Regression models show that long-term VPMs for ‘TotN’ and ‘PrpSensF’ were often the most useful predictors of the response variables, an indication that these response variables are likely largely dependent on longer-term processes affecting watershed condition. A major conclusion to draw from these results is that despite high correlations between predictor variables, incorporating multiple temporal scales provides a more complete characterization of the landscape dynamics that impact the various components of watershed condition. In regards to spatial scale, results were obtained in support of using global models. However, for each response variable evaluation, one of the three examined ecoregions produced results illustrating the improved utility of using ecoregion-specific models rather than the global model in certain situations. Although global models are generally more robust than ecoregion-specific models, the diminished specificity of the global model was too coarse to detect many subregional differences in the response variables. It may prove beneficial for future modeling efforts using regression tree analyses to model at an Ecoregion Level II scale or another logical grouping of ecoregions that would provide increased sample size yet emphasize more local variation in the dataset.
6.5 References Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth International Group, Belmont, CA.
109
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0.60
0.50
0.40
Equivalent 0.30 2 R
0.20
Static Static & VPM VPM 0.10 VPM 1ex VPM 1in VPM 5in
0.00 12345678910All sites
Figure 6 - 1. The resubstitution variance explained of ‘TotN’ from RTA for the seven dominant ecoregions in EPA Region 7. Eleven trees were generated for each set of predictor variables with the first ten using an 80/20 partition for training and testing. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results. The addition of VPMs increase the variance explained over static predictors. VPMs explained more variance when multiple VPM temporal scales (i.e., 1- year through 5-year averages) were combined.
110
TOTN (Training Sample)
Node 0 Mean 2.8640 Std. Dev. 3.1897 n 906 % 100.00 Predicted 2.8640
BDA4INCL Improvement=4.0868
<=-0.069276183500000005 >-0.069276183500000005
Node 1 Node 2 Mean 6.7117 Mean 1.8019 Std. Dev. 4.0464 Std. Dev. 1.8060 n 196 n 710 % 21.63 % 78.37 Predicted 6.7117 Predicted 1.8019
OVA3INCL Improvement=0.6709
<=0.27250087499999998 >0.27250087499999998
Node 3 Node 4 Mean 8.5461 Mean 5.0211 Std. Dev. 3.9573 Std. Dev. 3.3427 n 94 n 102 % 10.38 % 11.26 Predicted 8.5461 Predicted 5.0211
Figure 6 - 2. A regression tree model for predicting ‘TotN’ using the static-dynamic landscape predictor set. This model was generated using the ninth sub-sample and had resubstitution R2 = 0.47.
111 TOTN (Training Sample)
Node 0 Mean 2.8299 Std. Dev. 3.0197 n 936 % 100.00 Predicted 2.8299
CULTIVAT Improvement=3.4183
<=83.649336560115529 >83.649336560115529
Node 1 Node 2 Mean 1.8111 Mean 6.1852 Std. Dev. 1.8318 Std. Dev. 3.6686 n 718 n 218 % 76.71 % 23.29 Predicted 1.8111 Predicted 6.1852
MDA 1EXCL Improvement=0.5828
<=16.869395500000003 >16.869395500000003
Node 3 Node 4 Mean 5.5052 Mean 9.8651 Std. Dev. 3.2798 Std. Dev. 3.5097 n 184 n 34 % 19.66 % 3.63 Predicted 5.5052 Predicted 9.8651
OVA1INCL Improvement=0.2816
<=0.33825450499999998 >0.33825450499999998
Node 5 Node 6 Mean 6.0751 Mean 2.9912 Std. Dev. 3.3124 Std. Dev. 1.4578 n 150 n 34 % 16.03 % 3.63 Predicted 6.0751 Predicted 2.9912
Figure 6 - 3. A regression tree model for predicting ‘TotN’ using the static-dynamic landscape predictor set. This model was generated using the second sub-sample and had resubstitution R2 = 0.47.
112
TOTN (Training Sample)
Node 0 Mean 2.8322 Std. Dev. 3.1558 n 939 % 100.00 Pr edic ted 2.8322
BDA 5INCL Improvement=3.9676
<=-0.067669577000000009 >-0.067669577000000009
Node 1 Node 2 Mean 6.6610 Mean 1.7959 Std. Dev. 3.8378 Std. Dev. 1.9074 n 200 n 739 % 21.30 % 78.70 Predicted 6.6610 Predicted 1.7959
Figure 6 - 4. A regression tree model for predicting ‘TotN’ using the dynamic landscape predictor set. This model was generated using the fourth sub-sample and had resubstitution R2 = 0.54.
113
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0.60
0.50
0.40 Equivalent 2 0.30 R
0.20 Static Static & VPM VPM 0.10 VPM 1ex VPM 1in VPM 5in
0.00 12345678910All sites
Figure 6 - 5. The resubstitution variance explained from RTA for ‘PrpSensF’ across the seven dominant ecoregions in EPA Region 7. Eleven trees were generated for each set of predictor variables. The first ten trees used an 80/20 partition for model training and validation. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results. The addition of VPMs slightly increases the variance explained over static predictors. VPMs explained more variance when all VPM temporal windows were combined.
114
Figure 6 - 6. Areas where KFACT < 0.29 are highlighted in gray. State and Level III Ecoregion boundaries are shown in black.
115 PRPSENSF ( Tr aining Sample)
Node 0 Mean 0.1226 Std. Dev. 0.1297 n 507 % 100.00 Pr edic ted 0.1226
ECO_NUM Improvement=0.0054
39 25;27;28;40;44;47
Node 1 Node 2 Mean 0.3783 Mean 0.1013 Std. Dev. 0.0965 Std. Dev. 0.1075 n 39 n 468 % 7.69 % 92.31 Pr edic ted 0.3783 Pr edic ted 0.1013
KFACTMN Improvement=0.0025
<=0.28944004999999995 >0.28944004999999995
Node 3 Node 4 Mean 0.1755 Mean 0.0653 Std. Dev. 0.1180 Std. Dev. 0.0803 n 153 n 315 % 30.18 % 62.13 Pr edic ted 0.1755 Predicted 0.0653
GUS4INCL ECO_NUM Improvement=0.0009 Improvement=0.0005
<=0.017378163000000002 >0.017378163000000002 28 25;27;40;44;47
Node 5 Node 6 Node 7 Node 8 Mean 0.2103 Mean 0.0920 Mean 0.1673 Mean 0.0577 Std. Dev. 0.1140 Std. Dev. 0.0802 Std. Dev. 0.1082 Std. Dev. 0.0725 n 108 n 45 n 22 n 293 % 21.30 % 8.88 % 4.34 % 57.79 Pr edic ted 0.2103 Pr edic ted 0.0920 Predicted 0.1673 Predicted 0.0577
BDS4INCL Improvement=0.0005
<=0.0074572980000000002 >0.0074572980000000002
Node 9 Node 10 Mean 0.4615 Mean 0.2006 Std. Dev. 0.1466 Std. Dev. 0.1016 n 4 n 104 % 0.79 % 20.51 Pr edic ted 0.4615 Pr edic ted 0.2006
Figure 6 - 7. A regression tree model predicting ‘PrpSensF’ using the static-dynamic predictor set. This model was generated from the tenth sub-sample and had resubstitution R2 = 0.58.
116 PRPSENSF ( Tr aining Sample)
Node 0 Mean 0.1231 Std. Dev. 0.1321 n 503 % 100.00 Predicted 0.1231
OVA5EXCL Improvement=0.0062
<=0.44259857000000002 >0.44259857000000002
Node 1 Node 2 Mean 0.1012 Mean 0.4073 Std. Dev. 0.1076 Std. Dev. 0.0827 n 467 n 36 % 92.84 % 7.16 Predicted 0.1012 Predicted 0.4073
GUA5EXCL Improvement=0.0015
<=0.056928773000000002 >0.056928773000000002
Node 3 Node 4 Mean 0.0640 Mean 0.1444 Std. Dev. 0.0805 Std. Dev. 0.1185 n 251 n 216 % 49.90 % 42.94 Predicted 0.0640 Predicted 0.1444
DV S5INCL Improvement=0.0006
<=0.0241329175 >0.0241329175
Node 5 Node 6 Mean 0.0650 Mean 0.1614 Std. Dev. 0.0934 Std. Dev. 0.1166 n 38 n 178 % 7.55 % 35.39 Predicted 0.0650 Predicted 0.1614
BDS1EXCL Improvement=0.0006
<=0.010785135500000001 >0.010785135500000001
Node 7 Node 8 Mean 0.2313 Mean 0.1370 Std. Dev. 0.1205 Std. Dev. 0.1053 n 46 n 132 % 9.15 % 26.24 Predicted 0.2313 Predicted 0.1370
Figure 6 - 8. A regression tree model predicting ‘PrpSensF’ using the dynamic predictor set. The ninth sub-sample was used to generate this model and had resubstitution R2 = 0.51.
117
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0.60
0.50
0.40
Equivalent 0.30 2 R
0.20
Static Static & VPM VPM 0.10 VPM 1ex VPM 1in VPM 5in
0.00 12345678910All sites
Figure 6 - 9. The resubstitution variance explained of ‘InvFmRch’ from RTA for the seven dominant ecoregions in EPA Region 7. Eleven trees were generated for each set of predictor variables, with the first ten using an 80/20 partition for training and testing. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results. The addition of VPMs increase the variance explained over static predictors. VPMs explained more variance when VPM temporal windows (i.e., 5-year and 1-year) were combined.
118
FmRich (Training Sample)
Node 0 Mean 25.2876 Std. Dev. 11.0287 n 459 % 100.00 Predicted 25.2876
Eco_Num Improvement=34.3885
39 25;27;28;40;44;47
Node 1 Node 2 Mean 40.7069 Mean 23.0574 Std. Dev. 9.1709 Std. Dev. 9.3715 n 58 n 401 % 12.64 % 87.36 Predicted 40.7069 Predicted 23.0574
dda3excl mva5excl Improvement=4.9001 Improvement=16.6366
<=22.5869705 >22.5869705 <=0.70948434499999991 >0.70948434499999991
Node 3 Node 4 Node 5 Node 6 Mean 35.0937 Mean 47.6154 Mean 17.6456 Mean 26.5761 Std. Dev. 6.0873 Std. Dev. 7.4730 Std. Dev. 9.8983 Std. Dev. 7.0744 n 32 n 26 n 158 n 243 % 6.97 % 5.66 % 34.42 % 52.94 Predicted 35.0937 Predicted 47.6154 Predicted 17.6456 Predicted 26.5761
oda3incl Improvement=6.0728
<=8.2701632499999995 >8.2701632499999995
Node 7 Node 8 Mean 16.4966 Mean 33.0000 Std. Dev. 9.0337 Std. Dev. 8.2462 n 147 n 11 % 32.03 % 2.40 Predicted 16.4966 Predicted 33.0000
Figure 6 - 10. A regression tree model predicting ‘InvFmRch’ using the static-dynamic predictor set. This model was generated from the seventh sub-sample and had resubstitution R2 = 0.51.
119
FmRich (Training Sample)
Node 0 Mean 25.2876 Std. Dev. 11.0287 n 459 % 100.00 Predicted 25.2876
ava1incl Improvement=31.6876
<=0.63644682999999991 >0.63644682999999991
Node 1 Node 2 Mean 23.2321 Mean 40.7037 Std. Dev. 9.4288 Std. Dev. 9.9501 n 405 n 54 % 88.24 % 11.76 Predicted 23.2321 Predicted 40.7037
mva5excl dda3excl Improvement=17.0315 Improvement=4.9324
<=0.70948434499999991 >0.70948434499999991 <=22.592247499999999 >22.592247499999999
Node 3 Node 4 Node 5 Node 6 Mean 17.7673 Mean 26.7642 Mean 34.4643 Mean 47.4231 Std. Dev. 9.9856 Std. Dev. 7.0982 Std. Dev. 7.2187 Std. Dev. 7.9406 n 159 n 246 n 28 n 26 % 34.64 % 53.59 % 6.10 % 5.66 Predicted 17.7673 Predicted 26.7642 Predicted 34.4643 Predicted 47.4231
oda3incl Improvement=5.9741
<=8.2701632499999995 >8.2701632499999995
Node 7 Node 8 Mean 16.6351 Mean 33.0000 Std. Dev. 9.1593 Std. Dev. 8.2462 n 148 n 11 % 32.24 % 2.40 Predicted 16.6351 Predicted 33.0000
Figure 6 - 11. A regression tree model predicting ‘InvFmRch’ using the dynamic predictor set. This model was generated from the seventh sub-sample and had resubstitution R2 = 0.49.
120
0.7 Static Static & VPM VPM 0.6 VPM 1ex VPM 1in VPM 5in
0.5
0.4
Equivalent 0.3 2 R
0.2
0.1
0 12345678910All sites
Figure 6 - 12. The resubstitution variance explained of ‘InvFmEPT’ from RTA for the seven dominant ecoregions in EPA Region 7. Eleven trees were generated for each set of predictor variables, with the first ten using an 80/20 partition for training and testing. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results. All predictor sets produced relatively inconsistent, poor results.
121
TOTN (Training Sample)
Node 0 Mean 2.8322 Std. Dev. 3.1558 n 939 % 100.00 Pr edic ted 2.8322
BDA 5INCL Improvement=3.9676
<=-0.067669577000000009 >-0.067669577000000009
Node 1 Node 2 Mean 6.6610 Mean 1.7959 Std. Dev. 3.8378 Std. Dev. 1.9074 n 200 n 739 % 21.30 % 78.70 Predicted 6.6610 Predicted 1.7959
Figure 6 - 13. A regression tree model predicting ‘TotN’ using the 5-year dynamic predictor set. This model was generated from the fourth sub-sample and had resubstitution R2 = 0.40.
122 PRPSENSF (Training Sample)
Node 0 Mean 0.1210 Std. Dev. 0.1291 n 511 % 100.00 Predicted 0.1210
OV A 5INCL Improvement=0.0050
<=0.43217289999999997 >0.43217289999999997
Node 1 Node 2 Mean 0.1019 Mean 0.3810 Std. Dev. 0.1080 Std. Dev. 0.1120 n 476 n 35 % 93.15 % 6.85 Predicted 0.1019 Predicted 0.3810
GUA 5INCL BDS5INCL Improvement=0.0013 Improvement=0.0004
<=0.057354899500000001 >0.057354899500000001 <=0.01034441 >0.01034441
Node 3 Node 4 Node 5 Node 6 Mean 0.0665 Mean 0.1410 Mean 0.4030 Mean 0.1470 Std. Dev. 0.0811 Std. Dev. 0.1201 Std. Dev. 0.0865 Std. Dev. 0.0862 n 250 n 226 n 32 n 3 % 48.92 % 44.23 % 6.26 % 0.59 Predicted 0.0665 Predicted 0.1410 Predicted 0.4030 Predicted 0.1470
DV S5INCL Improvement=0.0006
<=0.0241329175 >0.0241329175
Node 7 Node 8 Mean 0.0608 Mean 0.1593 Std. Dev. 0.0962 Std. Dev. 0.1176 n 42 n 184 % 8.22 % 36.01 Predicted 0.0608 Predicted 0.1593
ODA 5INCL Improvement=0.0005
<=6.6066309499999996 >6.6066309499999996
Node 9 Node 10 Mean 0.0671 Mean 0.1745 Std. Dev. 0.0985 Std. Dev. 0.1138 n 26 n 158 % 5.09 % 30.92 Predicted 0.0671 Predicted 0.1745
Figure 6 - 14. A regression tree model predicting ‘PrpSensF’ using the 5-year dynamic predictor set. This model was generated from the sixth sub-sample and had resubstitution R2 = 0.47.
123 FmRich (Training Sample)
Node 0 Mean 25.1389 Std. Dev. 11.0110 n 475 % 100.00 Pr edic ted 25.1389
ova5incl Improvement=29.9747
<=0.43490494000000002 >0.43490494000000002
Node 1 Node 2 Mean 23.1781 Mean 40.4259 Std. Dev. 9.6660 Std. Dev. 8.6757 n 421 n 54 % 88.63 % 11.37 Pr edic ted 23.1781 Predicted 40.4259
mva5incl Improvement=15.4795
<=0.73869413500000003 >0.73869413500000003
Node 3 Node 4 Mean 18.8267 Mean 27.1918 Std. Dev. 10.4665 Std. Dev. 6.7287 n 202 n 219 % 42.53 % 46.11 Pr edic ted 18.8267 Pr edic ted 27.1918
oda5incl Improvement=5.9336
<=8.3253711500000005 >8.3253711500000005
Node 5 Node 6 Mean 17.7312 Mean 31.5625 Std. Dev. 9.9100 Std. Dev. 8.2943 n 186 n 16 % 39.16 % 3.37 Predicted 17.7312 Pr edic ted 31.5625
ova5incl Improvement=5.6625
<=0.34633437 >0.34633437
Node 7 Node 8 Mean 15.2672 Mean 23.6000 Std. Dev. 8.9191 Std. Dev. 9.7536 n 131 n 55 % 27.58 % 11.58 Predicted 15.2672 Pr edic ted 23.6000
Figure 6 - 15. A regression tree model predicting ‘InvFmRch’ using the 5-year dynamic predictor set. This model was generated from the sixth sub-sample and had resubstitution R2 = 0.47.
124
TOTN
Node 0 Mean 2.8126 Std. Dev. 3.1176 n 1158 % 100.00 Predicted 2.8126
BDA5EXCL Improvement=3.6191
<=-0.067344106000000001 >-0.067344106000000001
Node 1 Node 2 Mean 6.4567 Mean 1.8194 Std. Dev. 3.8964 Std. Dev. 1.9068 n 248 n 910 % 21.42 % 78.58 Predicted 6.4567 Predicted 1.8194
MDA 1EXCL Improvement=0.4303
<=16.869395500000003 >16.869395500000003
Node 3 Node 4 Mean 5.8075 Mean 9.5516 Std. Dev. 3.6352 Std. Dev. 3.6378 n 205 n 43 % 17.70 % 3.71 Predicted 5.8075 Predicted 9.5516
Figure 6 - 16. The final fixed form regression tree model for ‘TotN’ using all sample points. The tree was pruned to the fixed form, the largest common tree among the ten sub-samples.
125
0.70
0.60
0.50
0.40
Equivalent 0.30 2 R
0.20
0.10 VPM ex Top VPM ex VPM Fixed Form
0.00 12345678910All sites
Figure 6 - 17. The resubstitution proportion of variance explained of ‘TotN’ from RTA using subsets of the dynamic predictors. ‘Bda5ex’ and ‘mda1ex’ were identified as the top predictors and used to create the fixed form models. Eleven trees were generated for each set of predictor variables, with the first ten using an 80/20 partition for training and testing. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results
126
TOTN
Node 0 Mean 2.8126 Std. Dev. 3.1176 n 1158 % 100.00 Predicted 2.8126
BDA5EXCL Improvement=3.6191
<=-0.067344106000000001 >-0.067344106000000001
Node 1 Node 2 Mean 6.4567 Mean 1.8194 Std. Dev. 3.8964 Std. Dev. 1.9068 n 248 n 910 % 21.42 % 78.58 Predicted 6.4567 Predicted 1.8194
MDA 1EXCL BDA5EXCL Improvement=0.4303 Improvement=0.1508
<=16.869395500000003 >16.869395500000003 <=-0.056226666500000001 >-0.056226666500000001
Node 3 Node 4 Node 5 Node 6 Mean 5.8075 Mean 9.5516 Mean 3.2706 Mean 1.6872 Std. Dev. 3.6352 Std. Dev. 3.6378 Std. Dev. 2.2236 Std. Dev. 1.8201 n 205 n 43 n 76 n 834 % 17.70 % 3.71 % 6.56 % 72.02 Predicted 5.8075 Predicted 9.5516 Pr edic ted 3.2706 Predicted 1.6872
DVA1EXCL ODA5EXCL Improvement=0.1608 Improvement=0.1551
<=0.33231085999999999 >0.33231085999999999 <=5.0567765999999992 >5.0567765999999992
Node 7 Node 8 Node 9 Node 10 Mean 6.9176 Mean 4.9891 Mean 5.5280 Mean 1.6311 Std. Dev. 3.5805 Std. Dev. 3.4678 Std. Dev. 5.4032 Std. Dev. 1.6586 n 87 n 118 n 12 n 822 % 7.51 % 10.19 % 1.04 % 70.98 Predicted 6.9176 Predicted 4.9891 Predicted 5.5280 Predicted 1.6311
ODA5EXCL Improvement=0.1751
<=5.0128309499999997 >5.0128309499999997
Node 11 Node 12 Mean 3.1546 Mean 12.6483 Std. Dev. 3.7162 Std. Dev. 1.9834 n 9 n 3 % 0.78 % 0.26 Pr edic ted 3.1546 Predicted 12.6483
Figure 6 - 18. The regression tree model for ‘TotN’using the top five predictors, all sample points and cost-complexity pruning.
127
Predicted TotN 1.82 5.81 9.55 (a)
Observed TotN 0.038 - 1.820 1.821 - 9.549 9.550 - 19.400 (b)
Figure 6 - 19. A map depicting (a) predicted and (b) observed ‘TotN’ across EPA Region 7 using ‘bda5ex’ and ‘mda1ex’ as predictors. The regression tree model used to generate this map is illustrated in Figure 6-16.
128
TotN Residuals < -2 Std. Dev. -2 - -1 Std. Dev. + -1 Std. Dev. 1 - 2 Std. Dev. > 2 Std. Dev.
Figure 6 - 20. A map illustrating the residuals of the fixed form model used to predict ‘TotN’. Point classes are based on the standard deviation of the sample population of ‘TotN’ values (3.12).
129
0.700
0.600
0.500
0.400 Equivalent 2 0.300 R
0.200
VPM ex Top VPM VPM Fixed Form 0.100
0.000 12345678910All sites
Figure 6 - 21. The resubstitution proportion of variance explained of ‘PrpSensF’ from RTA using subsets of the dynamic predictors. ‘Gua5ex’ and ‘ova3ex’ were identified as the top predictors and used to create the fixed form models. Eleven trees were generated for each set of predictor variables, with the first ten using an 80/20 partition for training and testing. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results.
130
PRPSENSF
Node 0 Mean 0.1217 Std. Dev. 0.1290 n 638 % 100.00 Predicted 0.1217
OVA3EXCL Improvement=0.0051
<=0.42907130500000001 >0.42907130500000001
Node 1 Node 2 Mean 0.1018 Mean 0.3779 Std. Dev. 0.1077 Std. Dev. 0.1037 n 592 n 46 % 92.79 % 7.21 Predicted 0.1018 Predicted 0.3779
GUA5EXCL Improvement=0.0014
<=0.056928773000000002 >0.056928773000000002
Node 3 Node 4 Mean 0.0664 Mean 0.1431 Std. Dev. 0.0825 Std. Dev. 0.1187 n 319 n 273 % 50.00 % 42.79 Predicted 0.0664 Predicted 0.1431
Figure 6 - 22. A regression tree model predicting ‘PrpSensF’ using the top dynamic predictors and cost-complexity pruning. The tree form matched what was identified as the fixed model, the largest common tree structure among the ten sub-samples.
131
Predicted PrpSensF 0.0663 0.1431 0.3779 (a)
Observed PrpSensF 0.0000 - 0.0663 0.0664 - 0.3778 0.3779 - 0.6667 (b)
Figure 6 - 23. A map depicting (a) predicted and (b) observed ‘PrpSensF’ across EPA Region 7 using ‘ova3ex’ and ‘gua5ex’ as predictors. The regression tree model used in this map is similar to the tree illustrated in Figure 6-22.
132
PrpSensF Residuals < -2 Std. Dev. -2 - -1 Std. Dev. +-1 Std. Dev. 1 - 2 Std. Dev.
Figure 6 - 24. A map illustrating the residuals of the fixed form model used to predict ‘PrpSensF’. Point classes are based on the standard deviation of the sample population of ‘PrpSensF’ values (0.13).
133
FmRich
Node 0 Mean 25.3926 Std. Dev. 11.1257 n 591 % 100.00 Predicted 25.3926
mva5excl Improvement=29.6550
<=0.73538722000000001 >0.73538722000000001
Node 1 Node 2 Mean 18.7605 Mean 29.8640 Std. Dev. 10.3254 Std. Dev. 9.2683 n 238 n 353 % 40.27 % 59.73 Pr edic ted 18.7605 Predicted 29.8640
oda1excl ova1excl Improvement=5.4257 Improvement=19.5325
<=8.2139227500000001 >8.2139227500000001 <=0.44079870999999998 >0.44079870999999998
Node 3 Node 4 Node 5 Node 6 Mean 17.2878 Mean 27.9091 Mean 27.9369 Mean 46.8333 Std. Dev. 9.5692 Std. Dev. 10.2785 Std. Dev. 7.3439 Std. Dev. 6.8681 n 205 n 33 n 317 n 36 % 34.69 % 5.58 % 53.64 % 6.09 Pr edic ted 17.2878 Predicted 27.9091 Predicted 27.9369 Pr edic ted 46.8333
mva5excl Improvement=3.6412
<=0.61912807000000003 >0.61912807000000003
Node 7 Node 8 Mean 12.7391 Mean 19.5956 Std. Dev. 6.6391 Std. Dev. 10.0114 n 69 n 136 % 11.68 % 23.01 Predicted 12.7391 Pr edic ted 19.5956
Figure 6 - 25. The final fixed form regression tree model for ‘InvFmRch’ using all sample points. The tree was pruned to the fixed form, the largest common tree structure among the ten sub-samples.
134
FmRich
Node 0 Mean 25.3926 Std. Dev. 11.1257 n 591 % 100.00 Predicted 25.3926
mva5excl Improvement=29.6550
<=0.73538722000000001 >0.73538722000000001
Node 1 Node 2 Mean 18.7605 Mean 29.8640 Std. Dev. 10.3254 Std. Dev. 9.2683 n 238 n 353 % 40.27 % 59.73 Pr edic ted 18.7605 Predicted 29.8640
oda1excl ova1excl Improvement=5.4257 Improvement=19.5325
<=8.2139227500000001 >8.2139227500000001 <=0.44079870999999998 >0.44079870999999998
Node 3 Node 4 Node 5 Node 6 Mean 17.2878 Mean 27.9091 Mean 27.9369 Mean 46.8333 Std. Dev. 9.5692 Std. Dev. 10.2785 Std. Dev. 7.3439 Std. Dev. 6.8681 n 205 n 33 n 317 n 36 % 34.69 % 5.58 % 53.64 % 6.09 Pr edic ted 17.2878 Predicted 27.9091 Predicted 27.9369 Pr edic ted 46.8333
mva5excl ova1excl Improvement=3.6412 Improvement=4.6299
<=0.61912807000000003 >0.61912807000000003 <=0.37805251000000001 >0.37805251000000001
Node 7 Node 8 Node 9 Node 10 Mean 12.7391 Mean 19.5956 Mean 26.7111 Mean 34.9787 Std. Dev. 6.6391 Std. Dev. 10.0114 Std. Dev. 6.5275 Std. Dev. 7.8643 n 69 n 136 n 270 n 47 % 11.68 % 23.01 % 45.69 % 7.95 Predicted 12.7391 Pr edic ted 19.5956 Pr edic ted 26.7111 Predicted 34.9787
oda1excl Improvement=2.3473
<=5.2639673 >5.2639673
Node 11 Node 12 Mean 28.6667 Mean 18.4711 Std. Dev. 10.8342 Std. Dev. 9.3542 n 15 n 121 % 2.54 % 20.47 Pr edic ted 28.6667 Predicted 18.4711
Figure 6 - 26. The regression tree model for ‘InvFmRch’ using the top three predictors, all sample points and cost-complexity pruning.
135
0.70
0.60
0.50
0.40
Equivalent 0.30 2 R
0.20
0.10 VPM ex Top VPM ex VPM Fixed Form
0.00 12345678910All sites
Figure 6 - 27. The resubstitution proportion of variance explained of ‘InvFmRch’ from RTA using subsets of the dynamic predictors. ‘Mva5ex’, ‘oda1ex’, and ‘ova1ex’ were identified as the top predictors and used to create the fixed form models. Eleven trees were generated for each set of predictor variables, with the first ten using an 80/20 partition for training and testing. Data were not partitioned for the eleventh tree (All sites), which shows full sample resubstitution results.
136
Predicted InvFmRch 12.74 19.6 27.91; 27.94 46.83 (a)
Observed InvFmRch 1 - 13 14 - 29 30 - 45 46 - 59 (b)
Figure 6 - 28. A map depicting (a) predicted ‘InvFmRch’ and (b) observed ‘InvFmRch’ across EPA Region 7 using ‘mva5ex’, ‘ova1ex’and ‘oda1ex’ as predictors. The regression tree model used in this map is shown in Figure 6-25.
137
InvFmRch Residuals >-2 Std. Dev. -2 - -1 Std. Dev. +-1 Std. Dev. 1 - 2 Std. Dev.
Figure 6 - 29. A map illustrating the residuals of the regression tree model used to predict ‘InvFmRch’. Point classes are based on the standard deviation of the sample population of ‘InvFmRch’ values (11.13).
138 Table 6 - 1. The average R2 across ten random sub-samples using static and dynamic landscape predictors. The average variance explained was higher and in some cases, more stable with the addition of VPMs or when VPMs were used independently from static landscape predictors.
Training Validation Response Variable Predictor Set Mean SD Mean SD TotN Static 0.39 0.03 0.40 0.06 Static & VPM 0.47 0.09 0.43 0.07 VPM 0.48 0.10 0.42 0.09 PrpSensF Static 0.57 0.05 0.55 0.08 Static & VPM 0.62 0.07 0.56 0.07 VPM 0.56 0.06 0.44 0.11 InvFmRch Static 0.38 0.03 0.37 0.06 Static & VPM 0.59 0.07 0.51 0.07 VPM 0.56 0.07 0.50 0.05 PrpFmEPT Static 0.21 0.15 0.15 0.12 Static & VPM 0.41 0.14 0.23 0.13 VPM 0.42 0.13 0.21 0.08
Table 6 - 2. Importance values for the static landscape predictor set. Importance values were averaged (Avg) and weighted (WI) by variable frequency (Freq) across the ten sub- samples. TotN PrpSensF InvFmRch Predictor Avg Freq WI Predictor Avg Freq WI Predictor Avg Freq WI cropland 3.21 11 35.35 eco_num 0.00338 17 0.05750 eco_num 22.56 20 451.13 kfact 0.25 5 1.23 kfact 0.00224 10 0.02240 kfact 0.92 3 2.76 drden 0.00058 8 0.00464 shed_area 0.70 2 1.40 popden 0.00029 4 0.00116 grassland 0.00045 2 0.00090 cropland 0.00018 3 0.00054 area 0.00009 3 0.00027 slopemn 0.00011 1 0.00011 rdden 0.00005 2 0.00010 shape 0.00003 1 0.00003 drlen 0.00003 1 0.00003
139 Table 6 - 3. Importance values for the static-dynamic landscape predictor set. Importance values were averaged (Avg) and weighted (WI) by variable frequency (Freq) across the ten sub-samples. TotN PrpSensF InvFmRch Predictor Avg Freq WI Predictor Avg Freq WI Predictor Avg Freq WI bda5incl 1.471 4 5.88 eco_num 0.00339 17 0.05760 eco_num 30.09 9 270.82 cultivat 0.802 6 4.81 kfactmn 0.00224 10 0.02240 mva5excl 15.96 10 159.61 bda3incl 1.108 3 3.32 dds4excl 0.00035 4 0.00140 oda2incl 5.53 9 49.80 ova3incl 0.261 4 1.04 Popden 0.00021 3 0.00063 dda3excl 3.54 6 21.25 bda4incl 0.409 1 0.41 drlen 0.00012 3 0.00036 dva4incl 3.43 2 6.86 mda1excl 0.121 2 0.24 gus4incl 0.00018 2 0.00036 oda3incl 1.07 3 3.21 ova2incl 0.100 2 0.20 shed_area 0.00010 3 0.00030 dva4excl 0.97 3 2.92 dds2excl 0.029 1 0.03 slopemn 0.00013 2 0.00026 rdlen 0.82 3 2.45 ova1incl 0.028 1 0.03 bds4incl 0.00013 2 0.00026 ods1incl 1.04 2 2.07 slopemn 0.027 1 0.03 ava5excl 0.00007 2 0.00014 ova1excl 0.88 2 1.76 aca2incl 0.026 1 0.03 dvs1excl 0.00006 2 0.00012 oda4incl 0.78 2 1.56 gla1excl 0.018 1 0.02 dds5excl 0.00011 1 0.00011 ova4excl 0.72 2 1.44 bds1excl 0.017 1 0.02 mda4excl 0.00009 1 0.00009 oda5incl 0.54 2 1.08 ova5incl 0.014 1 0.01 bds2incl 0.00007 1 0.00007 ovs4excl 0.28 3 0.83 area30m 0.014 1 0.01 cropland 0.00005 1 0.00005 ods1excl 0.41 2 0.82 dda1excl 0.014 1 0.01 forest 0.00004 1 0.00004 oda1incl 0.37 2 0.74 ods2incl 0.014 1 0.01 acs4incl 0.00003 1 0.00003 ova5incl 0.58 1 0.58 mda3incl 0.013 1 0.01 bda1excl 0.00003 1 0.00003 area30m 0.35 1 0.35 slopestd 0.012 1 0.01 bda5excl 0.00003 1 0.00003 dva3excl 0.28 1 0.28 dvs1excl 0.012 1 0.01 dva5excl 0.00003 1 0.00003 gua2incl 0.28 1 0.28 ova4excl 0.011 1 0.01 dvs3incl 0.00003 1 0.00003 ovs5excl 0.28 1 0.28 gua5excl 0.00003 1 0.00003 mda1incl 0.27 1 0.27 ods1excl 0.00003 1 0.00003 gua1excl 0.26 1 0.26 slopestd 0.00003 1 0.00003 dda1excl 0.23 1 0.23 acs5incl 0.00002 1 0.00002 bda2incl 0.22 1 0.22 grassland 0.00002 1 0.00002 dds2incl 0.20 1 0.20 mva4excl 0.00002 1 0.00002 oda1excl 0.19 1 0.19 rdden 0.00002 1 0.00002 aca3excl 0.19 1 0.19 dds3ex 0.00011 1 0.00011 mva5incl 0.19 1 0.19 ova5excl 0.19 1 0.19 mda2excl 0.18 1 0.18 mda1excl 0.18 1 0.18 rdden 0.16 1 0.16 ods2incl 0.16 1 0.16 dda5excl 0.15 1 0.15 acs1excl 0.14 1 0.14
140 Table 6 - 4. Importance values for the dynamic landscape predictor set. Importance values were averaged (Avg) and weighted (WI) by variable frequency (Freq) across the ten sub-samples. TotN PrpSensF InvFmRch Predictor Avg Freq WI Predictor Avg Freq WI Predictor Avg Freq WI bda5incl 1.508 7 10.556 ova5incl 0.00214 4 0.00856 mva5excl 18.86 10 188.63 bda3incl 1.108 3 3.324 dvs5incl 0.00056 9 0.00504 ova1excl 9.12 11 100.36 bda4incl 0.774 3 2.321 gua5excl 0.00079 6 0.00474 oda2incl 5.58 8 44.66 ova3incl 0.184 3 0.551 gua5incl 0.00057 4 0.00228 aca3incl 6.64 2 13.28 bda5excl 0.356 1 0.356 ova3excl 0.00098 2 0.00196 ava1incl 6.12 2 12.23 ova4incl 0.088 3 0.264 bds1excl 0.00023 4 0.00092 ova5incl 1.72 3 5.16 dda1excl 0.053 3 0.160 ova5excl 0.00062 1 0.00062 aca2incl 3.46 1 3.46 ova2incl 0.062 2 0.125 ava2incl 0.00054 1 0.00054 dva4excl 1.04 3 3.12 ovs5excl 0.049 2 0.098 ova4excl 0.00051 1 0.00051 dva4incl 3.06 1 3.06 mda1excl 0.062 1 0.062 ava1incl 0.00039 1 0.00039 dva1incl 2.63 1 2.63 mda3excl 0.045 1 0.045 dva2excl 0.00012 2 0.00024 mva3excl 1.69 1 1.69 ava3incl 0.037 1 0.037 dvs4excl 0.0001 2 0.00020 ova4excl 0.80 2 1.59 aca2incl 0.026 1 0.026 ova2incl 0.00009 2 0.00018 oda3incl 0.60 1 0.60 gla5excl 0.023 1 0.023 mva2excl 0.00009 2 0.00018 ods1incl 0.52 1 0.52 gla3excl 0.023 1 0.023 mds3incl 0.00007 2 0.00014 ova3excl 0.52 1 0.52 dda3excl 0.022 1 0.022 bds4incl 0.00006 2 0.00012 oda4incl 0.51 1 0.51 gla1excl 0.021 1 0.021 dvs1excl 0.00005 2 0.00010 dda3excl 0.49 1 0.49 ovs1excl 0.020 1 0.020 bda4excl 0.00008 1 0.00008 ovs3incl 0.37 1 0.37 oda5excl 0.018 1 0.018 ods1incl 0.00007 1 0.00007 ovs1incl 0.29 1 0.29 ods3incl 0.017 1 0.017 oda4excl 0.00007 1 0.00007 oda5incl 0.29 1 0.29 bds1excl 0.017 1 0.017 oda2excl 0.00007 1 0.00007 oda5excl 0.28 1 0.28 mvs5excl 0.016 1 0.016 bds2incl 0.00007 1 0.00007 oda3excl 0.28 1 0.28 bda1incl 0.015 1 0.015 oda1excl 0.00006 1 0.00006 ovs5excl 0.28 1 0.28 ova5incl 0.014 1 0.014 gus2excl 0.00006 1 0.00006 dva1excl 0.26 1 0.26 mda3incl 0.013 1 0.013 mda2excl 0.00005 1 0.00005 dvs1excl 0.24 1 0.24 dda2incl 0.013 1 0.013 dva1excl 0.00005 1 0.00005 gua2incl 0.24 1 0.24 bds4excl 0.013 1 0.013 dda2excl 0.00005 1 0.00005 dva5excl 0.22 1 0.22 dva5excl 0.012 1 0.012 dda1excl 0.00005 1 0.00005 dda1excl 0.22 1 0.22 dvs1excl 0.012 1 0.012 ovs5incl 0.00004 1 0.00004 bda2incl 0.22 1 0.22 ova4excl 0.011 1 0.011 ovs1incl 0.00004 1 0.00004 mda1incl 0.20 1 0.20 ova1excl 0.00004 1 0.00004 aca3excl 0.19 1 0.19 mva3incl 0.00004 1 0.00004 mva5incl 0.19 1 0.19 gus3incl 0.00004 1 0.00004 dva2incl 0.18 1 0.18 dvs5excl 0.00004 1 0.00004 mda2excl 0.18 1 0.18 bda4incl 0.00004 1 0.00004 ods1excl 0.18 1 0.18 avs4incl 0.00004 1 0.00004 oda1incl 0.18 1 0.18 ovs4incl 0.00003 1 0.00003 mda2incl 0.17 1 0.17 ovs4excl 0.00003 1 0.00003 ova5excl 0.15 1 0.15 ods2incl 0.00003 1 0.00003 acs1excl 0.14 1 0.14 oda4incl 0.00003 1 0.00003 gla1incl 0.00003 1 0.00003 dva3excl 0.00003 1 0.00003 dva1incl 0.00003 1 0.00003 dds4excl 0.00003 1 0.00003 dda2incl 0.00003 1 0.00003 ovs5excl 0.00002 1 0.00002 ovs2excl 0.00002 1 0.00002 mds2incl 0.00002 1 0.00002
141 Table 6 - 5. The average and standard deviation of R2 across ten random 80-20 sub- samples for ecoregion-specific models are shown below. To obtain ‘global’ entries, 500,000 ecoregion-specific, random 80-20 data partitions were evaluated using simple resubstitution of these subsets into the global models, and coefficient of determination (R2) values were then calculated comparing model outputs to actual data values.
Training (80%) Validation (20%) Response Variable Sample Size Ecoregion Mean SD Mean SD TotN 187 CIP 0.53 0.31 0.46 0.37 1158 (all points) CIP (global) 0.02 0.01 0.06 0.08 131 OH 0.55 0.39 0.28 0.30 1158 (all points) OH (global) 0.34 0.10 0.35 0.30 346 WCPB 0.61 0.13 0.38 0.10 1158 (all points) WCBP (global) 0.60 0.02 0.60 0.08 PrpSensF 74 CIP 0.54 0.29 0.41 0.27 638 (all points) CIP (global) 0.23 0.07 0.31 0.23 49 OH 0.63 0.30 0.41 0.29 638 (all points) OH (global) 0.43 0.07 0.40 0.25 294 WCPB 0.66 0.07 0.45 0.10 638 (all points) WCBP (global) 0.54 0.02 0.54 0.08 InvFmRch 91 CIP 0.67 0.19 0.40 0.24 591 (all points) CIP (global) 0.45 0.04 0.46 0.15 80 OH 0.63 0.28 0.42 0.31 591 (all points) OH (global) 0.59 0.04 0.61 0.16 250 WCPB 0.69 0.07 0.43 0.13 591 (all points) WCBP (global) 0.29 0.03 0.30 0.13
Table 6 - 6. The average and standard deviation of R2 for global models across ten random sub-samples using three VPM temporal windows as predictor sets.
Training Validation Response Variable Predictor Set Mean SD Mean SD TotN 5in 0.39 0.03 0.39 0.06 1in 0.34 0.03 0.34 0.07 1ex 0.35 0.02 0.36 0.07 PrpSensF 5in 0.43 0.05 0.37 0.10 1in 0.30 0.05 0.27 0.09 1ex 0.31 0.11 0.25 0.11 InvFmRch 5in 0.47 0.02 0.42 0.08 1in 0.45 0.04 0.37 0.08 1ex 0.47 0.05 0.43 0.10
142 Table 6 - 7. Importance values for landscape predictor variables using a subset of the dynamic predictor set (VPMs with the sampling year excluded). Importance values were averaged (Avg) and weighted (WI) by variable frequency (Freq) across the ten sub- samples. TotN PrpSensF InvFmRch Predictor Avg Freq WI Predictor Avg Freq WI Predictor Avg Freq WI bda5ex 3.28 9 29.49 gua5ex 0.0011 8 0.00864 mva5excl 25.07 10 250.65 bda4ex 0.33 1 0.33 ova3ex 0.0021 4 0.00820 ova1excl 9.96 15 139.48 mda1ex 0.10 2 0.20 ova4ex 0.0016 3 0.00471 oda1excl 4.31 8 34.45 oda5ex 0.04 2 0.09 ava3ex 0.0009 2 0.00186 ova3excl 7.24 4 28.96 dva1ex 0.04 2 0.08 ova5ex 0.0006 1 0.00062 dva4excl 1.36 3 4.09 dva3ex 0.05 1 0.05 gua4ex 0.0001 1 0.00012 ava3excl 3.12 1 3.12 dda2ex 0.03 1 0.03 mva3ex 0.0001 1 0.00006 ova2excl 1.74 1 1.74 dda1ex 0.02 1 0.02 bda1ex 0.0001 1 0.00005 oda5excl 0.62 2 1.24 avs1ex 0.02 1 0.02 mda3ex 0.0001 1 0.00005 dda3excl 0.73 1 0.73 gla5ex 0.02 1 0.02 ods3ex 0.0000 1 0.00004 oda4excl 0.71 1 0.71 mva2ex 0.0000 1 0.00003 ova4excl 0.61 1 0.61 dva3excl 0.48 1 0.48 ovs2excl 0.22 1 0.22 dda1excl 0.22 1 0.22 mda1excl 0.21 1 0.21
Table 6 - 8. The average R2 across ten random sub-samples using the top VPM predictors. Regression trees were generated using cost-complexity pruning and a fixed model approach.
Training Validation Dynamic Response Variable Variable Tree Form Mean SD Mean SD TotN VPM ex Cost-Complexity Pruned 0.40 0.06 0.39 0.07 Top VPM ex Cost-Complexity Pruned 0.38 0.02 0.39 0.07 Top VPM ex Fixed Form 0.42 0.02 0.42 0.08 PrpSensF VPM ex Cost-Complexity Pruned 0.40 0.06 0.34 0.10 Top VPM ex Cost-Complexity Pruned 0.35 0.06 0.33 0.11 Top VPM ex Fixed Form 0.39 0.02 0.36 0.09 InvFmRch VPM ex Cost-Complexity Pruned 0.51 0.04 0.46 0.08 Top VPM ex Cost-Complexity Pruned 0.47 0.05 0.45 0.09 Top VPM ex Fixed Form 0.48 0.02 0.43 0.06
143 7.0 Results - Implementing a Model: The Stream Trace Map
7.1 Introduction In this section we provide an example of a stream trace map, in which each point in the stream network within the watershed is “predicted” using a final model from the decision tree analysis. To create the map, VPMs are extracted for each point in the stream network using each stream point’s respective upstream reach (which is based on the derived flow direction map). The model is then evaluated at each stream point using the extracted VPM information, and model outputs are written to a stream network map so that each stream point is assigned its predicted value from the model.
7.2 Study Area The Walnut River watershed is located in southeast Kansas (Figure 7-1). With a general north-south flow, much of the west side of the watershed receives drainage from land dominated by cropland, whereas most of the eastern half receives input from Flint Hills grasslands (see Figure 7-1 inset). The city of El Dorado is located just below El Dorado Lake, which is depicted in the inset map. The city of Wichita, though not in the watershed, is located immediately to the west of the watershed.
7.3 Results The all-ecoregion decision tree model developed for the ‘PrpSensF’ variable consists of three nodes, or three value classifications. In particular, the center value of Node 3 is 0.066, the center of Node 4 is 0.143, and the center of Node 2 is 0.378. Node assignment depends on two VPMs, ‘ov3ex’ (3-year average NDVI at green-up onset, excluding the measurement year) and ‘gu5ex’ (5-year average rate of green-up, excluding the measurement year). See Figure 6-22 in the decision tree section for details on the splitting criteria that determine node assignment for this model. The ‘PrpSensF’ model was applied to make predictions for two years, 1994 and 2004. Given the 1989-2003 temporal extent of the VPM database developed for this research, 1994 and 2004 represent the first and last possible years, respectively, for which predictions could be made due to the constraint imposed by the model’s dependency on the ‘gu5ex’ variable. Processing these two years allows for the creation of a change map, which may be useful for indicating locations where conditions have become more or less favorable for the indicator in question. Figure 7-2 shows results from the ‘PrpSensF’ stream trace classifications for 1994 and 2004. As somewhat anticipated, there appears to be a tendency for lower ‘PrpSensF’ values in the western side of the watershed, where the summary VPM statistics have more influence from cropland. Figure 7-3 shows the ‘PrpSensF’ change map. If a stream point was assigned to a node with a lesser value in 2004 than in 1994, then the point was assigned to the “decrease” class in the change map. Assignment to the “no change” and “increase” classes were similarly logically defined. With the exception of the southwest quadrant of the watershed, the model projections indicate that most areas have maintained or increased their ‘PrpSensF’ values when comparing 1994 to 2004. In regards to the
144 somewhat prevalent decrease in the southeast quadrant, much urban development occurred in this region during between 1994 and 2004, primarily between Wichita and Walnut River, providing one possible explanation for the decline in estimated ‘PrpSensF’ values if we assume urbanization has a negative impact on this metric. Considering that the ‘PrpSensF’ measure quantifies the “proportion of sensitive fish species,” predicting values for this variable at extreme, intermittent flowing headwaters is probably not a meaningful exercise. Consequently, we created a reduced stream trace map that should have a much greater concentration of perennial flowing stream segments. To do this, we changed the threshold for stream designation from 1500 pixels in the upstream reach to 10000 pixels. This reduced the number of 30-m stream pixels from 101,333 to 44,239. Figure 7-4(a) shows a comparison of the ‘snet1500’ and the ‘snet10000’ stream networks, and Figure 7-4(b) shows the ‘snet10000’ trace map overlaid on the percent cropland map. It is worth noting that in this watershed, the NHD stream trace map (not shown) is markedly more dense and extensive than even the ‘snet1500’. 1994 and 2004 ‘PrpSensF’ predictions for the ‘snet10000’ trace map are shown in Figure 7-5. The associated change map is shown in Figure 7-6. Values depicted in these maps are simply subsets of the values shown in Figures 7-2 and 7-3, and similar synoptic patterns are evident. Table 1 provides a quantitative summary of the results from application of the ‘PrpSensF’ decision tree model to the two stream trace maps. In both cases, approximately 10% of the stream points showed a decline in ‘PrpSensF’ value from 1994 to 2004, about 65% showed no change, and about 25% exhibited an increase.
145
Wichita
Figure 7 - 1. Location (in Kansas) of the portion of the Walnut River watershed used to demonstrate the stream trace map. The pour point is at the southern tip of the watershed. The inset blow-up of the watershed displays the ‘snet1500’ synthetic stream network along with the 1-km percent cropland map layer. El Dorado Lake is also shown in the inset.
(a) (b)
Figure 7 - 2. Decision tree model ‘PrpSensF’ predictions for the Walnut River watershed ‘snet1500’ synthetic stream network in (a) 1994 and (b) 2004.
146
Figure 7 - 3. ‘PrpSensF’ change map, comparing predicted values from 1994 and 2004 in the ‘snet1500’ synthetic stream network.
(a) (b)
Figure 7 - 4. (a) Density comparison between ‘snet1500’ and ‘snet10000’. (b) ‘snet10000’ stream network overlaid on the 1-km percent cropland map layer.
147
(a) (b)
Figure 7 - 5. Decision tree model ‘PrpSensF’ predictions for the Walnut River watershed ‘snet10000’ synthetic stream network in (a) 1994 and (b) 2004.
Figure 7 - 6. ‘PrpSensF’ change map, comparing predicted values from 1994 and 2004 in the ‘snet10000’ synthetic stream network.
148
Table 7 - 1. Summary of pixel-level results from application of the ‘PrpSensF’ decision tree model to the Walnut River watershed stream points.
Stream Node (Value) Change # of stream % of stream 2004 Network 3 (0.066) 4 (0.143) 2 (0.367) Class pixels pixels 1994 3 (0.066) 33608 24582 65 Decrease 9897 9.8% snet1500 4 (0.143) 9426 33115 61 No Change 66728 65.9% 2 (0.367) 399 72 5 Increase 24708 24.4% 3 (0.066) 15255 10956 3 Decrease 4774 10.8% snet10000 4 (0.143) 4496 13204 43 No Change 28463 64.3% 2 (0.367) 222 56 4 Increase 11002 24.9%
149 8.0 Summary
Significant accomplishments and conclusions are presented in the section. Major project tasks are outlined and described under Accomplishments. Under Conclusions, noteworthy results are highlighted. Sections 8.4 - 8.7 list publications, manuscripts in preparation, presentations, and graduate student support conducted under EPA Cooperative Agreement RD-83059701.
8.1 Accomplishments • A GIS database for the four-state EPA Region 7 study area was constructed. Major activities included (1) creating the 15-year VPM database, (2) acquiring various thematic data (e.g., soils, population), (3) DEM conditioning and building flow direction and flow accumulation grids, (4) creating synthetic streams and placing sampling locations on the resulting network, and (5) creating watershed grids that were used to extract summary statistics. • A regional field sample database for stream chemistry, benthic macro- invertebrates, and fish was constructed from multiple sources. Major activities included (1) building a consistent record format (i.e., aggregating multiple within- year samples, eliminating infrequently recorded attributes), (2) eliminating outliers, and (3) filtering the number of response variables based on statistical properties and expert knowledge. After processing the field sample database, three response variables were chosen for modeling: total nitrogen, benthic macroinvertebrate total taxa richness, and proportion sensitive fish species. • An analysis evaluating whether there is an area-of-influence effect on the predictor/response relationship was conducted. VPM statistics were extracted from 10 successively larger (nested) regions hydrologically near and upstream from the sample point, as well as the entire watershed. Bivariate analysis between the VPMs and three response variables suggested that statistics from the entire watershed were generally preferable to use. • An analysis evaluating the effect of watershed size on sample site ecological response values was conducted. Bivariate analysis revealed that each of the three response variables exhibited some dependence on watershed size. Further analysis examined how the VPM predictor/response relationship varied with watershed size. In general, stronger relationships occurred with the larger watersheds. • An analysis of predictor variables and development of a model using regression tree analysis (RTA) to estimate the three aquatic response variables. RTA results revealed the addition, or independent use, of dynamic predictors generally increased model performance over traditionally used static predictors. A unique set of VPMs corresponding to particular lagged temporal windows were identified as optimal for predicting each response variable. Final regression tree models explained 0.39-0.48 of the variation in the response variables. When comparing global and ecoregion-specific models, results supported the use of global models but also demonstrated the need for more localized models in some situations.
150 • A final model for proportion sensitive fish species from the decision tree analysis was selected to demonstrate how it might be applied in a classification. Using a stream trace map, each point in the stream network within the watershed was “predicted” and mapped for two years, 1994 and 2004. Based on these maps, a change map was created that depicts the response variable status according to “decrease”, “no change”, and “increase”.
8.2 Conclusions • VPMs are dynamic landscape predictors that explained 30-50% of the variance in the three response variables. • VPMs can be used to rank order (classify) watershed response conditions. • VPMs are generally better at predicting response variables than land use/land cover and other commonly used landscape predictors. • Although VPMs are correlated with land cover (e.g., percent cropland), they contain additional information reflecting, for example, annual variations in vegetation condition and cropping practice. It is this information that contributes to the stronger predictor/response relationship. • Although each response variable had a unique set of predictor VPM variables, rate of senescence was a common predictor for total nitrogen. Rate of senescence appeared to work as a surrogate for percent cropland and ecoregion, but also contained additional explanatory information. • Landscape fragmentation was not an important predictor. None of the spatial standard deviation statistics were important landscape predicators. • Sample point area-of-influence, or proximity, was not important. The strength of the predictor/response relationship was stronger when the entire watershed was considered. • Watersheds > 1,500 sq. km have a more consistent predictor/response relationship for total nitrogen. • Watersheds > 900 sq. km have a more consistent predictor/response relationship for proportion sensitive fish. • Watersheds > 100 sq. km have a more consistent predictor/response relationship for invertebrate family richness. • A regional field sample database can be successfully built from disparate sources and employed in region-wide water resource investigations.
8.3 Research Needs • Long-term study is needed to evaluate the utility of the classification scheme. • Additional research is needed to more fully characterize the relationship of response lag to the short-term and long-term VPM summary statistics. • Since AVHRR data have relatively coarse grain (1 km), the use of fine-resolution data such as those from the 250-m Moderate Resolution Imaging Spectroradiometer (MODIS) is needed to explore issues related to landscape granularity.
151 8.4 Publications Thorp, J.H., M.C. Thoms, and M.D. Delong. 2006. The riverine ecosystem synthesis: biocomplexity in river networks across space and time. River Research and Applications 22(2):123-147.
Thorp, J.H. and S. Mantovani. 2005. Zooplankton in turbid and hydrologically dynamic, prairie rivers. Freshwater Biology 50(9):1474-1491.
8.5 Presentations Desotelle, M. and J. Thorp. 2007. Trophic dynamics of aquatic organisms in grassland and Ozark ecoregions. Annual meeting of the North American Benthological Society. 2006. Anchorage, Alaska.
Martinko, E. A., Peterson, D., Whistler, J., and Jakubauskas, M.E. 2006. Linking interannual land use/land cover dynamics with stream water quality for watershed vulnerability assessment: A hierarchical statistical approach using time series satellite imagery. 2006 USGS North America Land Cover Summit, Washington DC, September 20-22.
Peterson, D.L., Whistler, J.W., Jakubauskas, M.E., and Martinko, E.A. 2006. Derivation of watersheds and stream networks using digital elevation data. 2006 MidAmerica GIS Conference, Kansas City, April 23-27, 2006.
8.6 Manuscripts in Preparation Desotelle, M., J. Thorp, J. Robards, et al.* Food web responses of riverine communities to watershed and riverine conditions in forested and prairie ecoregions. For submission to Freshwater Biology.
Kastens, J., J.Whistler, D. Peterson, D. Huggins, et al.* The effect of area-of-influence on predicting watershed aquatic response variables. For submission to Ecological Applications.
Kastens, J., J.Whistler, D. Peterson, D. Huggins, et al.* The effect of watershed size on predicting watershed aquatic response variables. For submission to Ecological Applications.
Peterson, D., J. Kastens, J.Whistler, D. Huggins, et al.* Using landscape and phenology metrics to classify watershed aquatic response variables in a tree framework. For submission to International Journal of Remote Sensing.
Thorp, J., R. Hagen, S. Campbell, et al.* The structure of fish communities in response to watershed and riverine conditions in the U.S. Central Plains. For submission to Transactions of the American Fisheries Society.
* Authors and author order are not finalized.
152 8.7 Graduate Students Supported Ms. Micaleila Desotelle (Masters thesis 2007)
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