# The Relationship between River Flow Regimes and Climate Indices of ENSO and IOD on Code River, Southern Indonesia

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. One of the main rivers in the province is Opak River. Many streams of Opak River tributaries cross in the center of the province in Yogyakarta City. One of the tributaries is Code River, a well-known stream, which often represents Yogyakarta City. Code River basin occupies an area of approximately 40 km

^{2}. Code River joins Opak River after traveling south for 41 km from its spring on Mount Merapi, north of Yogyakarta (Figure 1). As the stream is situated in a strategic location, Code River holds not only cultural value but also aesthetic value and tourism potential [23].

_{w}) climate type. Sometimes, this region has a tropical monsoon (A

_{m}) climate type. The region has dry months from May to October (MJJASO)—with August as the driest—and wet months from November to April (NDJFMA)—with January or February as the wettest. The annual rainfall varies between 400 to 3600 mm. The average temperature varies from 22 °C in the upstream area to 27 °C in the downstream area. The lowest temperatures occur in the dry months (June to August). The dry months have lower temperatures compared with the wet months owing to the cold wind from the southern hemisphere (Australia) winter [24].

## 3. Data and Methods

#### 3.1. Data

_{50}(50% percentile flow), the high flow was Q

_{10}(10% percentile flow), and the low flow was Q

_{90}(90% percentile flow). The high flow index is important for flood prevention, while the low flow index is useful for drought anticipation and environmental flow setting.

#### 3.2. Methods

_{50}, Q

_{10}, and Q

_{90}from the 1-month daily data. The significance of the correlation was evaluated using a two-tailed t-test at the 95% confidence level.

_{50}), high (Q

_{10}), and low (Q

_{90}) flow indices. We found that the correlation coefficient between monthly SOI and DMI is −0.316, which is statistically insignificant. However, the deviation from the dependent part has importance. Therefore, we used both SOI and DMI on the prediction of streamflow using multiple regression models. Multiple regression models were developed using first-, second-, and third-order polynomial functions. The calculation of regression model parameters was performed at a 95% confidence level.

_{0}+ β

_{1 × 1}+ β

_{2}x

_{2}+ ε.

_{0}+ β

_{1}x

_{1}+ β

_{2}x

_{2}+ β

_{3}x

_{1}

^{2}+ β

_{4}x

_{2}

^{2}+ β

_{5}x

_{1}x

_{2}+ ε.

_{0}+ β

_{1}x

_{1}+ β

_{2}x

_{2}+ β

_{3}x

_{1}

^{2}+ β

_{4}x

_{2}

^{2}+ β

_{5}x

_{1}x

_{2}+ β

_{6}x

_{1}

^{3}+ β

_{7}x

_{2}

^{3}+ β

_{8}x

_{1}

^{2}x

_{2}+ β

_{9}x

_{1}x

_{2}

^{2}+ ε

_{50}, Q

_{10}, Q

_{90});

_{1}= SOI;

_{2}= DMI;

_{1}, x

_{2}, and y.

## 4. Results

#### 4.1. Correlation Analysis

_{50}, Q

_{10}, and Q

_{90}, respectively. These results signal that the ENSO effect has a longer timescale than 1 month and that the peak is at the 6-month scale. On the other hand, the moving average datasets of DMI did not show a noticeable change from the original datasets.

_{50}, Q

_{10}, and Q

_{90}.

_{50}in the 3- and 6-month moving average by this calculation are 0.440 and 0.516, respectively. The status of the significancy also did not change.

#### 4.2. Multiple Regression Analysis

_{50}, Q

_{10}, and Q

_{90}using SOI and DMI as predictors, with the original dataset and 3- and 6-month moving average datasets. The regression models were evaluated by correlation coefficients (R) between the estimated and the observed flow regime (Q

_{50}, Q

_{10}, and Q

_{90}), root mean square error (RMSE, Equation (3), and the adjusted coefficient of determination (R

^{2}).

_{50}in the 6-month moving average timescale. The higher order MRs and a longer timescale of moving average were identified as having a lower RMSE and a higher adjusted R

^{2}(Figure 3). The results suggest that the best model’s skill was achieved by the 6-month moving average dataset with third-order MR. Due to the much lower model’s skill achieved by first-order MR, from now on the first-order MR will be omitted from the analysis.

_{50}had the most accurate estimates and that the Q

_{10}had the least accurate estimates. For all flow indices, both second- and third-order MR models had a tendency to underestimate in higher flows. On all flow indices, the third-order MR estimate tended to have a higher value compared with the second-order estimate. The MR models shown in time series (Figure 4) showed that the models had the highest accuracy, mostly in the extreme values, corresponding to strong (positive and negative) SOI values, such as in late 1994, mid-1998, early 2011, and late 2015.

#### 4.3. Lagged Multiple Regression Analysis

^{2}showed that the lag6 regressions had a lower error and higher R

^{2}compared with lag0, but not by much. This indicates that lagged-time regressions had a slightly better accuracy over the same-time regressions in predicting the flow regimes using SOI and DMI. With these evaluation results, the lag6 MR is able to make forecasts regarding streamflow.

## 5. Discussion

#### 5.1. IOD Climate Effects

#### 5.2. Flow Regimes Forecasting

_{50}can be beneficially used for the general purpose of water resource management, while Q

_{10}and Q

_{90}can be used for anticipating flood and drought events, respectively. Six months in advance is a good period for forecasting the flow regime in the sense of water resource management. This provides sufficient time for counteracting the impact of the flow regime behavior in the future. The evaluation of the 6-month lagged multiple regression models in this study showed a good correlation and moderate accuracy (Table 3). This indicates that the current last 6-month average of SOI and DMI would be able to predict the Q

_{50}, Q

_{10}, and Q

_{90}6 months in the future using the regression model coefficients developed in this study (Table 4), with some notes on the accuracy.

_{50}MR models had similar accuracy in second- and third-order MR (Figure 5), indicating that both regression orders can be used to forecast Q

_{50}with a tendency to underestimate. The only noticeable difference between the two MR orders was in the combination event of strong negative IOD (less than −0.5) and strong positive ENSO (greater than 0.5). In such an event, which was captured only once in this study (in 1997), the third-order MR estimated an immediate reduced flow, while the second-order MR did not (Figure 5, bottom row). For the general purpose of river flow information, a simpler equation with second-order regression may be better.

_{10}MR models have the least accuracy among the three flow indices (Figure 5). The most accurate estimation of the model was only found in two events with a combination of positive SOI and positive DMI, in 2011–2012 and 2018. Although the accuracy of both was similar, the third-order MR was better than the second-order regression in forecasting Q

_{10}. This is because the third-order MR tended to produce a higher estimate than the second-order MR (especially in the event of positive SOI and DMI). A higher estimation of high flow is usually favored to set a safety margin in the event of floods.

_{90}MR models had better accuracy in the third-order MR than in the second-order MR (Figure 5). The MR models of Q

_{90}had almost equal numbers in producing underestimated and overestimated values. However, the underestimated (overestimated) values tended to be in the higher (lower) level of Q

_{90,}while an underestimation is more favorable for anticipating drought and conserving ecosystems in rivers.

#### 5.3. Model Validation

## 6. Conclusions

_{50}and Q

_{10}) in the positive ENSO phases.

^{2}.

_{50}was found to have the most stable and accurate estimates and thus, it is recommended for use with second-order MR for forecasting. Q

_{10}and Q

_{90}demonstrated lower model accuracy, and we recommend using third-order MR for forecasting. It is beneficial for water resource managers to be able to forecast the flow regime indices in the next 6 months using climate indices.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Code River location in southern Indonesia. The small red box in the left figure (map of Indonesia) shows the location of the right figure (satellite image of Yogyakarta Region).

**Figure 2.**Time series of Code River downstream flow, Southern Oscillation Index (SOI), and Dipole Mode Index (DMI), with a 6-month moving average and 3-month moving average (light color). The streamflow data of the years 2006 to 2009 are missing.

**Figure 3.**The root mean square error (RMSE) and adjusted R

^{2}of the multiple regression (MR) models. The 1st-, 2nd-, and 3rd-order are the respective MR orders. The 3 m M.A. and 6 m M.A. are the 3-month and 6-month moving average, respectively.

**Figure 4.**Comparison between the observed variables and the estimated flow regimes by multiple polynomial regression model with 6-month moving average dataset. There are two figures: (

**a**) The scatterplots of the estimated versus observed values; (

**b**) The time series of observed (Q

_{50}, Q

_{10}, Q

_{90}, SOI, and DMI) and estimated (Q

_{50}, Q

_{10}, and Q

_{90}) values in 1994–2005 (left side of the separation line) and 2010–2018 (right-side of the separation line).

**Figure 5.**Comparison between the observed variables and the estimated flow regimes by 6-month lagged multiple polynomial regression model with 6-month moving average dataset. There are two figures: (

**a**) The scatterplots of the estimated versus observed values; (

**b**) The time series of observed (Q

_{50}, Q

_{10}, Q

_{90}, SOI, and DMI) and estimated (Q

_{50}, Q

_{10}, Q

_{90}) values in 1994–2005 (left side of the separation line) and 2010–2018 (right-side of the separation line). The months showed at the x-axis are for the streamflow only. The months for the climate indices are 6 months before the streamflow months.

**Figure 6.**Dummy simulations of second- and third-order multiple regression (6-month moving average) to show the modulation effect of DMI to SOI–streamflow relationship produced by the models. Dummy dataset of DMI (−0.8 to 0.8) and SOI (−2.0 to 2.0) were used in these simulations.

**Table 1.**The coefficients of the correlation between the observed flow regime indices and climate indices (SOI and DMI) in the monthly datasets.

Correlation Variables | No Moving Average | 3-Month Moving Average | 6-Month Moving Average |
---|---|---|---|

Q_{50} with SOI | 0.342 | 0.436 | 0.509 |

Q_{10} with SOI | 0.330 | 0.407 | 0.466 |

Q_{90} with SOI | 0.347 | 0.413 | 0.504 |

Q_{50} with DMI | −0.031 | −0.047 | −0.029 |

Q_{10} with DMI | −0.052 | −0.046 | −0.015 |

Q_{90} with DMI | −0.099 | −0.109 | −0.104 |

**Table 2.**The Pearson correlation coefficient (R) between the estimated and observed values of streamflow regimes on second- and third-order multiple polynomial regressions with SOI and DMI as predictors.

Flow Regime Indices | Multiple Regression Order | Correlation Coefficient (R) of Estimated-Observed | ||
---|---|---|---|---|

No Moving Average | 3-Month Moving Average | 6-Month Moving Average | ||

Q_{50} | first-order | 0.350 | 0.459 | 0.564 |

Q_{50} | second-order | 0.509 | 0.633 | 0.708 |

Q_{50} | third-order | 0.553 | 0.650 | 0.746 |

Q_{10} | first-order | 0.334 | 0.429 | 0.522 |

Q_{10} | second-order | 0.474 | 0.586 | 0.644 |

Q_{10} | third-order | 0.495 | 0.608 | 0.701 |

Q_{90} | first-order | 0.347 | 0.418 | 0.527 |

Q_{90} | second-order | 0.474 | 0.563 | 0.652 |

Q_{90} | third-order | 0.542 | 0.594 | 0.688 |

**Table 3.**Multiple regression (MR) model evaluation for a 6-month moving average dataset in not-lagged (lag0) and 6-month lagged (lag6) MR. R is the Pearson correlation coefficient between the estimated and observed flow regime indices. RMSE is the root mean square error in percentage to the observed average. Adj. R

^{2}is the Adjusted R

^{2}.

Flow Regime Indices | Multiple Regression Order | Lag0 | Lag6 | ||||
---|---|---|---|---|---|---|---|

R | RMSE | Adj. R^{2} | R | RMSE | Adj. R^{2} | ||

Q_{50} | second-order | 0.708 | 49% | 0.490 | 0.763 | 45% | 0.572 |

third-order | 0.746 | 47% | 0.539 | 0.779 | 44% | 0.590 | |

Q_{10} | second-order | 0.644 | 55% | 0.402 | 0.701 | 51% | 0.480 |

third-order | 0.701 | 51% | 0.472 | 0.724 | 50% | 0.505 | |

Q_{90} | second-order | 0.652 | 52% | 0.413 | 0.694 | 49% | 0.470 |

third-order | 0.688 | 50% | 0.452 | 0.742 | 46% | 0.532 |

**Table 4.**Multiple regression (MR) model coefficients developed from a 6-month moving average dataset and lagged regression with climate indices lead streamflow indices by 6 months. To be used with the corresponding equations provided in the Section 3.2.

Flow Regime Indices | Multiple Regression Order | Coefficients | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

β_{0} | β_{1} | β_{2} | β_{3} | β_{4} | β_{5} | β_{6} | β_{7} | β_{8} | β_{9} | ||

Intercept | SOI | DMI | SOI^{2} | DMI^{2} | SOI.DMI | SOI^{3} | DMI^{3} | SOI^{2}.DMI | SOI.DMI^{2} | ||

Q_{50} | second-order | 1.449 | 0.225 | −0.457 | 1.133 | 1.588 | 2.189 | ||||

third-order | 1.452 | −0.004 | −0.993 | 1.252 | −0.203 | 1.293 | −0.002 | 8.920 | −0.133 | 4.938 | |

Q_{10} | second-order | 2.210 | 0.164 | −0.173 | 1.614 | 5.990 | 5.247 | ||||

third-order | 2.182 | −0.001 | −1.406 | 1.777 | 0.699 | 1.978 | −0.135 | 19.498 | 1.865 | 15.137 | |

Q_{90} | second-order | 1.141 | 0.316 | −0.263 | 0.616 | −1.181 | −0.080 | ||||

third-order | 1.041 | 0.114 | −0.276 | 1.091 | −0.181 | 1.111 | −0.140 | 2.738 | −1.974 | −0.958 |

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## Share and Cite

**MDPI and ACS Style**

Nugroho, A.R.; Tamagawa, I.; Harada, M.
The Relationship between River Flow Regimes and Climate Indices of ENSO and IOD on Code River, Southern Indonesia. *Water* **2021**, *13*, 1375.
https://doi.org/10.3390/w13101375

**AMA Style**

Nugroho AR, Tamagawa I, Harada M.
The Relationship between River Flow Regimes and Climate Indices of ENSO and IOD on Code River, Southern Indonesia. *Water*. 2021; 13(10):1375.
https://doi.org/10.3390/w13101375

**Chicago/Turabian Style**

Nugroho, Adam Rus, Ichiro Tamagawa, and Morihiro Harada.
2021. "The Relationship between River Flow Regimes and Climate Indices of ENSO and IOD on Code River, Southern Indonesia" *Water* 13, no. 10: 1375.
https://doi.org/10.3390/w13101375