# Improving Parameter Transferability of GR4J Model under Changing Environments Considering Nonstationarity

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. The Original GR4J Model and GR4J Model with Time-Varying Parameter

_{1}, P

_{2}, P

_{3,}PET

_{1}, PET

_{2}and PET

_{3}) and NDVI (Normalized Difference Vegetation Index) of current month (NDVI

_{0}), one-month shifted NDVI (NDVI

_{1}) (as shown in Table 2), were considered as candidate covariates for the time-varying parameter.

#### 2.2. Model Calibration and Evaluation

#### 2.3. Temporal Transferability Test of Model Parameters

^{th}parameter set, respectively. Here, N takes the value of 5000. Note that PTC with a value above 0 indicates a better parameter transferability for the GR4J-T model over the original GR4J model when transferred from sub-period D to sub-period R.

## 3. Study Data and Area

^{2}above Huaxian hydrological station, as shown in Figure 2. The elevation within Weihe Basin ranges from 3671 m in the western upstream region to 318 m in the eastern downstream region. Dominated by the semi-arid continental monsoon climate, most precipitation and flood events in Weihe Basin occur in late summer and early autumn. For Weihe Basin, climate variability is significant and human activities have been proved to be the main cause of the alternation of flow regimes. Previous studies have shown that the annual streamflow of the gauge Huaxian has been declining over the past decades [47,48,49], mainly due to the increasing human activities including the agricultural irrigation, the construction of large water control projects and the implementation of the water-soil conservation projects [50,51]. In addition, the variations of the annual precipitation have also contributed to the reduced annual streamflow in Weihe Basin [52].

^{2}with Fushun hydrological station as the catchment outlet. The elevation within Tuojiang Basin ranges from 264 to 4741 m and decreases from northwest to southeast. Tuojiang Basin is dominated by the subtropical monsoon climate, with most precipitation and flood events occurring in summer and early autumn. The annual streamflow of Tuojiang Basin was also in a downtrend. However, few recent studies focus on Tuojiang Basin and the reason for the declined annual streamflow remains unclear.

## 4. Results and Discussion

#### 4.1. Diagnostics of Hydrological Nonstationarity

#### 4.2. Parameter Estimation for the GR4J and GR4J-T Model

_{1}and NDVI

_{0}for Weihe Basin. In the case of Tuojiang Basin, the covariates with high correlation coefficient are P

_{2}and NDVI

_{0}. This correlation analysis was done to justify the reasonability of incorporating the abovementioned external covariates into the time-varying parameters. It may be arbitrary to assert that an external covariate with a weak correlation coefficient is inappropriate and useless. In this study, all 8 external covariates were applied to construct the time-varying parameters for both Weihe Basin and Tuojiang Basin, which is detailed in the following section.

#### 4.3. Streamflow Simulation Performance of the GR4J and GR4J-T Model

#### 4.4. Parameter Transferability of the GR4J and GR4J-T Model

## 5. Conclusions

_{1}, P

_{2}, P

_{3,}PET

_{1}, PET

_{2,}and PET

_{3}) and 2 watershed-related covariates (NDVI

_{0}and NDVI

_{1}) were accounted for to describe the dynamic variation of the selected parameter. More covariates should be investigated in further researches. Besides, the key factor that leads to the alternation in flow regimes also differs for different catchments. Thus, more emphases should be placed on the careful identification of proper external covariates when applying time-varying parameter.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the generalized split-sample test (GSST) procedure (example with 15 years available and 5-year subperiods). (Adapted from the work of Coron et al. [40]).

**Figure 2.**Location of Weihe Basin and Tuojiang Basin in China and the meteorological and hydrological gauges.

**Figure 3.**Relative long-term hydro-meteorological variability of (

**a**) precipitation (P), (

**b**) potential evapotranspiration (PET), (

**c**) runoff (Q), and (

**d**) runoff ratio (RR) over Weihe Basin and Tuojiang Basin.

**Figure 4.**Monthly total-order sensitivity indices of GR4J parameters for (

**a**) Weihe Basin and (

**b**) Tuojiang Basin. For each basin, the left panel and the right panel share the same sensitivity indices, but they are sorted by monthly total precipitation (left) and monthly streamflow (right), respectively.

**Figure 5.**Spearman rank correlation coefficient between monthly covariates and monthly runoff ratio (RR) for Weihe Basin and Tuojiang Basin for the whole period (1981–2010).

**Figure 6.**Temporal comparison of (

**a**) the values of the parameter ${x}_{1}$ and (

**b**) the simulated daily streamflow of the GR4J model and the GR4J-T model for Weihe Basin during SP1 (only the period from 1 January 1982 to 31 December 1983 are presented here). The uncertainty bounds associated with model parameter are derived from the streamflow simulation results using the corresponding 5000 parameter sets.

**Figure 7.**Temporal comparison of the values of the parameter (

**a**) ${x}_{1}$ and (

**b**) ${x}_{3}$, and (

**c**) the simulated daily streamflow of the GR4J model and the GR4J-T model for Tuojiang Basin during SP1 (only the period from 1 January 1982 to 31 December 1983 are presented here). The uncertainty bounds associated with model parameter are derived from the streamflow simulation results using the corresponding 5000 parameter sets.

**Figure 8.**Comparison of streamflow simulation performance in terms of KGE when parameter sets calibrated during P1 are transferred to other sub-periods (SP6–SP26) for the GR4J model and the GR4J-T model in Weihe Basin. The boxplots represent the KGE values using the 5000 parameter sets obtained from SP1. The PTC values indicate the difference of the average simulation performance between the GR4J model and the GR4J-T model during the validation procedure.

**Figure 9.**Comparison of streamflow simulation performance in terms of KGE when parameter sets calibrated during P1 are transferred to other sub-periods (SP6–SP26) for the GR4J model and the GR4J-T model in Tuojiang Basin.

**Figure 10.**PTC values of the parameter transferability test for (

**a**) Weihe Basin and (

**b**) Tuojiang Basin.

Parameter | Description | Unit | Feasible Range | |
---|---|---|---|---|

Lower Bound | Upper Bound | |||

${x}_{1}$ | production storage capacity | mm | 20 | 1200 |

${x}_{2}$ | groundwater exchange coefficient | mm | −5 | 3 |

${x}_{3}$ | one day ahead maximum capacity of the routing store | mm | 20 | 500 |

${x}_{4}$ | time base of unit hydrograph | days | 1 | 5 |

Covariates | Unit | Description |
---|---|---|

P_{1} | mm | One-month antecedent monthly total precipitation |

P_{2} | mm | Two-month antecedent monthly total precipitation |

P_{3} | mm | Three-month antecedent monthly total precipitation |

PET_{1} | mm | One-month antecedent monthly total potential evapotranspiration |

PET_{2} | mm | Two-month antecedent monthly total potential evapotranspiration |

PET_{3} | mm | Three-month antecedent monthly total potential evapotranspiration |

NDVI_{0} | - | NDVI value for the current month |

NDVI_{1} | - | NDVI value for the previous month |

**Table 3.**Mann-Kendal (MK) test results of the annual hydro-meteorological data series, the annual runoff ratios and the annual NDVI data series for Weihe Basin and Tuojiang Basin. The critical value of the MK statistic is ${Z}_{1-\alpha /2}=1.960$ with $\alpha =0.05$.

Basin | Data | Z statistic | Trend |
---|---|---|---|

Weihe Basin | Annual P | −1.22 | ↓ |

Annual PET | 1.56 | ↑ | |

Annual Q | −2.61 | ↓** | |

Annual RR | −2.56 | ↓** | |

Annual NDVI | 3.96 | ↑** | |

Tuojiang Basin | Annual P | −1.32 | ↓ |

Annual PET | −3.51 | ↓** | |

Annual Q | −2.75 | ↓** | |

Annual RR | −2.78 | ↓** | |

Annual NDVI | 0.46 | ↑ |

**Table 4.**Comparison of streamflow simulation performance of the GR4J model (C0) and the GR4J-T model (C1–C7) in Weihe Basin during the sub-period 1 (SP1, from 1981 to 1985).

Case | Covariate | $\mathbf{Equation}\text{}\mathbf{for}\text{}\mathbf{Time}-\mathbf{Varying}\text{}\mathbf{Parameter}\text{}{\mathit{x}}_{1,\mathit{t}}$ | KGE (-) | BIAS (%) | ||
---|---|---|---|---|---|---|

${\mathit{P}}_{1}$ | $\mathit{P}\mathit{E}{\mathit{T}}_{1}$ | $\mathit{N}\mathit{D}\mathit{V}{\mathit{I}}_{0}$ | ||||

C0 | ${x}_{1,t}=320.1$ | 0.727 | −16.1 | |||

C1 | ✓ | ${x}_{1,t}=290.3+0.28{P}_{1,t}$ | 0.752 | −6.3 | ||

C2 | ✓ | ${x}_{1,t}=306.5+0.54PE{T}_{1,t}$ | 0.749 | −8.1 | ||

C3 | ✓ | ${x}_{1,t}=296.8+99.8NDV{I}_{0,t}$ | 0.751 | −11.2 | ||

C4 | ✓ | ✓ | ${x}_{1,t}=271.8+0.19{P}_{1,t}+0.27PE{T}_{1,t}$ | 0.755 | −6.2 | |

C5 | ✓ | ✓ | ${x}_{1,t}=312.5+0.17PE{T}_{1,t}+60.6NDV{I}_{1,t}$ | 0.759 | −6.4 | |

C6 | ✓ | ✓ | ${x}_{1,t}=298.4+0.25{P}_{1,t}+41.8NDV{I}_{0,t}$ | 0.751 | −9.3 | |

C7 | ✓ | ✓ | ✓ | ${x}_{1,t}=303.4+0.18{P}_{1,t}+0.28PE{T}_{1,t}+32.6NDV{I}_{0,t}$ | 0.761 | −6.1 |

**Table 5.**Comparison of streamflow simulation performance of the GR4J model and the GR4J-T model in Weihe Basin for all sub-periods (SP1–SP26).

Sub-Period | GR4J Model | GR4J-T Model | ||||
---|---|---|---|---|---|---|

$\mathbf{Value}\text{}\mathbf{of}\text{}{\mathit{x}}_{1}$ | KGE (-) | BIAS (%) | $\mathbf{Equation}\text{}\mathbf{for}\text{}\mathbf{Time}-\mathbf{Varying}\text{}\mathbf{Parameter}\text{}{\mathit{x}}_{1,\mathit{t}}$ | KGE (-) | BIAS (%) | |

SP1 | 320.1 | 0.727 | −16.1 | ${x}_{1,t}=303.4+0.18{P}_{1,t}+0.28PE{T}_{1,t}+32.6NDV{I}_{0,t}$ | 0.761 | −6.1 |

SP2 | 443.2 | 0.617 | −17.3 | ${x}_{1,t}=278.6+0.16{P}_{1,t}+0.17PE{T}_{1,t}+57.7NDV{I}_{0,t}$ | 0.631 | −14.5 |

SP3 | 324.1 | 0.571 | −19.1 | ${x}_{1,t}=309.2+0.25{P}_{1,t}-0.14PE{T}_{1,t}-28.6NDV{I}_{0,t}$ | 0.572 | −11.6 |

SP4 | 263.5 | 0.509 | −26.2 | ${x}_{1,t}=251.5+0.35{P}_{1,t}-0.19PE{T}_{1,t}+38.6NDV{I}_{0,t}$ | 0.591 | −20.2 |

SP5 | 447.3 | 0.611 | −16.2 | ${x}_{1,t}=399.5+0.27{P}_{1,t}-0.15PE{T}_{1,t}-4.3NDV{I}_{0,t}$ | 0.635 | −13.2 |

SP6 | 375.5 | 0.389 | −22.2 | ${x}_{1,t}=259.1+0.38{P}_{1,t}-0.21PE{T}_{1,t}+44.6NDV{I}_{0,t}$ | 0.481 | −20.3 |

SP7 | 367.4 | 0.392 | −22.9 | ${x}_{1,t}=292.7+0.29{P}_{1,t}-0.19PE{T}_{1,t}+44.2NDV{I}_{0,t}$ | 0.514 | −27.9 |

SP8 | 300.9 | 0.442 | −25.7 | ${x}_{1,t}=251.5+0.35{P}_{1,t}+0.15PE{T}_{1,t}+21.7NDV{I}_{0,t}$ | 0.575 | −26.4 |

SP9 | 256.3 | 0.341 | −23.3 | ${x}_{1,t}=205.6+0.45{P}_{1,t}-0.37PE{T}_{1,t}+61.9NDV{I}_{0,t}$ | 0.504 | −19.6 |

SP10 | 414.5 | 0.403 | −18.1 | ${x}_{1,t}=283.5+0.48{P}_{1,t}-0.12PE{T}_{1,t}+17.1NDV{I}_{0,t}$ | 0.442 | −15.2 |

SP11 | 417.6 | 0.392 | −26.4 | ${x}_{1,t}=233.5+0.17{P}_{1,t}-0.09PE{T}_{1,t}-7.6NDV{I}_{0,t}$ | 0.438 | −26.6 |

SP12 | 244.1 | 0.483 | −25.2 | ${x}_{1,t}=241.5+0.37{P}_{1,t}-0.49PE{T}_{1,t}+48.2NDV{I}_{0,t}$ | 0.536 | −19.7 |

SP13 | 182.4 | 0.230 | −42.9 | ${x}_{1,t}=194.1+0.67{P}_{1,t}+0.34PE{T}_{1,t}-27.9NDV{I}_{0,t}$ | 0.432 | −40.3 |

SP14 | 340.4 | 0.499 | −23.6 | ${x}_{1,t}=305.8+0.47{P}_{1,t}-0.15PE{T}_{1,t}-34.8NDV{I}_{0,t}$ | 0.535 | −17.9 |

SP15 | 424.1 | 0.659 | −13.7 | ${x}_{1,t}=341.5+0.53{P}_{1,t}-0.09PE{T}_{1,t}-13.6NDV{I}_{0,t}$ | 0.713 | −7.8 |

SP16 | 208.1 | 0.601 | −28.2 | ${x}_{1,t}=221.6+0.19{P}_{1,t}+0.09PE{T}_{1,t}-6.3NDV{I}_{0,t}$ | 0.622 | −26.4 |

SP17 | 295.5 | 0.582 | −18.4 | ${x}_{1,t}=329.4+0.54{P}_{1,t}-0.03PE{T}_{1,t}-28.1NDV{I}_{0,t}$ | 0.639 | −10.1 |

SP18 | 315.3 | 0.489 | −24.5 | ${x}_{1,t}=300.7+0.52{P}_{1,t}-0.35PE{T}_{1,t}-12.2NDV{I}_{0,t}$ | 0.543 | −17.5 |

SP19 | 378.7 | 0.734 | −23.3 | ${x}_{1,t}=308.3-0.13{P}_{1,t}+0.52PE{T}_{1,t}-23.6NDV{I}_{0,t}$ | 0.763 | −16 |

SP20 | 429.1 | 0.779 | −21.5 | ${x}_{1,t}=229.8+0.57PE{T}_{1,t}-29.2NDV{I}_{0,t}$ | 0.801 | −17.4 |

SP21 | 339.5 | 0.732 | −4.6 | ${x}_{1,t}=325.1-0.51{P}_{1,t}+0.27PE{T}_{1,t}+29.1NDV{I}_{0,t}$ | 0.771 | −1.5 |

SP22 | 460.1 | 0.746 | −4.7 | ${x}_{1,t}=334.5-0.13{P}_{1,t}+0.25PE{T}_{1,t}-12.1NDV{I}_{0,t}$ | 0.765 | −3.2 |

SP23 | 382.8 | 0.729 | −15.3 | ${x}_{1,t}=281.9-0.17{P}_{1,t}-0.09PE{T}_{1,t}+22.4NDV{I}_{0,t}$ | 0.772 | −13.8 |

SP24 | 334.5 | 0.563 | −24.6 | ${x}_{1,t}=336.7+0.34{P}_{1,t}-0.13PE{T}_{1,t}+15.2NDV{I}_{0,t}$ | 0.654 | −10.6 |

SP25 | 223.1 | 0.522 | −37.5 | ${x}_{1,t}=284.1+17.5{P}_{1,t}+0.09PE{T}_{1,t}+11.5NDV{I}_{0,t}$ | 0.583 | −22.3 |

SP26 | 426.5 | 0.586 | −18.7 | ${x}_{1,t}=316.2+0.51{P}_{1,t}-0.28PE{T}_{1,t}+33.8NDV{I}_{0,t}$ | 0.691 | −13.8 |

**Table 6.**Comparison of streamflow simulation performance of the GR4J model and the GR4J-Model in Tuojiang Basin for all sub-periods (SP1–SP26).

Sub-Period | GR4J Model | GR4J-T Model | ||||
---|---|---|---|---|---|---|

$\mathbf{Values}\text{}\mathbf{of}\text{}{\mathit{x}}_{1}$ $\mathbf{and}\text{}{\mathit{x}}_{3}$ | KGE (-) | BIAS (%) | $\mathbf{Equations}\text{}\mathbf{for}\text{}{\mathit{x}}_{1,\mathit{t}}$$\text{}\mathbf{and}\text{}{\mathit{x}}_{3,\mathit{t}}$ | KGE (-) | BIAS (%) | |

SP1 | ${x}_{1}=153.5$ ${x}_{3}=129.3$ | 0.706 | −4.7 | ${x}_{1,t}=179.9+0.23PE{T}_{1,t}-52.3NDV{I}_{0,t}$ ${x}_{3,t}=125.9+0.28PE{T}_{1,t}-50.1NDV{I}_{0,t}$ | 0.729 | −3.8 |

SP2 | ${x}_{1}=210.1$ ${x}_{3}=225.3$ | 0.619 | −5.2 | ${x}_{1,t}=221.5+0.14{P}_{2,t}+0.18PE{T}_{1,t}-50.1NDV{I}_{0,t}$ ${x}_{3,t}=185.2+0.34PE{T}_{1,t}-41.5NDV{I}_{0,t}$ | 0.654 | −3.2 |

SP3 | ${x}_{1}=119.1$ ${x}_{3}=180.2$ | 0.677 | −4.4 | ${x}_{1,t}=287.7-0.23PE{T}_{1,t}-66.3NDV{I}_{0,t}$ ${x}_{3,t}=156.9+0.18PE{T}_{1,t}-31.7NDV{I}_{0,t}$ | 0.701 | −4.2 |

SP4 | ${x}_{1}=191.5$ ${x}_{3}=255.9$ | 0.725 | −4.5 | ${x}_{1,t}=233.8+0.37PE{T}_{1,t}+7.2NDV{I}_{0,t}$ ${x}_{3,t}=289.1+0.12PE{T}_{1,t}-33.2NDV{I}_{0,t}$ | 0.738 | −1.9 |

SP5 | ${x}_{1}=183.2$ ${x}_{3}=293.9$ | 0.696 | −4.9 | ${x}_{1,t}=253.2-0.14PE{T}_{1,t}-38.7NDV{I}_{0,t}$ ${x}_{3,t}=217.9-0.41PE{T}_{1,t}-48.3NDV{I}_{0,t}$ | 0.702 | −6.3 |

SP6 | ${x}_{1}=230.7$ ${x}_{3}=110.1$ | 0.738 | −5.2 | ${x}_{1,t}=286.8-0.56PE{T}_{1,t}+19.6NDV{I}_{0,t}$ ${x}_{3,t}=131.2-39.1NDV{I}_{0,t}$ | 0.754 | −4.1 |

SP7 | ${x}_{1}=239.2$ ${x}_{3}=124.6$ | 0.724 | −2.2 | ${x}_{1,t}=263.1-0.27PE{T}_{1,t}-35.1NDV{I}_{0,t}$ ${x}_{3,t}=217.9-0.24PE{T}_{1,t}-18.5NDV{I}_{0,t}$ | 0.743 | −0.7 |

SP8 | x_{1} = 201.3x _{3} = 281.2 | 0.725 | −2.5 | x_{1,t} = 267.8 + 0.18PET_{1,t} − 36.5NDVI_{0,t}x _{3,t} = 237.5 + 0.24P_{2,t} − 0.31PET_{1,t} − 18.9NDVI_{0,t} | 0.752 | −4.4 |

SP9 | x_{1} = 259.7x _{3} = 115.8 | 0.771 | −3.5 | x_{1,t} = 161.5 + 0.32PET_{1,t} + 56.6NDVI_{0,t}x _{3,t} = 237.9 + 0.14P_{2,t} − 0.28PET_{1,t} − 45.7NDVI_{0,t} | 0.792 | −0.1 |

SP10 | x_{1} = 234.6x _{3} = 122.7 | 0.756 | −5.1 | x_{1,t} = 191.3 + 0.64PET_{1,t} − 18.9NDVI_{0,t}x _{3,t} = 187.2 + 0.19P_{2,t} − 72.1NDVI_{0,t} | 0.776 | −4.8 |

SP11 | x_{1} = 217.4x _{3} = 220.8 | 0.759 | −2.3 | x_{1,t} = 285.1 − 0.22P_{2,t} − 24.3NDVI_{0,t}x _{3,t} = 188.2 + 0.12P_{2,t} + 0.28PET_{1,t} − 35.1NDVI_{0,t} | 0.771 | −7.7 |

SP12 | x_{1} = 137.3x _{3} = 199.3 | 0.764 | −4.9 | x_{1,t} = 216.5 + 0.36PET_{1,t} − 62.7NDVI_{0,t}x _{3,t} = 244.7 + 0.34PET_{1,t} − 46.8NDVI_{0,t} | 0.779 | −8.6 |

SP13 | x_{1} = 261.8x _{3} = 161.6 | 0.726 | −7.5 | x_{1,t} = 307.8 + 0.18P_{2,t} − 0.42PET_{1,t} − 42.9NDVI_{0,t}x _{3,t} = 155.8 + 0.52PET_{1,t} − 29.1NDVI_{0,t} | 0.739 | −10.1 |

SP14 | x_{1} = 240.4x _{3} = 152.5
| 0.728 | −2.1 | x_{1,t} = 271.9 − 0.19PET_{1,t} − 56.3NDVI_{0,t}x _{3,t} = 141.4 + 0.43PET_{1,t} − 42.7NDVI_{0,t} | 0.736 | −2.5 |

SP15 | x_{1} = 240.1x _{3} = 177.2
| 0.725 | −6.7 | ${x}_{1,t}=234.7-0.16PE{T}_{1,t}-36.1NDV{I}_{0,t}$ ${x}_{3,t}=185.5-0.16PE{T}_{1,t}-24.2NDV{I}_{0,t}$ | 0.728 | −8.2 |

SP16 | ${x}_{1}=265.3$ ${x}_{3}=178.9$ | 0.691 | 0.8 | ${x}_{1,t}=292.1-0.42PE{T}_{1,t}-40.9NDV{I}_{0,t}$ ${x}_{3,t}=248.4-61.6NDV{I}_{0,t}$ | 0.703 | 3.4 |

SP17 | ${x}_{1}=239.6$ ${x}_{3}=123.4$ | 0.721 | −3.7 | ${x}_{1,t}=209.8-0.43PE{T}_{1,t}+22.3NDV{I}_{0,t}$ ${x}_{3,t}=144.3+0.21{P}_{2,t}-0.18PE{T}_{1,t}+18.3NDV{I}_{0,t}$ | 0.727 | −2.3 |

SP18 | ${x}_{1}=236.7$ ${x}_{3}=152.2$ | 0.745 | −3.9 | ${x}_{1,t}=267.4-0.36PE{T}_{1,t}$ ${x}_{3,t}=195.9-0.52PE{T}_{1,t}+18.3NDV{I}_{0,t}$ | 0.751 | −3.0 |

SP19 | ${x}_{1}=210.5$ ${x}_{3}=138.8$ | 0.728 | −9.1 | ${x}_{1,t}=188.3+0.13PE{T}_{1,t}-51.1NDV{I}_{0,t}$ ${x}_{3,t}=137.8+0.15{P}_{2,t}-0.28PE{T}_{1,t}+15.4NDV{I}_{0,t}$ | 0.739 | −9.9 |

SP20 | ${x}_{1}=221.5$ ${x}_{3}=138.4$ | 0.717 | −11.9 | ${x}_{1,t}=107.6+0.12{P}_{2,t}+97.3NDV{I}_{0,t}$ ${x}_{3,t}=153.2-0.16PE{T}_{1,t}-42.4NDV{I}_{0,t}$ | 0.747 | −7.4 |

SP21 | ${x}_{1}=234.4$ ${x}_{3}=162.3$ | 0.795 | −7.1 | ${x}_{1,t}=219.4-0.28PE{T}_{1,t}+75.1NDV{I}_{0,t}$ ${x}_{3,t}=143.1-0.31PE{T}_{1,t}-42.4NDV{I}_{0,t}$ | 0.812 | −5.2 |

SP22 | ${x}_{1}=165.4$ ${x}_{3}=211.6$ | 0.714 | −8.8 | ${x}_{1,t}=138.7+0.56PE{T}_{1,t}-62.3NDV{I}_{0,t}$ ${x}_{3,t}=200.6-0.34PE{T}_{1,t}-39.4NDV{I}_{0,t}$ | 0.745 | −6.6 |

SP23 | ${x}_{1}=303.5$ ${x}_{3}=185.2$ | 0.749 | −6.6 | ${x}_{1,t}=339.1-0.38PE{T}_{1,t}-60.8NDV{I}_{0,t}$ ${x}_{3,t}=139.9+0.35PE{T}_{1,t}-62.4NDV{I}_{0,t}$ | 0.766 | −7.1 |

SP24 | ${x}_{1}=285.9$ ${x}_{3}=112.5$ | 0.688 | −9.4 | ${x}_{1,t}=138.7+0.34PE{T}_{1,t}+41.6NDV{I}_{0,t}$ ${x}_{3,t}=225.9-0.45PE{T}_{1,t}-68.5NDV{I}_{0,t}$ | 0.716 | −7.5 |

SP25 | ${x}_{1}=224.5$ ${x}_{3}=168.7$ | 0.678 | −9.4 | ${x}_{1,t}=136.8+0.18PE{T}_{1,t}+57.9NDV{I}_{0,t}$ ${x}_{3,t}=257.1-0.42PE{T}_{1,t}-61.3NDV{I}_{0,t}$ | 0.681 | −6.9 |

SP26 | ${x}_{1}=185.9$ ${x}_{3}=129.7$ | 0.687 | −9.7 | ${x}_{1,t}=200.1-0.58PE{T}_{1,t}+72.6NDV{I}_{0,t}$ ${x}_{3,t}=244.9+0.18{P}_{2,t}-0.48PE{T}_{1,t}-71.2NDV{I}_{0,t}$ | 0.708 | −7.4 |

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## Share and Cite

**MDPI and ACS Style**

Zeng, L.; Xiong, L.; Liu, D.; Chen, J.; Kim, J.-S. Improving Parameter Transferability of GR4J Model under Changing Environments Considering Nonstationarity. *Water* **2019**, *11*, 2029.
https://doi.org/10.3390/w11102029

**AMA Style**

Zeng L, Xiong L, Liu D, Chen J, Kim J-S. Improving Parameter Transferability of GR4J Model under Changing Environments Considering Nonstationarity. *Water*. 2019; 11(10):2029.
https://doi.org/10.3390/w11102029

**Chicago/Turabian Style**

Zeng, Ling, Lihua Xiong, Dedi Liu, Jie Chen, and Jong-Suk Kim. 2019. "Improving Parameter Transferability of GR4J Model under Changing Environments Considering Nonstationarity" *Water* 11, no. 10: 2029.
https://doi.org/10.3390/w11102029