**5. Discussion**

*5.1. Objective Functions Evaluation*  In the current study, eight objective functions were selected for model calibration, which belong to different classes. According to the above results, the logarithmic and inverse transformation formats shows a pronounced difference. This may be due to the The hydrological models have been popularly applied in water research and application, while the objective functions that are suitable for calibrating the hydrological models for low flow simulation are unclear, especially in relatively arid regions. Therefore, a

comprehensive evaluation of different kinds of objective functions in relatively dry areas will provide valuable information.

#### *5.1. Objective Functions Evaluation*

In the current study, eight objective functions were selected for model calibration, which belong to different classes. According to the above results, the logarithmic and inverse transformation formats shows a pronounced difference. This may be due to the high sensitiveness of the inverse transformation to extreme low values, as analyzed by Pushpalatha et al. [34]. In the model error term part, the inverse transformation gave more emphasis on low flows than the logarithm transformation. Another explanation may be that, at relatively arid regions, very low values appear frequently in observed flow, which enhances the weight on low flows. Second, our results suggest applying logarithm transformation rather than the inverse transformation in low flow studies, which differs from Pushpalatha et al. [34]. One possible reason may be that Pushpalatha et al. [34] applied NSE, and NSE is regarded to give more emphasis on high flow than KGE, which, thus, balances the low flow weight to some extent. Furthermore, despite the FDC simulation, the FDC-based multi objectives did not exhibit a better performance than the time series-based partners, which concurs with Garcia et al. [3]. As confirmed by the above results and analysis, OBJ3 is suggested for low flow simulation studies in relatively arid regions. It fails to agree with the finding by Garcia et al. [3], who recommended the OBJ4 as the sufficient calibration objective for low flow simulation based on the evaluation in a humid region. Therefore, the climate and geographic conditions may be the main factor for the disagreement between the two studies.

Comparing the single and the combined multi objective group from the performance over different aspects, the general performance applying combined multi objectives seems better. This result confirms the notion that the combined objectives could achieve an overall better benefit (e.g., [40]). The single objective is difficult to simulate all the hydrograph shape characteristics simultaneously (e.g., [41,42]). Furthermore, whether based on the time series or FDC, the performance difference between multi objectives appears smaller than between the single objectives. That means the simulation uncertainty is relatively smaller when applying the multi objectives, which is in line with the knowledge that multi objective calibration could mitigate the uncertainty issues (e.g., [43]). Regarding the performance from spit objectives, which is proposed and recommended by Fowler et al. [35], it seems the worst among all groups, especially for the simulation of low flow indices.

#### *5.2. Climatic Robustness Assessment*

To additionally explore their climatic robustness, the evaluation of their performance was based on two different calibration periods and a validation period, whose climatic conditions varied. Assessing from two calibration periods, the general observed characteristics of the results are consistent, although the performance values showed some differences. Furthermore, even though the average precipitation changed more than 20%, shown as the validation and calibration periods in this study, no noticeable changes were detected for the general observed characteristics. This is unlike the finding by Garcia et al. [3], who asserts that the robustness depends on the climate variability rather than the objective function. This difference of opinion may be related to the different magnitude. For example, the climate difference between the calibration and validation period in the current study is not big enough to explore the climatic influence. At the same time, a minor but interesting characteristic from the validation results is that the general performance difference between single and multi-objectives seems more significant based on the calibration with more considerable climate variability.

#### **6. Conclusions**

The accuracy of low flow simulation yield from the hydrological models presents an apparent effect on water management. Research on the suitableness evaluation of the calibration objectives is of importance. Aiming to enhance insight into the objective influence on low flow simulation in relatively arid regions, which prior to our research was very limited, this study evaluated eight different kinds of objective functions with varied climate conditions. The analysis was performed using the observation at Ma Du Wang station in the Bahe basin, China, located in a semi-arid and semi-humid continental climate region. The main conclusions from the study are summarized in the following points:


Although this study evaluated the performance of different objectives under varied climates and achieved additional valuable knowledge, the current study has some limitations. First, including more hydrological models could help obtain more solid conclusions and deepen the understanding of model influence. In addition, assessing the performance under an increased number of varied climate conditions could broaden the knowledge about the climatic influence, which is essential for research concerning the changing climate.

**Author Contributions:** Conceptualization, X.Y. and B.Z.; methodology, X.Y.; software, X.Y.; validation, C.Y. and X.L.; formal analysis, X.L.; investigation, C.Y.; resources, J.L.; data curation, J.X.; writing—original draft preparation, X.Y.; writing—review and editing, X.Y. and C.Y.; visualization, X.L.; supervision, B.Z.; project administration, J.L.; funding acquisition, J.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Education Department of Shaanxi Provincial Government (Project No. 21JT032) and Xi'an University of Technology (Project No. 256082016). The APC was funded by Xi'an University of Technology (Project No. 256082016).

**Data Availability Statement:** Data available upon request.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.
