# Comparison of Deterministic and Statistical Models for Water Quality Compliance Forecasting in the San Joaquin River Basin, California

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## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Real-Time Salinity Management

#### 3.1. WARMF Water Quality Simulation Model

#### 3.2. ANN-Based Statistical Models

#### 3.3. Simple Regression Model

_{grad}= (Q

_{t}− Q

_{(t−1)})/Q

_{(t−1)}

_{t}is the flow at time t, and Q

_{(t−1)}is the flow at the previous time step.

_{grad}= −0.5396 × Q

_{grad}+ 0.0038

_{t}− ⟦EC

_{(t−1)})/⟦EC)

_{(t−1)}] = −0.5396 × Q

_{t}− Q

_{(t−1)})/Q

_{(t−1)}+ 0.0038

_{t}= ⟦EC]

_{(t−1)}− [0.5396 × (Q

_{t}− Q

_{(t−1)})/Q

_{(t−1)}+ 0.0038] × ⟦EC]

_{(t−1)}

_{t}= ⟦EC]

_{(t−1)}+ [−0.4413 × (Q

_{t}− Q

_{(t−1)})/Q

_{(t−1)}+ 0.0036] × ⟦EC]

_{(t−1)}

## 4. Comparison of the SJR WARMF and Regression Model Applications

## 5. Time Series Comparisons of the WARMF and Regression Models

## 6. Statistical Analyses

- Visual examination of the observed EC data and Regression and WARMF model EC forecasts at selected forecast lead times using boxplot graphical output.
- Statistical testing of the normality of the observed EC data and model EC forecasts using the Shapiro–Wilks test at selected forecast lead times.
- Statistical testing to determine whether the observed EC data and model EC forecasts have similar variances using the Fligner–Killeen test at selected forecast lead times.
- Scatterplots of the output from the Regression and WARMF model forecasts data at selected forecast lead times.
- Developing linear models using a forecast response variable and observation explanatory variable and computing the adjusted R-squared as an indicator of model goodness of fit at selected forecast lead times.
- Matched pair permutation testing to evaluate the whether the means of the observed EC and model forecast EC are statistically significant at the selected forecast lead times.

- Visual analysis and statistical tests indicate that although both observed EC and model forecast EC are not normally distributed their variance are sufficiently similar to validate the use of the matched pair permutation test to test whether the mean of the EC observations and model EC forecasts are statistically similar.
- The Regression model has consistently higher adjusted R-squared values than the WARMF model at all lead times indicating it has a relatively better goodness of fit.
- The matched pair permutation testing suggests that both models can make reasonably good EC forecasts out to approximately 7 days.

#### Discussion of Model Evaluations

## 7. Case Study: Forecasts of EC Exceedances during Spring 2021

## 8. Stakeholder Response and Coordination

## 9. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- United States Environmental Protection Agency (USEPA). Impaired Waters and TMDLs: Overview of Total Maximum Daily Loads (TMDLs). 2018. Available online: http://www.epa.gov/tmdl/overview-total-maximum-daily-loads-tmdls#6 (accessed on 6 March 2020).
- Ambrose, R.B.; Martin, J.L.; McCutcheon, S.C. Technical Guidance Manual for Performing Waste Load Allocations, Book III: Estuaries, Part 2: Application of Estuarine Waste Load Allocation Models; U.S. Environmental Protection Agency Report EPA-823-R-92-003; Office of Water: Washington, DC, USA, 1990. [Google Scholar] [CrossRef]
- Martin, J.L.; McCutcheon, S.C. Hydrodynamics and Transport for Water Quality Modeling; CRC Press: New York, NY, USA, 1999. [Google Scholar]
- McCutcheon, S.C. Water Quality Modeling: Volume I, River Transport and Surface Exchange; CRC Press: Boca Raton, FL, USA, 1989. [Google Scholar]
- McCutcheon, S.C.; Zhu, D.W.; Bird, S.L. Model calibration, validation and use. In Technical Guidance Manual for Performing Waste Load Allocations, Book III Estuaries, Part 2 Application of Estuarine Waste Load Allocation Models; EPA 823 R 92 003; Ambrose, R.B., Martin, J.L., McCutcheon, S.C., Eds.; United States Environmental Protection Office of Water: Washington, DC, USA, 1990; p. 77. [Google Scholar]
- Borah, D.K.; Ahmadisharaf, E.; Padmanabhan, G.; Imen, S.; Mohamoud, Y.M. Watershed models for development and implementation of total maximum daily loads. J. Hydrol. Eng.
**2019**, 24, 03118001. [Google Scholar] [CrossRef] - Chapra, S.C. Engineering water quality models and TMDLs. J. Water Resour. Plan. Manag.
**2003**, 129, 247–256. [Google Scholar] [CrossRef] - Zhang, H.X.; Quinn, N.W.T. Simple models and analytical procedures for total maximum daily load assessment. J. Hydrol. Eng.
**2019**, 24, 02518002. [Google Scholar] [CrossRef] [Green Version] - Task Committee on TMDL Modeling and Analysis. Total Maximum Daily Load Analysis and Modeling: Assessment of the Practice; Environmental and Water Resources Institute, American Society of Civil Engineers: Reston, VA, USA, 2017. [Google Scholar]
- Ahmadisharaf, E.; Camacho, R.A.; Zhang, H.X.; Hantush, M.M.; Mohamoud, Y.M. Calibration and validation of watershed models and advances in uncertainty analysis in TMDL studies. J. Hydrol. Eng.
**2019**, 24, 03119001. [Google Scholar] [CrossRef] - Ahmadisharaf, E.; Benham, B. Risk-based decision making to evaluate pollutant reduction scenarios. Sci. Total Environ.
**2020**, 70, 135022. [Google Scholar] [CrossRef] [PubMed] - California Environmental Protection Agency. Total Maximum Daily Load for Salinity and Boron in the Lower San Joaquin River; Staff Report; Regional Water Quality Control Board: Central Valley Region: Sacramento, CA, USA, 2002. [Google Scholar]
- California Regional Water Quality Control Board. Amendments to the Water Quality Control Plan for the Sacramento River and San Joaquin River Basin; Draft Final Staff Report and Technical TMDL Report; California Regional Water Quality Control Board: Sacramento, CA, USA, 2004. [Google Scholar]
- Quinn, N.W.T. Policy Innovation and Governance for Irrigation Sustainability in the Arid, Saline San Joaquin River Basin. Sustainability
**2020**, 12, 4733. [Google Scholar] [CrossRef] - Quinn, N.W.T.; Hanna, W.M. A decision support system for adaptive real-time management of seasonal wetlands in California. Environ. Modeling Softw.
**2003**, 18, 503–511. [Google Scholar] [CrossRef] [Green Version] - Quinn, N.W.T.; Karkoski, J. Real-time management of water quality in the San Joaquin River Basin. California. Am. Water Resour. Assoc.
**1998**, 34, 1473–1486. [Google Scholar] [CrossRef] - Arax, M.; Wartzman, R. The King of California: J.G. Boswell and the Making of a Secret American Empire; Public Affairs: New York City, NY, USA, 2005; ISBN 1-58648-281-5. [Google Scholar]
- Oster, J.D.; Wichelns, D.E.W. Hilgard and the history of irrigation in the San Joaquin Valley: Stunning productivity, slowly undone by inadequate drainage. In Salinity and Drainage in San Joaquin Valley, California: Science, Technology, and Policy; Chang, A.C., Silva, D.B., Eds.; Springer: Dordrecht, The Netherlands, 2014; pp. 7–46. [Google Scholar]
- Quinn, N.W.T. The San Joaquin Valley: Salinity and Drainage Problems and the Framework for a Response. In Salinity and Drainage in San Joaquin Valley, California: Science, Technology, and Policy, Global Issues in Water Policy 5; LBNL Topical, Report–LBL-38498; Chang, A.C., Brawer Silva, D., Eds.; Springer Science+Business Media: Dordrecht, The Netherlands, 2014. [Google Scholar] [CrossRef]
- Brownell, J. Potential SJR Daily Salt Discharge Exceedance Fees by Subarea (10-Year Period: 2001–2012); Analysis Performed by CRWQCB Staff to Estimate Potential Annual Fee Schedules for Subareas Contributing Salt to the SJR; California Regional Water Quality Control Board: Sacramento, CA, USA, 2012. [Google Scholar]
- California Regional Water Quality Control Board. Amendments to the Water Quality Control Plan (Basin Plan) for the Sacramento River Basin and San Joaquin River Basin (with Amendments) Final Staff Report; California Regional Water Quality Control Board: Sacramento, CA, USA, 2018. [Google Scholar]
- Chen, C.W.; Herr, J.; Gomez, L.E.; Quinn, N.W.T.; Kipps, J.; Landis, P.J.; Cummings, E.W. Design and Development of a Graphic User Interface for Real-Time Water Quality Management of the San Joaquin River; California Department of Water Resources: San Joaquin, CA, USA, 1996. [Google Scholar]
- Herr, J.; Weintraub, L.H.Z.; Chen, C.W. User’s Guide to WARMF: Documentation of Graphical User Interface; Topical report; EPRI: Palo Alto, CA, USA, 2001. [Google Scholar]
- Herr, J.; Chen, C.W. San Joaquin River Model: Calibration Report. CALFED Project ERP-02D- P63 Monitoring and Investigations for the San Joaquin River and Tributaries Related to Dissolved Oxygen; Systech Water Resources Inc.: San Ramon, CA, USA, 2006. [Google Scholar]
- Herr, J.W.; Chen, C.W. WARMF: Model use, calibration, and validation. Trans. ASABE
**2012**, 55, 1387–1394. [Google Scholar] [CrossRef] - California State Water Resources Control Board. Regulation of Agricultural Drainage to the San Joaquin River; Final Report, Order No. WQ 85-1; California State Water Resources Control Board: Sacramento, CA, USA, 1985. [Google Scholar]
- Kratzer, C.R.; Pickett, P.J.; Rashimawi, E.A.; Cross, C.L.; Bergerson, K.D. An Input-Output Model of the San Joaquin River from the Lander Avenue Bridge to the Airport Way Bridge; Technical Committee Report No. N.Q. 85-1; California Water Resources Control Board: Sacramento, CA, USA, 1987. [Google Scholar]
- Quinn, N.W.T.; Amye, O.; Herr, J.; Wang, J.; Raley, E. WARMF-Online—A Web-Based Portal Supporting Real-time Salinity Management in the San Joaquin River Basin. Open Water J.
**2017**, 4, 4. [Google Scholar] - Lu, J.; Wang, J.; Raley, E.; Quinn, N.W.T.; Kabir, J. An Alternative Approach to Salinity Forecasting in the Lower San Joaquin River; Modern Environmental Science and Engineering; MESE20191018-2; California Water Resources Control Board: Sacramento, CA, USA, 2019. [Google Scholar]
- Chen, Y.; Song, L.; Liu, Y.; Yang, L.; Li, D.A. Review of the Artificial Neural Network Models for Water Quality Prediction. Appl. Sci.
**2020**, 10, 5776. [Google Scholar] [CrossRef]

**Figure 1.**Major subareas within the SJR Basin that drain to the SJR as defined in the salinity TMDL [13]. Reach 83 shown in the figure is the reach for which water quality (salinity) is regulated through the recognition of three compliance monitoring stations at Crows Landing, Maze Road Bridge and Vernalis. The most salient feature of the SJR Basin is that drainage from sources to the west of the SJR are elevated in salinity by virtue of native salts in alluvial sediments deposited from the coastal range mountains west of the Valley floor and the importation of irrigation water supply from the Sacramento-San Joaquin Delta that is also salt impacted. Tributary inflow from land areas to the east of the SJR are of high quality, derived from snowmelt from the Sierra Nevada mountains. Real-time management is essentially a scheduling activity—coordinating salt load assimilative capacity consumed by west-side saline drainage with salt load assimilative capacity supplied by east-side reservoir releases along the major tributaries.

**Figure 2.**Map of the SJR Basin represented as major contributing watersheds within the WARMF model. The WARMF model allows further disaggregation of these watersheds into small contributing subareas and allows the substitution of available data at the major outlets of these subareas for model-derived flow and water quality estimates.

**Figure 3.**A unique feature of the WARMF model is the availability of customized model outputs such as the “Gowdy” output (named after its developer) shown here. This depicts a Lagrangian view of the SJR at any point in time showing the major inflow to and diversions from the river approximately every ½ mile (800 m) along its main reach as well as the incremental flow and EC concentration from the origin at Lander Avenue to the EC compliance monitoring station at Vernalis [23,25].

**Figure 4.**Flow and EC observations at Vernalis compliance monitoring station on the SJR for the period 2000–2018.

**Figure 5.**Means of the observed (OBS) EC and Forecast (FC) EC for the Regression and WARMF models for all forecast lead times between 22 February 2018 and 22 May 2020.

**Figure 6.**Comparison of mean differences in forecasted EC and observed EC for the Regression and WARMF models for the period between 22 February 2018 and 22 May 2020.

**Figure 7.**(

**a**,

**b**). Comparison of the standard deviations of forecasted EC and observed EC and standard deviations of differences between EC forecasts and EC observations for the Regression and WARMF models by lead time in the period between 22 February 2018 and 22 May 2020.

**Figure 8.**Comparison of means of forecasted EC and observed EC for the Regression and WARMF models for the period between 22 February 2018 and 22 May 2020. Data censored to include only over (positive) predictions.

**Figure 9.**Comparison of means of forecasted and observed EC for the Regression and WARMF models for the period between 22 February 2018 and 22 May 2020. Data censored to include only under (negative)-predictions.

**Figure 10.**Comparison of the percentages of higher (positive bias) EC forecasts for the Regression and WARMF models for the period between 22 February 2018 and 22 May 2020.

**Figure 11.**Comparison of Regression model forecasts and observations of EC at various lead times for the period between 22 February 2018 and 22 May 2020.

**Figure 12.**Comparison of WARMF model forecasts and observations of EC at various lead times for the period between 22 February 2018 and 22 May 2020.

**Figure 13.**(

**a**,

**b**). Boxplots of observed EC and forecast EC by the Regression (

**a**) and WARMF (

**b**) models are shown for forecast lead time ∆ Day + 12. Fligner–Killeen variance p values are 0.6244 and 0.2703 for the Regression and WARMF models, respectively.

**Figure 14.**(

**a**,

**b**). Calculated linear regression relationship (solid blue line) for the Regression (

**a**) and WARMF (

**b**) models together with a scatterplot of the underlying observed EC data and model forecast EC for lead time ∆ Day + 12.

**Figure 15.**(

**a**,

**b**). Histograms of the mean differences between observed EC and model forecast EC for the Regression (

**a**) and WARMF (

**b**) models for model forecast lead time ∆ Day + 12.

**Figure 16.**Adjusted R-squared values for the Regression and WARMF models for all EC forecast lead times.

**Figure 17.**Comparison of daily WARMF and Regression model forecasts for EC at the Crows Landing compliance monitoring station on 22 February 2021 (

**a,b**); 26 April 2021 (

**c,d,e,f**); and 1 June 2021 (

**g,h**). Graphs (

**e,f**) show the 30-day running average EC forecast on 26 April 2021 relative to the the 30-day running average EC compliance objective. Conversion of flow in cfs to m

^{3}/s: 100 cfs = 2.83 m

^{3}/s.

**Figure 18.**Comparison of daily WARMF and Regression model forecasts for EC at the Crows Land-ing compliance monitoring station on 22 February 2021 (

**a,b**); 26 April 2021 (

**c,d,e,f**); and 1 June 2021 (

**g,h**). Graphs (

**e,f**) show the 30-day running average EC forecast on 26 April 2021 relative to the the 30-day running average EC compliance objective. Conversion of flow in cfs to m3/s: 100 cfs = 2.83 m

^{3}/s.

**Figure 19.**Comparison of daily WARMF and Regression model forecasts for EC at the Crows Landing compliance monitoring station on 1 June 2021. Figures (

**a**,

**b**) show the 30 day running average EC and forecast for 1 June 2021. Figure (

**c**) shows the SLAC at the Crows landing station. By early May wetland drainage no longer dominates Mud and Salt Sloughs and daily SLAC in the river increases. The 30 day running average SLAC crosses the zero line around 28 May 2021. Breaks in the plot are the result of temporary EC sensor malfunction at the Crows Landing station. Conversion of flow in cfs to m

^{3}/s: 100 cfs = 2.83 m

^{3}/s.

**Table 1.**Hypothetical SJR daily salt discharge exceedance fees by subarea (10-year period 2001–2012) using an assumed $5000/day fine for exceedance of the 30-day running average mean EC objective [20].

LSJR Salt Discharge Exceedence Fees by TMDL Subarea for a 10 Year Period 2001–2012 | |||||
---|---|---|---|---|---|

Northwest Side | Grasslands | Upstream San Joaquin River | East Valley Floor | ||

days exceeded by period | Oct | 0 | 0 | 0 | 0 |

Nov | 90 | 60 | 0 | 0 | |

Dec | 124 | 248 | 0 | 0 | |

Jan | 186 | 0 | 310 | 0 | |

Feb | 28 | 196 | 0 | 0 | |

Mar | 0 | 279 | 0 | 0 | |

Apr | 28 | 56 | 42 | 14 | |

VAMP | 0 | 0 | 30 | 30 | |

May | 0 | 0 | 51 | 17 | |

Jun | 30 | 30 | 210 | 90 | |

Jul | 0 | 0 | 248 | 91 | |

Aug | 0 | 0 | 248 | 31 | |

Sep | 0 | 0 | 0 | 0 | |

Total days of exceedences | 486 | 869 | 1139 | 273 | |

$5000 per day penalty | $5000 | $5000 | $5000 | $5000 | |

Total penalties | $2,430,000 | $4,345,000 | $5,695,000 | $1,365,000 | |

Years calculated | 8 | 10 | 10 | 3 | |

Average penalty per year | $303,750 | $434,500 | $569,500 | $455,000 | |

Acres of agriculture | 118,000 | 353,000 | 187,000 | 201,000 | |

Average penalty per acre | $2.57 | $1.23 | $3.05 | $2.26 |

**Table 2.**Statistics of observed (OBS) and forecasted (FC) EC (µS/cm) for the Regression and WARMF models made between 22 February 2018 and 22 May 2020 by lead time.

Regression Model EC Data | WARMF Model EC Data | ||||||
---|---|---|---|---|---|---|---|

Count | Mean | Std Dev | Count | Mean | Std Dev | ||

OBS Day + 0 | 399 | 397 | 224 | OBS Day + 0 | 131 | 401 | 235 |

FC Day + 0 | 397 | 223 | FC Day + 0 | 384 | 192 | ||

OBS Day + 1 | 399 | 395 | 224 | OBS Day + 1 | 131 | 383 | 214 |

FC Day + 1 | 397 | 225 | FC Day + 1 | 381 | 182 | ||

OBS Day + 2 | 399 | 393 | 224 | OBS Day + 2 | 131 | 376 | 211 |

FC Day + 2 | 394 | 225 | FC Day + 2 | 375 | 178 | ||

OBS Day + 3 | 399 | 393 | 225 | OBS Day + 3 | 131 | 377 | 208 |

FC Day + 3 | 393 | 225 | FC Day + 3 | 374 | 182 | ||

OBS Day + 4 | 399 | 394 | 223 | OBS Day + 4 | 131 | 374 | 209 |

FC Day + 4 | 393 | 226 | FC Day + 4 | 372 | 183 | ||

OBS Day + 5 | 399 | 393 | 222 | OBS Day + 5 | 131 | 370 | 207 |

FC Day + 5 | 394 | 224 | FC Day + 5 | 375 | 187 | ||

OBS Day + 6 | 398 | 391 | 219 | OBS Day + 6 | 131 | 371 | 201 |

FC Day + 6 | 395 | 222 | FC Day + 6 | 380 | 190 | ||

OBS Day + 7 | 347 | 394 | 218 | OBS Day + 7 | 131 | 373 | 204 |

FC Day + 7 | 400 | 218 | FC Day + 7 | 387 | 194 | ||

OBS Day + 8 | 347 | 393 | 217 | OBS Day + 8 | 129 | 370 | 203 |

FC Day + 8 | 402 | 220 | FC Day + 8 | 390 | 200 | ||

OBS Day + 9 | 347 | 392 | 218 | OBS Day + 9 | 129 | 366 | 202 |

FC Day + 9 | 405 | 223 | FC Day + 9 | 391 | 204 | ||

OBS Day + 10 | 347 | 395 | 222 | OBS Day + 10 | 128 | 366 | 204 |

FC Day + 10 | 408 | 225 | FC Day + 10 | 393 | 208 | ||

OBS Day + 11 | 347 | 398 | 224 | OBS Day + 11 | 128 | 366 | 207 |

FC Day + 11 | 408 | 225 | FC Day + 11 | 393 | 211 | ||

OBS Day + 12 | 347 | 397 | 223 | OBS Day + 12 | 126 | 363 | 203 |

FC Day + 12 | 408 | 225 | FC Day + 12 | 395 | 213 | ||

OBS Day + 13 | 347 | 397 | 225 | OBS Day + 13 | 126 | 363 | 204 |

FC Day + 13 | 408 | 225 | FC Day + 13 | 395 | 214 | ||

OBS Day + 14 | 347 | 398 | 229 | OBS Day + 14 | 124 | 370 | 209 |

FC Day + 14 | 408 | 224 | FC Day + 14 | 399 | 214 |

**Table 3.**Comparison of mean differences (∆) between forecasted EC and observed EC (µS/cm) for all model forecasts made between 22 February 2018 and 22 May 2020.

Regression Model EC Differences | WARMF Model EC Differences | ||||||
---|---|---|---|---|---|---|---|

Count | Mean ∆ | Std Dev ∆ | Count | Mean ∆ | Std Dev ∆ | ||

∆ Day + 0 | 398 | 0 | 14 | ∆ Day + 0 | 131 | 1 | 78 |

∆ Day + 1 | 397 | 2 | 37 | ∆ Day + 1 | 131 | −2 | 85 |

∆ Day + 2 | 396 | 2 | 48 | ∆ Day + 2 | 131 | −1 | 92 |

∆ Day + 3 | 395 | 1 | 57 | ∆ Day + 3 | 131 | −3 | 86 |

∆ Day + 4 | 394 | 1 | 69 | ∆ Day + 4 | 130 | −2 | 100 |

∆ Day + 5 | 394 | 3 | 80 | ∆ Day + 5 | 130 | 5 | 105 |

∆ Day + 6 | 393 | 5 | 86 | ∆ Day + 6 | 130 | 9 | 108 |

∆ Day + 7 | 341 | 7 | 91 | ∆ Day + 7 | 130 | 14 | 115 |

∆ Day + 8 | 340 | 12 | 103 | ∆ Day + 8 | 128 | 20 | 122 |

∆ Day + 9 | 339 | 15 | 116 | ∆ Day + 9 | 128 | 25 | 134 |

∆ Day + 10 | 338 | 15 | 131 | ∆ Day + 10 | 127 | 27 | 142 |

∆ Day + 11 | 337 | 13 | 144 | ∆ Day + 11 | 126 | 27 | 151 |

∆ Day + 12 | 337 | 14 | 153 | ∆ Day + 12 | 124 | 33 | 164 |

∆ Day + 13 | 337 | 14 | 163 | ∆ Day + 13 | 124 | 33 | 173 |

∆ Day + 14 | 336 | 12 | 171 | ∆ Day + 14 | 122 | 30 | 179 |

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**MDPI and ACS Style**

Quinn, N.W.T.; Tansey, M.K.; Lu, J.
Comparison of Deterministic and Statistical Models for Water Quality Compliance Forecasting in the San Joaquin River Basin, California. *Water* **2021**, *13*, 2661.
https://doi.org/10.3390/w13192661

**AMA Style**

Quinn NWT, Tansey MK, Lu J.
Comparison of Deterministic and Statistical Models for Water Quality Compliance Forecasting in the San Joaquin River Basin, California. *Water*. 2021; 13(19):2661.
https://doi.org/10.3390/w13192661

**Chicago/Turabian Style**

Quinn, Nigel W. T., Michael K. Tansey, and James Lu.
2021. "Comparison of Deterministic and Statistical Models for Water Quality Compliance Forecasting in the San Joaquin River Basin, California" *Water* 13, no. 19: 2661.
https://doi.org/10.3390/w13192661