The SPARROW Surface Water-Quality Model: Theory, Application and User Documentation

U.S. Geological Survey Techniques and Methods
Book 6, Section B, Chapter 3

By G.E. Schwarz, A.B. Hoos, R.B. Alexander, and R.A. Smith

Contents

Abstract            1

Acknowledgment            1

Part 1:  A theoretical and practical introduction to SPARROW            2

1.1 Introduction            2

1.2 SPARROW modeling concepts            3

1.2.1 Model objectives            3

1.2.1.1 Water-quality description            3

1.2.1.2 Contaminant source analysis            4

1.2.1.3 Water-quality simulation            5

1.2.1.4 Hypothesis testing: examining the importance of explanatory factors and processes            5

1.2.1.5  Design of sampling networks            6

1.2.2 Mass balance approach            7

1.2.3 Time and space scales of the model            9

1.2.4 Accuracy and complexity of SPARROW models            11

1.2.5 Comparison of SPARROW with other watershed models            15

1.3 SPARROW model infrastructure            18

1.3.1 Monitoring station flux estimation            19

1.3.1.1 Model specification for monitoring station flux estimation            21

1.3.1.2 Monitoring station flux prediction (advanced)            24

1.3.1.3 Mean detrended flux (advanced)            26

1.3.1.4 Tools for flux estimation            28

1.3.1.5 Guidance on station and record selection            30

1.3.1.6 Guidance for specifying monitoring station flux models            31

1.3.1.7 Related topics            32

1.3.1.8 Mean flow-weighted concentration (advanced)            32

1.3.1.9 Mean time-weighted concentration (advanced)            33

1.3.2 Stream network topology            34

1.3.3 Watershed sources and explanatory variables            37

1.4 Model specification            39

1.4.1 Model equation and specification of terms            39

1.4.2 Contaminant sources            42

1.4.3 Landscape variables            46

1.4.4 Stream transport            48

1.4.5 Reservoir/lake transport            54

1.4.6 Regional model coefficients and nested model designs            57

1.5 Model estimation            59

1.5.1 A guide to nonlinear estimation            59

1.5.1.1 Brief review of ordinary least squares            59

1.5.1.2 Nonlinear weighted least squares            61

1.5.1.3 The asymptotic covariance matrix            64

1.5.1.4 Estimation of leverage in the nonlinear model (advanced)            64

1.5.1.5 Estimation of gradients (advanced)            65

1.5.2 Asymptotic properties of the estimators (advanced)            66

1.5.2.1 Implications of asymptotic normality (advanced)            68

1.5.2.2 Asymptotic properties within a single basin—three examples (advanced)            69

1.5.3 Coefficient bias and uncertainty—additional issues            74

1.5.3.1 Bootstrap estimate of coefficient bias (advanced)            75

1.5.3.2 Bootstrap estimate of the coefficient covariance matrix (advanced)            76

1.5.3.3 Bootstrap coefficient confidence interval (advanced)            76

1.5.3.4 Discussion of bootstrap methods for coefficient estimation            77

1.5.3.5 Measurement error (advanced)            78

1.5.4 Evaluation of the model parameters            80

1.5.4.1 Statistical evaluations            80

1.5.4.2  Physical interpretations            82

1.5.4.3 Statistical insignificance and multicollinearity            84

1.5.5 Evaluation of model errors            90

1.5.5.1 Heteroscedasticity            90

1.5.5.2 Spatial biases            94

1.5.5.3 Statistical outliers            95

1.5.6 Measures of model performance and fit            96

1.5.7 Non-nested tests (advanced)            98

1.6 Model predictions            99

1.6.1 Prediction equation            99

1.6.2 Parametric predictions            101

1.6.3 Bias-corrected predictions based on bootstrapping (advanced)            102

1.6.4 Prediction standard errors based on bootstrapping (advanced)            105

1.6.5 Prediction intervals based on bootstrapping (advanced)            107

1.6.6 Discussion            111

1.6.6.1 The effect of error in measured flux (advanced)            112

1.6.7 Share of flux delivered to a target reach            113

1.7 Summary            115

1.8 References            116

Part 2:  SPARROW User’s Guide            123

2.1 Introduction            123

2.2 System requirements            123

2.3 Obtaining and installing software            123

2.4 Input/output structure            125

2.5 Navigating in SAS for Windows            127

2.5.1 The basic workspace            127

2.5.2 Active windows and menus            128

2.5.3 Opening SAS program files            128

2.5.4 Viewing SAS data files            130

2.5.5 Moving around in the SAS Explorer window            130

2.6 Model input            131

2.6.1 Data file            131

2.6.1.1 Reach topology            133

2.6.1.2 Reach attributes            133

2.6.1.3 Contaminant flux            133

2.6.2 Geographic Information System (GIS) base maps (optional)           134

2.6.3 Control file            134

2.6.3.1 Directory and input data            135

2.6.3.2 Bootstrap iterations and seeds (advanced)            136

2.6.3.3 Model specification            138

2.6.3.4 Process specification            144

2.6.3.5 Advanced process specification            150

2.6.3.6 Additional variable definitions            155

2.6.3.7 Options for model execution            158

2.6.3.8 Data modifications            162

2.7 Executing the model            164

2.8 Model output            166

2.8.1 Estimation output            167

2.8.1.1 Nonlinear optimization results and diagnostics            167

2.8.1.2 Coefficients and diagnostic statistics for the nonlinear weighted least squares model            172

2.8.1.3 Graphical output            173

2.8.1.4 Estimation output data files            179

2.8.1.5 Summary estimation output            182

2.8.2 Prediction output            182

2.8.2.1 Summary results            182

2.8.2.2 Prediction output data files            184

2.8.3 Other file output            187

2.8.3.1 Ouput file “comments_all”            187

2.8.3.2 Text file output (optional)            187

2.8.3.3 Bootstrap intermediate files (optional)            187

2.8.4 GIS maps (optional)            188

2.8.4.1 Residuals map            188

2.8.4.2 Reach map            191

2.9 Common execution errors and diagnostic tests            193

2.9.1 Errors during data preparation            193

2.9.2 Estimation execution errors            195

2.9.2.1 Estimation execution errors caused by systematic errors in input data            195

2.9.2.2 Estimation execution errors caused by numerical overflow—using the test-calibration mode            197

2.9.2.3 Estimation execution errors related to bootstrap analysis            198

2.9.3 Prediction execution errors            199

2.9.3.1 Test-prediction mode            199

2.9.3.2 Evaluation of summary table of reach predictions            200

2.10 References            202

Appendix

A. Determination of the Bootstrap Confidence Interval Quantiles            203

B. Hydrologic Network Development            204

C. SAS/GIS Mapfile Creation            208

D. Descriptions of Output Files            217

D.1 Estimation Output File “summary_betaest”            217

D.2 Estimation Output File “cov_betaest”            221

D.3 Estimation Output File “resids”            222

D.4 Estimation Output File “boot_betaest_all”            226

D.5 Estimation Output File “test_resids”            227

D.6 Prediction Output File “predict”            228

D.7 Prediction Output File “summary_predict”            239

D.8 Prediction Output File “lu_yield_percentiles”            239

D.9 Prediction Output File “test_data”            239

D.10 Prediction Output File “test_predict”            243

D.11 Prediction Output Files with Bootstrap Intermediate Results (“store_[variable_name]”)            247

Back