1. Introduction
Precipitation is one of the most crucial inputs in catchment runoff modeling and measuring rainfall is essential for determining hydrological catchment response [
1,
2]. However, because precipitation is generated by extremely complicated, non-linear, and sensitive atmospheric physical process [
3], it shows highly spatial and temporal variability at the basin scale [
4,
5,
6,
7].
Due to the importance of precipitation in modeling, prior work has evaluated the effect of uncertainty in precipitation on the response of simulated streams in hydrological models. Wilson et al. [
8] found that peak runoff, total runoff volume, and peak timing are considerably influenced by the spatial distribution and precision of rainfall measurements. Singh [
9] provided a detailed literature review on the influence of spatial–temporal variability in hydrological factors on rainfall runoff modeling. Sun et al. [
10] found that runoff prediction errors at the catchment scale were significantly related to the representation of rainfall data spatial variability. Shen et al. [
11] showed that noticeable uncertainty in stream flow and non-point source pollution modeling was caused by spatial rainfall uncertainty obtained from different precipitation interpolation methods.
Traditionally, there are three mechanisms for measuring or observing precipitation: rain gauges, weather radar, and satellite-based sensors [
12,
13,
14]. Rain gauge networks remain the most common method for measuring precipitation [
15,
16,
17] due to their higher accuracy in representing rainfall at their respective locations [
18,
19] and longer recording period for investigating long-term rainfall runoff processes [
20]. Because a rain gauge is a point measurement for precipitation, representing rainfall spatial variability must be affected by the density and distribution of rain gauge networks. To address this relationship, Pardo-Igúzquiza [
21] tried to optimize the rain gauge distribution and quantity in a given catchment. Chen et al. [
22] proved that more pluviometers distributed in a catchment resulted in higher precision in areal precipitation calculation. Xu et al. [
23] and Girons Lopez et al. [
24] found there is a threshold value of rain gauge density, before which the presentation of rainfall improves significantly with increasing rain gauge numbers.
Significant early research focused on the effect of density and distribution of rain gauge networks on catchment modeling. However, most were only concerned with the impact of density. Michaud and Sorooshian [
25] showed that poor rain gauge densities caused an inadequate simulation of flood peak in a midsized semi-arid catchment. Chaplot et al. [
26] selected rain gauges with a certain empirical distribution. Andreassian et al. [
27], Anctil et al. [
28], and Xu et al. [
23] randomly selected several subsets of different numbers of gauges to achieve the same level of rain gauge density and evaluated the relationship between density and modeling results. Similarly, Drogue and Khediri [
29] employed approximately 100 subsets with the same number of rain gauges and used the mean average of rainfall data for their evaluated.
In the study of Bardossy and Das [
30], distributions of rain gauges with different densities were obtained from an optimization algorithm. Some studies have considered pluviometer density and distribution at the same time [
31], while other researchers have investigated the effect of udometer distribution on conceptual models [
27,
29,
32]. These studies have evaluated the individual responses of different process-based models [
26,
31], compared a couple of models [
33], and even applied a neural network to rainfall-runoff modeling [
28]. However, a comprehensive comparison of the performances of different models impacted by different rain gauge network distributions, especially networks with varying numbers of gauges, has yet to be presented.
Identifying the effect of different rain gauges’ distribution on the hydrological response of conceptual and process-based models will be helpful in (1) optimizing rain gauge networks and (2) selecting hydrological models for a given basin. Therefore, this study aims to advance the discipline by comparing the impact of rain gauge distribution on typical conceptual and process-based distributed models. Furthermore, the potential influence of uncertainty in model calibrations is investigated. The paper is organized as follows:
Section 2 introduces the study area, datasets, applied models and design scenarios.
Section 3 provides the simulation results in two parts: for the whole validation period and a typical month within the validation period.
Section 4 discusses the results and compares them with previous research.
Section 5 provides the study conclusions.
3. Results
Daily streamflow reproduction performance of the three models for 16 rain gauge scenarios during the validation period is investigated in two parts. In part I, general model performance during the entire validation period (1 January 2012 to 31 December 2013) is assessed using the statistical results from the evaluating indicators described in
Section 2.3.4. In part II, model performance is discussed for a single month (June 2012) with a detailed daily flow hydrograph comparison.
3.1. Model Performance in the Calibration and Validation Period
To compare model performance between HYMOD, XAJ, and WetSpa for the 16 rain gauge scenarios, the statistical criteria in the calibration and validation period are provided in
Table 3,
Table 4 and
Table 5. Boxplots for the validation period are shown in
Figure 2.
Table 3 indicates stable NSE and CC values between the calibration and validation periods for HYMOD in all 16 scenarios. However, there is an clear improvement in the BIAS value from the calibration to validation period. XAJ shows similar behavior (
Table 4). WetSpa shows a slight improvement in NSE and CC values in most scenarios (
Table 5).
Figure 2a–c illustrates the accuracy of the streamflow simulations, as indicated by NSE. Generally, metrics for the validation period are acceptable for all three models despite different pluviometer selection scenarios; average NSE values are greater than 0.6. In more detail, results for XAJ are better than those for HYMOD and WetSpa, and the latter two are comparable in most scenarios. Notably, there are discrepancies between the NSE values for the three models. Interquartile ranges for HYMOD are significantly larger than those for XAJ, followed by those for WetSpa, which has the narrowest interquartile NSE range. WetSpa shows the best stability in model performance in every calibration trial, while HYMOD has the largest uncertainty.
When rain gauge selections are taken into consideration, results for all three models perform consistently. With the reduction in rain gauge numbers (scenario 20_C, 15_C, 10_C and 5_C), the mean NSE values for all models show lower variability. The NSE amplitudes for HYMOD and XAJ are rather small, showing robustness for a simple decline in the quantity of udometers. In contrast, the values for WetSpa show greater sensitivity toward changes in rain gauge quantity.
The impacts of the spatial distribution of rain gauges show similar trends in terms of NSE metrics for all models. With the same number of rain gauges (15), all models in scenario 15_SE and 15_NW perform comparably with those in 15_C. However, the accuracy of the results in scenario 15_SW is generally lower. Unexpectedly, model performances for 10_SE and 5_SE are poorest among scenarios with the same number of rain gauges. Similarly, model performance worsens with a decrease in rain gauges from 15 to 5 when the rain gauges are concentrated in the north-west part of the basin (scenarios 15_NW, 10_NW, and 5_NW). Furthermore, variations in the number of rain gauges concentrated in the south-west and north-east has few impacts on streamflow simulations, except for WetSpa in scenario 5_NE, which shows a dramatic reduction in both average and variation in NSE values. Similar results are found for the CC values, as illustrated in
Figure 2d–f.
Figure 2g–h shows the ability of the three models to recreate the water balance for the 16 rain gauge scenarios. Generally, HYMOD and XAJ exhibit better performance in water balance simulations; HYMOD overestimates and XAJ underestimates the average within about 5%. WetSpa poorly estimates water balance with a BIAS of approximately 20%. Interquartile ranges for BIAS indicate that WetSpa has most stable model performance, while HYMOD has the lowest under multiple calibrations, as indicated previously.
3.2. Monthly Analysis for 2012
Monthly performance is another important mechanism for comparing models’ responses due to different rain gauge distributions.
Figure 3 illustrates the monthly average runoff and precipitation in the Jinjiang River Basin. Clearly, the wet season in 2012 ranges from March to July, resulting in a flood season with average flow above 200 m
3/s. However, dry seasons are not particularly dry; most months, except for August and October, have average precipitation over 100 mm per month.
Monthly comparisons for HYMOD, XAJ, and WetSpa are shown in
Figure 4. As shown in
Figure 4a–c, all three models tend to simulate streamflow in the flood season better, but poorly reproduce runoff in the dry season, especially in August and October. Specifically, HYMOD shows better adaptability than XAJ and WetSpa, achieving acceptable NSE values in more months, especially in January and September. However, WetSpa performs worse than the other models in March, May, July, and November. In addition, HYMOD monthly performances show no distinct trends indicating an impact of rain gauge distributions. XAJ demonstrates higher usability in the flood season. However, it is more likely to be affected by the distribution of rain gauges. June, for example, has the highest NSE value (0.50) in scenario 15_SE, but the lowest NSE value (0) in 5_NW. Finally, WetSpa only achieves acceptable results in the flood season. NSE values in the dry season are no higher than 0.1, except for December, in which NSE values are about 0.3.
The overall deviations for all three models vary significantly from month to month (
Figure 4d–f). Of the three models, HYMOD generates relatively accurate overall estimates in most months. However, it overestimates total flood volume in August and underestimates total flood volume in January, November, and December. XAJ produces results that vary between overestimates and underestimates. The WetSpa model achieves the best performance in March, but produces more than 30% overestimates from July to October, which confirms the results in
Figure 4c.
3.3. Model Performance in June 2012
To investigate the performance of three models based on data precision for different precipitation values, daily time series of the simulated and observed hydrographs in a typical wet season month in the Jinjiang River basin (June 2012) are compared. June 2012 has two complete flood peaks, and the two peak flows are neither too high nor too low. Therefore, analyzing model performance in June 2012 is appropriate.
As presented in
Figure 5, the accumulative precipitation in June 2012 ranges from 187.1 mm to 355.3 mm. The rain center is located in the central area of the basin captured by rain gauge LC. Therefore, three scenarios, 20_C as a benchmark, 10_SE absent LC, and 5_NE with LC (see
Table 2), are investigated as LC presence could be a critical factor affecting runoff modeling.
Figure 6a indicates that in scenario 20_C, HYMOD results generally agree with daily observed streamflow in June 2012. However, hydrographs in every trial range widely compared with XAJ (
Figure 6b) and WetSpa (
Figure 6c). XAJ and WetSpa misrepresent the first peak flow in June, while capturing the second. XAJ underestimates the lower streamflow, while WetSpa slightly overestimates them.
Absent the key rain gauge LC in scenario 10_SE (
Figure 6d–f), the standard deviations in measured rain data on 25 June 2012 are clearly smaller than in 20_C. The remaining rain gauges do not correctly reflect the spatial variability in actual precipitation for the entire basin. All three models underestimate the second peak flow that they precisely captured in 20_C. For 5_NE, all models overestimate the second peak flow as the rainfall data from LC are assumed to represent the areal rainfall input from most sub-watersheds (
Figure 6g–i).
Meanwhile, variations in simulated second peak flow for WetSpa increase notably and the simulated runoff time series can be divided into three groups. Most hydrographs in one group tend to appreciably overestimate the second peak flow. While those in another group tend to significantly overestimate the second peak flow, e.g., XAJ. The remainder in the third group tend to miss the second peak flow.
5. Conclusions
This study compared the performance and uncertainties of the HYMOD, XAJ, and WetSpa conceptual and process-based models with varying rain gauge numbers and distributions in the Jinjiang River Basin, China. Long time series, monthly, and daily performance was analyzed using several statistical indicators.
The results for all three models showed that a reduction in the number of rain gauges only resulted in worse performance when the rain gauge distribution was inhomogeneous. This observation demonstrates that appropriate rain gauge configuration is of greater importance than their deployment density in a certain catchment. Furthermore, the stable performance between different model structures indicates that rainfall spatial variability does not impact model performance due to the model mechanism.
The analyses also show that the simpler conceptual model HYMOD suffers from greater variations during multiple calibrations, while the complex process-based model WetSpa is more stable across different calibration trials. This behavior indicates that the uncertainty in the model calibration is more related to model structure than rainfall spatial variability.
Notably, this study was conducted for a middle-scale semi-humid river basin, which is suitable for rainfall runoff simulation. Future work should build on these results by extending the types of study areas encompassing a range of climates, surface areas, and environmental conditions.