# Novel Salinity Modeling Using Deep Learning for the Sacramento–San Joaquin Delta of California

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

^{2}of farmlands [10]. The Delta is also used by millions for recreation and transportation [11]. Upstream riverine runoff (typically controlled by reservoirs) provides water to meet the water supply needs of the projects, and to meet Delta salinity requirements for both agriculture and wildlife. Within the Delta, consumptive uses of water include evaporation, seepage, and crop evapotranspiration. Salinity levels across the Delta depend upon the complex interactions between fresh water and seawater, which vary by location and are affected by river channel geometry, physical structures such as gates and barriers, diversions, and upstream reservoir releases.

#### 1.2. Literature Review

#### 1.3. Scope of the Current Work

## 2. Methodology

#### 2.1. Study Area and Dataset

#### 2.2. Machine Learning Models

#### 2.3. Input Preprocessing

#### 2.4. Forecasting Setup

**Step****1:**- We prepare model inputs the same way as discussed in Section 2.3, which consists of ${\widehat{x}}_{i}^{t},\dots ,{\widehat{x}}_{i}^{(t-7)}$ ($1\le i\le 8$) and $\overline{{\widehat{x}}_{i}^{(t-8)\to (t-18)}},\dots ,\overline{{\widehat{x}}_{i}^{(t-107)\to (t-117)}}$.
**Step****2:**- We formulate the target output values by shifting the salinity values forward by ${t}_{l}$ days, represented by ${y}_{k}^{t+{t}_{l}},k=1,2,\cdots ,23$.

#### 2.5. Evaluation Metrics

#### 2.6. Implementation Details

## 3. Results

#### 3.1. Model Performance on the Daily Scale

#### 3.2. Forecasting Performance

#### 3.3. Model Performance on the Hourly Scale

## 4. Discussions

#### 4.1. Overfitting Potential versus Model Complexity

#### 4.2. Comparing with a Process-Based Model

#### 4.3. Implications

#### 4.4. Limitations and Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Data Sources

## Appendix B. Summary of Datasets from Previous Studies

Study | Dataset |
---|---|

Rath et al. (2016) [2] | The input features of this study are daily freshwater flow to the estuary, daily mean coastal water level, and the daily tidal range for water years 1922–2012. Labels are salinity data from nine locations collected from sensors in the Delta. |

Chen et al. (2018) [28] | In this study, the machine learning emulator is based on data generated using DSM2 (a process-based model) including its outputs at 17 locations for 10 scenarios (two decades each). The use of 10 scenarios is intended to augment the dataset to bound the range of possible water management operations. The study period 1990–2010 was strategically selected as it contains widely varying hydrology and is a period where the DSM2 model is well-calibrated. |

Mosavi et al. (2018) [31] | In this study, the authors examined studies that used field data from rain gauges and other sensing devices, including data from remote sensing technologies. |

He et al. (2020) [10] | The dataset includes a 24-year period (WY 1991–2014) of daily observed water stage at Martinez, Martinez salinity and the net Delta outflow. |

Jayasundara et al. (2020) [26] | Input features used are Northern flow, San Joaquin River flow, exports, Delta cross channel gate operation, net Delta consumptive use, tidal energy, and San Joaquin River inflow salinity at Vernalis. Labels include multiple sets of DSM2 simulated salinity data representing a range of operational conditions. |

Qi et al. (2021) [27] | The input features in this study are the same as Jayasundara et al. (2020) and the labels are DSM2-simulated salinity data at 12 locations. |

Qi et al. (2022) [29] | The input features of this study are eight inputs representing boundary flows or operating rules for Delta flow and salinity management. DSM2 simulated daily salinity at the 28 study locations during 1990–2019 is used as the training label dataset. |

## Appendix C. Diagrams of MLP, ResNet, LSTM and GRU Networks

**Figure A1.**Diagram of the MLP network from [29]. The number in the input layer denotes input shape and those in the subsequent FC layers represent the numbers of neurons of the layers.

**Figure A2.**Diagram of the ResNet network from [29]. The number in the input layer denotes input shape and those in the FC layers represent the numbers of units/neurons of the layers. In the convolutional layers following the input layer, “f” denotes the number of convolutional filters, “k” denotes size of convolutional kernels and “s” denotes stride.

**Figure A3.**Diagram of the LSTM network from [29]. The number in the input layer denotes input shape and those in the subsequent layers represent the numbers of units/neurons of the layers.

**Figure A4.**Diagram of the GRU network from [29]. The number in the input layer denotes input shape and those in the subsequent layers represent the numbers of units/neurons of the layers.

## Appendix D. Detailed Values for Figure 7 and Figure 12

${\mathit{r}}^{2}$ | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.9529 | 0.5940 | 0.6464 |

SLCBN002 | 0.9748 | 0.8334 | 0.6973 |

SLSUS012 | 0.9909 | 0.8803 | 0.8518 |

SLMZU011 | 0.9904 | 0.9111 | 0.9003 |

RSAC075 | 0.9760 | 0.8008 | 0.7332 |

SLMZU025 | 0.9777 | 0.7759 | 0.7619 |

RSAC081 | 0.9623 | 0.7956 | 0.7625 |

RSAN007 | 0.9568 | 0.8286 | 0.8028 |

ROLD059 | 0.9728 | 0.7287 | 0.6267 |

RSAN058 | 0.9809 | 0.9135 | 0.9437 |

OLD MID | 0.9817 | 0.8729 | 0.6846 |

RSAN072 | 0.9860 | 0.8975 | 0.8538 |

SLDUT007 | 0.9905 | 0.9156 | 0.9509 |

CHDMC006 | 0.9064 | 0.6368 | 0.5679 |

CHSWP003 | 0.9379 | 0.5695 | 0.4932 |

RSAN018 | 0.9434 | 0.7981 | 0.7969 |

CHVCT000 | 0.9894 | 0.9708 | 0.9405 |

ROLD024 | 0.9860 | 0.8916 | 0.8700 |

SLTRM004 | 0.9027 | 0.7200 | 0.8676 |

RSAC092 | 0.5819 | 0.8165 | 0.8177 |

RSAN037 | 0.9815 | 0.9221 | 0.8310 |

RSAN032 | 0.8751 | 0.7713 | 0.7742 |

RSMKL008 | 0.9484 | 0.7347 | 0.8541 |

Bias | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.4684 | −2.8600 | −3.7659 |

SLCBN002 | −1.3600 | −0.8149 | −1.4523 |

SLSUS012 | 0.2163 | −0.1661 | −0.6855 |

SLMZU011 | −0.2336 | −0.7538 | −1.0799 |

RSAC075 | 1.5492 | −0.4411 | −0.8134 |

SLMZU025 | 2.1184 | −0.0241 | −1.2001 |

RSAC081 | 4.8211 | −0.0190 | −1.6114 |

RSAN007 | −2.6612 | −0.8044 | −2.3899 |

ROLD059 | 0.0202 | −1.0317 | −1.8503 |

RSAN058 | −0.3692 | −1.2292 | −1.3330 |

OLD MID | −0.0381 | −0.3858 | −0.9698 |

RSAN072 | 0.5610 | −0.1732 | −0.1627 |

SLDUT007 | 1.9058 | 0.8568 | −0.0001 |

CHDMC006 | 1.3642 | −1.4991 | −3.1108 |

CHSWP003 | 0.9000 | −1.1438 | −3.7689 |

RSAN018 | 3.4133 | 2.5636 | −2.7383 |

CHVCT000 | 0.5407 | 0.2339 | 0.1670 |

ROLD024 | 0.5134 | 0.3675 | 0.1518 |

SLTRM004 | −1.2958 | −0.8454 | −1.6861 |

RSAC092 | −1.6766 | 1.0572 | −3.6682 |

RSAN037 | 0.9873 | 0.2697 | −0.8718 |

RSAN032 | −1.3944 | −0.8808 | −4.2074 |

RSMKL008 | 0.6971 | −0.2226 | −0.6141 |

RSR | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.2200 | 0.8297 | 0.8356 |

SLCBN002 | 0.1609 | 0.4508 | 0.6052 |

SLSUS012 | 0.0960 | 0.3660 | 0.4214 |

SLMZU011 | 0.0981 | 0.3109 | 0.3718 |

RSAC075 | 0.1582 | 0.4841 | 0.5874 |

SLMZU025 | 0.1552 | 0.5096 | 0.5669 |

RSAC081 | 0.2087 | 0.4888 | 0.5559 |

RSAN007 | 0.2201 | 0.4363 | 0.5086 |

ROLD059 | 0.1661 | 0.6113 | 0.7402 |

RSAN058 | 0.1385 | 0.3238 | 0.2714 |

OLD MID | 0.1359 | 0.3856 | 0.6345 |

RSAN072 | 0.1191 | 0.3383 | 0.4005 |

SLDUT007 | 0.1023 | 0.3063 | 0.2214 |

CHDMC006 | 0.3243 | 0.7288 | 0.8950 |

CHSWP003 | 0.2598 | 0.8280 | 0.9698 |

RSAN018 | 0.2541 | 0.5150 | 0.4731 |

CHVCT000 | 0.1037 | 0.1754 | 0.2459 |

ROLD024 | 0.1207 | 0.3509 | 0.3848 |

SLTRM004 | 0.3391 | 0.6186 | 0.3708 |

RSAC092 | 0.9923 | 0.4407 | 0.4853 |

RSAN037 | 0.1392 | 0.2900 | 0.4270 |

RSAN032 | 0.3860 | 0.5242 | 0.5271 |

RSMKL008 | 0.2320 | 0.5844 | 0.4060 |

NSE | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.9516 | 0.3117 | 0.3017 |

SLCBN002 | 0.9741 | 0.7968 | 0.6337 |

SLSUS012 | 0.9908 | 0.8660 | 0.8224 |

SLMZU011 | 0.9904 | 0.9033 | 0.8618 |

RSAC075 | 0.9750 | 0.7657 | 0.6549 |

SLMZU025 | 0.9759 | 0.7403 | 0.6786 |

RSAC081 | 0.9564 | 0.7611 | 0.6910 |

RSAN007 | 0.9516 | 0.8096 | 0.7413 |

ROLD059 | 0.9724 | 0.6263 | 0.4521 |

RSAN058 | 0.9808 | 0.8952 | 0.9264 |

OLD MID | 0.9815 | 0.8513 | 0.5975 |

RSAN072 | 0.9858 | 0.8856 | 0.8396 |

SLDUT007 | 0.9895 | 0.9062 | 0.9510 |

CHDMC006 | 0.8948 | 0.4689 | 0.1990 |

CHSWP003 | 0.9325 | 0.3145 | 0.0595 |

RSAN018 | 0.9354 | 0.7348 | 0.7762 |

CHVCT000 | 0.9892 | 0.9692 | 0.9395 |

ROLD024 | 0.9854 | 0.8769 | 0.8519 |

SLTRM004 | 0.8850 | 0.6174 | 0.8625 |

RSAC092 | 0.0154 | 0.8058 | 0.7645 |

RSAN037 | 0.9806 | 0.9159 | 0.8177 |

RSAN032 | 0.8510 | 0.7252 | 0.7222 |

RSMKL008 | 0.9462 | 0.6585 | 0.8351 |

${\mathit{r}}^{2}$ | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.9744 | 0.5923 | 0.7580 |

SLCBN002 | 0.9854 | 0.8367 | 0.6724 |

SLSUS012 | 0.9915 | 0.8796 | 0.8667 |

SLMZU011 | 0.9865 | 0.8907 | 0.8532 |

RSAC075 | 0.9836 | 0.8220 | 0.7386 |

SLMZU025 | 0.9834 | 0.8091 | 0.7832 |

RSAC081 | 0.9764 | 0.8359 | 0.7744 |

RSAN007 | 0.9730 | 0.8189 | 0.7607 |

ROLD059 | 0.9805 | 0.7518 | 0.7275 |

RSAN058 | 0.9797 | 0.9156 | 0.9489 |

OLD MID | 0.9792 | 0.8817 | 0.6887 |

RSAN072 | 0.9834 | 0.9060 | 0.8040 |

SLDUT007 | 0.9910 | 0.9033 | 0.9512 |

CHDMC006 | 0.9697 | 0.7823 | 0.8735 |

CHSWP003 | 0.9720 | 0.7799 | 0.8500 |

RSAN018 | 0.9801 | 0.7914 | 0.8068 |

CHVCT000 | 0.9855 | 0.9608 | 0.9206 |

ROLD024 | 0.9852 | 0.8897 | 0.8608 |

SLTRM004 | 0.9730 | 0.8626 | 0.8684 |

RSAC092 | 0.8405 | 0.8825 | 0.8410 |

RSAN037 | 0.9850 | 0.9560 | 0.8381 |

RSAN032 | 0.9575 | 0.8381 | 0.7932 |

RSMKL008 | 0.9572 | 0.8070 | 0.9379 |

Bias | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 3.6008 | −1.2224 | −1.6747 |

SLCBN002 | 3.7842 | 1.2626 | −0.3216 |

SLSUS012 | 4.7572 | 1.8593 | 0.4100 |

SLMZU011 | 0.9901 | 0.0644 | −0.6901 |

RSAC075 | −1.6408 | −1.1783 | −1.2080 |

SLMZU025 | −2.5367 | −0.9088 | −1.4725 |

RSAC081 | −2.2831 | −1.7392 | −1.0961 |

RSAN007 | 2.0662 | −0.4297 | −0.7600 |

ROLD059 | 1.9174 | 0.1989 | −0.3832 |

RSAN058 | −0.5765 | −1.3418 | −0.4266 |

OLD MID | 0.4040 | −0.0756 | −0.7731 |

RSAN072 | −2.1535 | −1.7981 | −1.3735 |

SLDUT007 | 3.1500 | 1.0906 | −0.1996 |

CHDMC006 | 0.3502 | −1.3688 | −0.7877 |

CHSWP003 | 1.0587 | −0.6732 | −0.5765 |

RSAN018 | −1.9600 | −0.1313 | −2.5437 |

CHVCT000 | −0.7863 | −0.4636 | −1.1248 |

ROLD024 | 3.5323 | 0.7066 | 0.0888 |

SLTRM004 | 6.3652 | 0.9577 | −0.8914 |

RSAC092 | −11.2734 | −2.8386 | −1.7970 |

RSAN037 | −2.6610 | −2.3256 | −2.4599 |

RSAN032 | 0.4398 | −0.0980 | −2.0932 |

RSMKL008 | −1.2886 | −1.8978 | −1.8280 |

RSR | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.1681 | 0.7889 | 0.6164 |

SLCBN002 | 0.1332 | 0.4571 | 0.5819 |

SLSUS012 | 0.1194 | 0.4326 | 0.3862 |

SLMZU011 | 0.1183 | 0.3456 | 0.3991 |

RSAC075 | 0.1287 | 0.4669 | 0.6117 |

SLMZU025 | 0.1359 | 0.4665 | 0.5618 |

RSAC081 | 0.1552 | 0.4445 | 0.5323 |

RSAN007 | 0.1716 | 0.4434 | 0.5567 |

ROLD059 | 0.1446 | 0.5735 | 0.5859 |

RSAN058 | 0.1420 | 0.3179 | 0.2296 |

OLD MID | 0.1433 | 0.3778 | 0.6007 |

RSAN072 | 0.1329 | 0.3776 | 0.5197 |

SLDUT007 | 0.1010 | 0.3287 | 0.1968 |

CHDMC006 | 0.1745 | 0.5584 | 0.3696 |

CHSWP003 | 0.1681 | 0.5464 | 0.4189 |

RSAN018 | 0.1459 | 0.4913 | 0.4763 |

CHVCT000 | 0.1201 | 0.2027 | 0.3275 |

ROLD024 | 0.1358 | 0.3567 | 0.3865 |

SLTRM004 | 0.1801 | 0.3922 | 0.3667 |

RSAC092 | 0.4723 | 0.3580 | 0.4551 |

RSAN037 | 0.1303 | 0.2589 | 0.5091 |

RSAN032 | 0.2149 | 0.4265 | 0.5118 |

RSMKL008 | 0.2116 | 0.5490 | 0.2906 |

NSE | 0∼75% | 75∼95% | 95∼100% |
---|---|---|---|

RSAC064 | 0.9718 | 0.3777 | 0.6201 |

SLCBN002 | 0.9823 | 0.7910 | 0.6613 |

SLSUS012 | 0.9857 | 0.8129 | 0.8508 |

SLMZU011 | 0.9860 | 0.8806 | 0.8407 |

RSAC075 | 0.9834 | 0.7820 | 0.6258 |

SLMZU025 | 0.9815 | 0.7824 | 0.6843 |

RSAC081 | 0.9759 | 0.8024 | 0.7166 |

RSAN007 | 0.9705 | 0.8034 | 0.6901 |

ROLD059 | 0.9791 | 0.6711 | 0.6567 |

RSAN058 | 0.9798 | 0.8989 | 0.9473 |

OLD MID | 0.9795 | 0.8572 | 0.6392 |

RSAN072 | 0.9823 | 0.8574 | 0.7299 |

SLDUT007 | 0.9898 | 0.8920 | 0.9613 |

CHDMC006 | 0.9696 | 0.6881 | 0.8634 |

CHSWP003 | 0.9718 | 0.7015 | 0.8246 |

RSAN018 | 0.9787 | 0.7586 | 0.7731 |

CHVCT000 | 0.9856 | 0.9589 | 0.8927 |

ROLD024 | 0.9816 | 0.8727 | 0.8506 |

SLTRM004 | 0.9676 | 0.8461 | 0.8655 |

RSAC092 | 0.7769 | 0.8718 | 0.7929 |

RSAN037 | 0.9830 | 0.9330 | 0.7408 |

RSAN032 | 0.9538 | 0.8181 | 0.7381 |

RSMKL008 | 0.9552 | 0.6986 | 0.9155 |

## Appendix E. Numbers of Parameters in Simplified or Complicated Architectures

Number of Units in the Recurrent Layer | LSTM | GRU |
---|---|---|

322 | 627,279 | 486,243 |

276 | 486,887 | 378,695 |

230 | 363,423 | 283,843 |

184 (Baseline) | 256,887 | 201,687 |

138 | 167,279 | 132,227 |

92 | 94,599 | 75,463 |

46 | 38,847 | 31,395 |

23 | 17,319 | 14,122 |

**Table A11.**Numbers of parameters of simplified or complicated MLP, ResNet, Res-LSTM and Res-GRU models.

Numbers of Neurons in Hidden Layers | MLP | ResNet | Res-LSTM | Res-GRU |
---|---|---|---|---|

368,184 | 125,511 | 768,119 | 256,292 | 237,340 |

368,92 | 89,447 | 732,055 | 220,228 | 201,276 |

184,184 | 64,975 | 386,503 | 140,004 | 129,516 |

184,138 | 55,407 | 376,935 | 130,436 | 119,948 |

184,92 (Baseline) | 367,367 | 367,367 | 120,868 | 110,380 |

184,46 | 36,271 | 357,799 | 111,300 | 100,812 |

138,46 | 27,485 | 268,743 | 88,576 | 80,204 |

92,46 | 18,699 | 179,687 | 65,852 | 59,596 |

46,46 | 9913 | 90,631 | 43,128 | 38,988 |

46,23 | 8303 | 89,021 | 41,518 | 37,378 |

## Appendix F. Preliminary Data Distortion and Cross-Validation Results

**Figure A5.**Comparison of six models on observed data without (“w/o”) or with (“w/”) data distortion.

**Figure A6.**Comparison of the 5-fold cross-validation on the MLP architecture using observed data. “SP” stands for “split”.

**Figure A7.**Comparison of the 5-fold cross-validation on the Res-LSTM architecture using observed data. “SP” stands for “split”.

**Figure A8.**Comparison of the 5-fold cross-validation on the Res-GRU architecture using observed data. “SP” stands for “split”.

## Appendix G. Time Series Plots of Observed Salinity Levels Versus Model Simulations

**Figure A9.**Time series plots of observed salinity levels versus Res-LSTM simulations and DSM2 simulations of the 23 stations. Detailed values of four evaluation metrics of Res-LSTM and DSM2 are marked for each station.

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**Figure 1.**Schematic showing the Sacramento–San Joaquin Delta (Delta), the 23 study locations, and the DSM2 model domain.

**Figure 2.**Boxplot of salinity observations (represented by electrical conductivity) at study locations, sorted by their medians. Numbers next to each station’s box represent the ratios of available observations in the dataset during the 20-year study period. Each box represents the interquartile range from the 25th to the 75th percentiles. The line inside each box represents the median value. The open circles represent outliers.

**Figure 3.**Diagram of the proposed Res-LSTM network. The number in the input layer denotes input shape and those in the subsequent layers represent the numbers of units / neurons of those layers.

**Figure 4.**Diagram of the proposed Res-GRU network. The number in the input layer denotes input shape and those in the subsequent layers represent the numbers of units / neurons of those layers.

**Figure 6.**Exceedance probability plot and time series plot of Res-LSTM simulated versus observed salinity at daily time step.

**Figure 7.**Heatmap showing Res-LSTM performance at different salinity ranges on the daily time step: low–middle range (lowest 75%), high range (75 to 95 percentile), and extreme high range (highest 5%) at the study locations.

**Figure 11.**Exceedance probability plot and time series plot of Res-LSTM simulated versus observed salinity at daily time step with daily inputs.

**Figure 12.**Heatmap showing Res-LSTM performance at different salinity ranges on the hourly time step: low–middle range (lowest 75%), high range (75 to 95 percentile), and extreme high range (highest 5%) at the study locations.

**Figure 13.**Model performance versus total numbers of parameters of the proposed models and their variants with varying structural complexities.

**Figure 14.**Time series plots of observed salinity levels versus Res-LSTM simulations and DSM2 simulations of six key stations. Detailed values of four evaluation metrics of Res-LSTM and DSM2 are marked for each station.

Index | Input Feature Name | Definition |
---|---|---|

1 | Northern Flow | Sum of Sacramento, Yolo Bypass, Mokelumne River, Cosumnes River, and Calaveras River flows. |

2 | San Joaquin River Flow | San Joaquin River at Vernalis Flow. |

3 | Pumping | Sum of pumping from Banks Pumping Plant, Jones Pumping Plant, and Contra Costa Water District at Rock Slough, Old River, and Victoria Canal. |

4 | Delta Cross-Channel Gate Operation | Delta Cross-Channel Gate Openings. |

5 | Consumptive Use | Net Delta Consumptive use estimated by Delta Channel Depletion (DCD) and Suisun Marsh Channel Depletion (SMCD) models. |

6 | Martinez Tidal Energy | Tidal energy at Martinez, calculated as the daily maximum–the daily minimum astronomical tide at Martinez. |

7 | San Joaquin River EC | Electrical conductivity measured at San Joaquin River at Vernalis. |

8 | Sacramento River EC | Electrical conductivity measured at Sacramento River at Greens Landing. |

Architecture | MLP | ResNet | LSTM | GRU | Res-LSTM | Res-GRU |
---|---|---|---|---|---|---|

Number of parameters | 36, 271 | 357,799 | 227,263 | 201,687 | 111,300 | 100,812 |

Name | Definition | Formula |
---|---|---|

MSE | Mean Squared Error | MSE $={\sum}_{t={t}_{l}+1}^{T}{({S}_{Observed}^{t}-{S}_{ANN}^{t})}^{2}$ |

${r}^{2}$ | Squared Correlation Coefficient | ${r}^{2}$$={\left(\frac{{\sum}_{t={t}_{l}+1}^{T}|({S}_{Observed}^{t}-\overline{{S}_{Observed}})\times ({S}_{ANN}^{t}-\overline{{S}_{ANN}})|}{T\times {\sigma}_{Observed}\times {\sigma}_{ANN}}\right)}^{2}$ |

Bias | Percent Bias | Bias $=\frac{{\sum}_{t={t}_{l}+1}^{T}({S}_{ANN}^{t}-{S}_{Observed}^{t})}{{\sum}_{t={t}_{l}+1}^{T}{S}_{Observed}^{t}}\times 100\%$ |

RSR | RMSE-observations standard deviation ratio | RSR $=\frac{\sqrt{{\sum}_{t={t}_{l}+1}^{T}{({S}_{Observed}^{t}-{S}_{ANN}^{t})}^{2}}}{\sqrt{{\sum}_{t={t}_{l}+1}^{T}{({S}_{Observed}^{t}-\overline{{S}_{Observed}})}^{2}}}$ |

NSE | Nash-Sutcliffe Efficiency coefficient | NSE $=1-\frac{{\sum}_{t={t}_{l}+1}^{T}{({S}_{Observed}^{t}-{S}_{ANN}^{t})}^{2}}{{\sum}_{t={t}_{l}+1}^{T}{({S}_{Observed}^{t}-\overline{{S}_{Observed}})}^{2}}$ |

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## Share and Cite

**MDPI and ACS Style**

Qi, S.; He, M.; Bai, Z.; Ding, Z.; Sandhu, P.; Chung, F.; Namadi, P.; Zhou, Y.; Hoang, R.; Tom, B.; Anderson, J.; Roh, D.M. Novel Salinity Modeling Using Deep Learning for the Sacramento–San Joaquin Delta of California. *Water* **2022**, *14*, 3628.
https://doi.org/10.3390/w14223628

**AMA Style**

Qi S, He M, Bai Z, Ding Z, Sandhu P, Chung F, Namadi P, Zhou Y, Hoang R, Tom B, Anderson J, Roh DM. Novel Salinity Modeling Using Deep Learning for the Sacramento–San Joaquin Delta of California. *Water*. 2022; 14(22):3628.
https://doi.org/10.3390/w14223628

**Chicago/Turabian Style**

Qi, Siyu, Minxue He, Zhaojun Bai, Zhi Ding, Prabhjot Sandhu, Francis Chung, Peyman Namadi, Yu Zhou, Raymond Hoang, Bradley Tom, Jamie Anderson, and Dong Min Roh. 2022. "Novel Salinity Modeling Using Deep Learning for the Sacramento–San Joaquin Delta of California" *Water* 14, no. 22: 3628.
https://doi.org/10.3390/w14223628