5.1. Discharge Process Estimations
The results of annual average water balance components and water yields estimated by different objective functions using the best parameter sets in the calibration process are shown in Figure 5
. The results showed that the estimated water balance components and water yields differed by the types of objective functions used. The estimated annual average evapotranspiration (ET) by different objective functions ranged from 656.60 to 756.30 mm (48.99% to 56.42% of the total rainfall), whereas the estimated annual average surface runoff (SurQ) ranged from 116.27 to 560.05 mm (8.67% to 41.78% of the total rainfall) (Figure 5
a). The ratios of estimated annual average lateral flow (LatQ) and groundwater flow (GWQ) to the total rainfall generated by those objective functions ranged from 0.51% (6.83 mm) to 26.02% (348.76 mm) and 0.31% (4.17 mm) to 13.18% (176.7 mm), respectively. Additionally, the ratios of estimated annual average deep aquifer recharge (DAR) and amount of water moving from the shallow aquifer to plant/soil profile (Revap) to the total rainfall generated by those objective functions ranged from 0.26% (3.51 mm) to 0.89% (11.92 mm) and 0.86% (11.54 mm) to 11.84% (158.66 mm), respectively. For the estimated annual average water yield (Figure 5
b), with the MNS objective function, the model generated the lowest annual average water yield of 456.49 mm, whereas the highest annual average water yield of 679.79 mm was given by the model when we used the bR2
objective function. The result showed that the estimated water balance components and water yields of the NSE and RSR objective functions were the same.
In a study conducted by Shimizu et al. [47
], almost all mountainous regions of west Cambodia (where this study area was also located) had annual renewable freshwater resources (water yield) of 500 mm. Thus, NSE and RSR objective functions provided closer annual average water yield estimations than other objective functions at the same value of 492 mm, followed by the MNS, KGE, and PBIAS objective functions, which generated water yields of 456.49, 544.45, and 548.98 mm, respectively. For the results of the water balance components estimation, of the objective functions used in this study, the MNS, NSE, RSR, PBIAS, and KGE objective functions provided the most reasonable estimation results of annual average evapotranspiration (ET) of 756.3, 726.2, 726.2, 723.9, and 721.7 mm, respectively. These results closely corresponded to the ET value obtained from MODIS ET of 745 mm on average annually (Figure 6
) and the findings in the study conducted by JICA [48
] in southern Cambodia with an estimated annual average ET of 743.9 mm. The goodness of the ET simulated by these objective functions were also confirmed by the linear regression with the ET obtained from MODIS ET as shown in Figure 7
. Again, the PBIAS, NSE, RSR, MNS, and KGE objective functions provided relatively small estimated values of groundwater flow (GWQ), and these objective functions, except for the PBIAS objective function, generated a small proportion of surface runoff (SurQ) compared to a proportion of lateral flow (LatQ), which reflected the flow characteristics of this study area. A detailed description of the discharge characteristics and physiographic condition of the river basin is presented in Section 5.4
5.2. Best Parameter Sets and Sensitivity Rank
shows the fitted parameter values and sensitivity rank of the parameters used in this study obtained from different objective functions during the calibration process. Besides the NSE and RSR objective functions, different objective functions generated different values of best parameter sets and sensitivity rank. The fitted parameter sets of the NSE, RSR, and MNS objective functions were in a reasonable range in this study. When we used the R2
objective function, the relative value of the parameter change for CN2 was high (+13%), whereas the existing parameter value of CN2 of the initial model was (between 55 and 92) approximately 78 on average, which was already high for the land-use and soil types of this study area. This led to a big runoff (surface and lateral flow) amount, as shown in Figure 5
a, and high simulated peak flows, as shown in Figure 3
. This objective function produced a small threshold value of GWQMN of 1680.42 mm, which led to more groundwater flow, and a small coefficient of GW_REVAP of 0.03, which generated a lower evapotranspiration rate and revap because of the limitation of movement of water from the shallow aquifer to the root zone. Moreover, these three parameters were among the five most sensitive parameters, which highly controlled the simulation results of the R2
objective function. Even worst, the bR2
objective function produced a higher relative value of the parameter change for CN2 of +15%, a smaller threshold value of GWQMN of 291.86, a low coefficient of GW_REVAP of 0.07, and a large value of ESCO, which then led to a large runoff, greater groundwater flow, smaller evapotranspiration, and lower revap (Figure 5
a). Consequently, this objective function highly overestimated the peak flows as shown in Figure 3
. Furthermore, while the value of the initial model of SOL_AWC was small between 84 and 371 mm (approximately 186 mm on average), the fitted value of the relative change was still underestimated at +16%, and also, the fitted value of SLSUBBSN was overestimated at 68.03 m. As a result, a huge surface runoff and a neglected lateral flow occurred for this objective function. Additionally, the calibrated value of the average slope steepness (HRU_SLP) of bR2
was small. However, this parameter was the least sensitive, which may not have as a considerable effect as the earlier mentioned six parameters (they were the top six sensitive parameters).
Regarding the SSQR objective function, the problems were that the fitted value of the relative change of SOL_AWC was small (18%), whereas the fitted value of SLSUBBSN was large (37.25 m), which were the fifth and seventh most sensitive parameters, respectively. This resulted in a large surface runoff and small lateral flow (Figure 5
a). Moreover, the large value of ESCO (0.95), which was the third most sensitive parameter, led to a low evapotranspiration; the small value of GW_REVAP (0.04), which was the second most sensitive parameter, led to big groundwater flow and small revap; and the small value of REVAPMN (5.75), which was the sixth most sensitive parameter, contributed to a slightly high deep aquifer recharge. Regarding the KGE objective function, the problems included the calibrated parameter set being slightly large for the relative change of CN2 (8%), which was the fifth most sensitive parameter, the slightly small value of GWQMN (1731.04), which was the third most sensitive parameter, and the slightly small value of GW_REVAP (0.07), which was the most sensitive parameter. As the result, runoff (surface and lateral flow) and groundwater flow generated by this objective function were slightly large, and the revap was relatively small (Figure 5
a). For the PBIAS objective function, the calibrated parameter value of the relative change of CN2, which was the most sensitive parameter, was huge (+14%), whereas the value of the relative change of SOL_AWC, which was the second most sensitive parameter, was negative (−10%) and the value of SLSUBBSN, which was the fourth most sensitive parameter, was too long (118.23 m). Consequently, the runoff obtained from this objective function was large with a huge surface runoff and a very small lateral flow (Figure 5
a). This is shown in Figure 3
as an overestimation of the peak flows. This objective function also produced a very small value for ESCO, which was the third most sensitive parameter, which should produce a large evaporative demand from the soil. However, owing to the limited available plant water (small SOL_AWC), evaporative demand from the soil was also restricted, leading to an evapotranspiration restriction.
5.3. Hydrograph Components Estimation
To evaluate how different objective functions performed the simulation of each hydrological process, the monthly calibrated results of discharge and observed data were classified into base flow, rising limb, peak flow, and falling limb phases. Based on the monthly average hydrograph in Section 5.4
, base flow, which is the period of low flow, was considered from January to March. Then, the rising limb or concentration curve, the ascending portion of the hydrograph, was considered from April to August. Peak flow or crest segment, the inflection point on the rising limb to the falling limb, was considered from September to October; and the falling limb or recession curve, the descending portion from the point of inflection at the end of the crest segment to the base flow, was considered from November to December for each year of the calibration period from 1995 to 2008. In this section, the results of RSR objective function was not further presented and discussed as it is equivalent to and produced the same results with NSE objective function.
presents the scatter plots of the simulated versus observed discharge of base flow period for different objective functions. All of the objective functions generally overestimated the base flows. This behavior can be explained by the small fitted parameter values of GWQMN below 3000 mm as generated by many of the objective functions and the small fitted parameter values of GW_REVAP below 0.05 as defined by some of the objective functions (Table 5
). A study conducted by Rafiei Emam et al. [49
] in central Vietnam, which is also predominant by forest, defined the final range for GWQMN between 3133 and 3756 mm. However, among them, NSE and MNS objective functions produced better simulation results for the base flows with higher R2
values, better slope (optimum value of 1) and intercept (optimum value of 0), and smaller RMSD value. The simulated base flows of the MNS objective function achieved an R2
of 0.45, slope of 0.48, intercept of 3.59, and RMSD of 7.78, whereas the simulation results of the NSE objective function provided a value of R2
of 0.48, slope of 0.41, intercept of 2.84, and RMSD of 10.76.
For the rising limb estimation, none of the simulation results of these objective functions showed a reasonable correlation with the observed data with an R2
of 0.21 at most and large intercepts; however, the correlation slopes of some of them reached a value that was greater than 0.6. Again, NSE objective function provided the closest simulation results (Figure 9
) with R2
, slope, intercept, and RMSD values of 0.21, 0.67, 35.16, and 63.97, respectively.
Conversely, the simulated peak flows of these objective functions gave a reverse performance result (Figure 10
). The simulated peak flows of the PBIAS, bR2
, and KGE objective functions attained slightly higher R2
values compared to the results of the other objective functions at slightly larger than 0.50, whereas those of the remaining objective functions were a little less than 0.50. However, the regression slopes of the results obtained from the NSE and MNS objective functions reached a satisfactory value of above 0.70, and those obtained from the other objective functions were between 0.54 and 0.64. The intercepts obtained from all objective functions were between 76.82 and 102.54, and the RMSD values were between 106.67 and 127.61.
For the falling limb estimation, the performances of most objective functions were good (Figure 11
). The MNS objective function performed well in simulating the falling limbs with an R2
of 0.79 with a good slope of 1.01, a small intercept of −9.62, and a RMSD of 37.38. The NSE and KGE objective functions performed similarly but were lower with an R2
of approximately 0.78 and RMSD of approximately 41. However, the regression slope and intercept obtained from the NSE objective function were at 0.97 and −14.46, respectively, whereas those obtained from KGE were 0.90 and −5.52, respectively.
The results showed that the NSE and MNS objective functions provided overall better estimation results for all the components of the hydrograph for this river basin. However, KGE, R2
, SSQR, and PBIAS were among the more poor objective functions, especially for the simulation during low flow periods. For NSE, the differences between the observed and predicted values were calculated as squared values. As a result, larger values in a time series are strongly overestimated, whereas lower values are neglected [45
]. Additionally, runoff peaks will tend to be underestimated when NSE is used in the optimization [34
]. However, NSE is good for use with continuous long-term simulations and can be used to determine how well a model simulates trends for the output response of concern [46
]. Because the calibration duration of this study was 14 years, it is likely that the NSE objective function could capture this long-term trend of the discharge. For the MNS objective function, which was the modified form of NSE with the modified factor of p
= 1 used in this study, it can be expected that the modified forms are more sensitive to significant over- or under-prediction than the squared forms [30
]. However, in this study, the performance of the MNS objective function was only slightly better than the performance of the NSE objective function when we simulated the falling limbs, but it always slightly performed worse than the NSE objective function when we simulated the other components of the hydrograph.
Another objective function used in this study, KGE, is a decomposition of NSE. Similar to NSE, the runoff peaks will tend to be underestimated, but when the KGE optimization is used, the underestimation will not be as severe [34
]. As a result, the simulated peak flows of KGE exhibited a slightly better correlation than that of NSE. However, the slope of the regression line for NSE was better (Figure 10
), which was because of the suitability of NSE in regressing the observed against the simulated values [34
]. The R2
objective function is widely used in hydrological modeling studies, but it is oversensitive to high extreme values and insensitive to additive and proportional differences between model predictions and measured data [45
]. For the bR2
objective function, the under- or over-predictions are quantified together with the dynamics, which results in a more comprehensive reflection of model results [30
]. The SSQR objective function aims at fitting the distribution of the flows, ensuring that the full range of the flows is represented but without considering the time of occurrence of a given value of the flows [33
]. Perhaps due this characteristic, the estimated recession curves (falling limbs) were typically flatter than the observed data, and the estimated base flows were shortened (Figure 3
). As a result, the simulation performances of the falling limbs (Figure 11
) and base flows (Figure 8
) of this objective function were relatively low. For the PBIAS objective function, it is useful for continuous long-term simulations and can be used to determine how well the model simulates the average magnitudes for the output response of interest [46
]. PBIAS can provide a deceptive rating of model performance when the model over-predicts as much as it under-predicts, in which case PBIAS will be close to zero even though the model simulation is poor [46
]. This may be why there were several sudden peak and drop points of the simulated result of this objective function during the base flow and rising limb periods (Figure 3
), leading to poor model performances in simulating the base flows and rising limbs, as shown in Figure 6
and Figure 7
5.4. Objective Functions Corresponding to the Characteristics of the River Basin
shows the monthly average hydrograph of the observed flow at Bak Trakuon Station and rainfall at Kravanh Station during the calibration period from 1995 to 2008 (data between 1997 and 1998 were excluded due to missing data). The validation period was not included because this study focused on the effect of different objective functions on model calibration. Because the dry season, which extends from December to April, is influenced by the northeast monsoon system [22
], the river discharge is relatively low, approaching zero between January and March. This indicated that groundwater from the upstream area did not contribute considerably to the river discharge. However the river discharge begins to rise from April when the wet season starts, and the first peak occurs in May as the monsoon rain travels north [22
]. This peak is followed by a period of lower rainfall between June and August. The greatest peak occurs between the months of September and October and is caused by a southerly shift in the monsoon circulation pattern, which is characterized by heavy rainfall. This indicated that the flow characteristic in this river basin is highly controlled by the monsoon rainfall pattern, especially during the wettest period from August of November when the correlation between the monthly discharge and the monthly rainfall was so high.
Additionally, the physiographic condition likely influences the hydrological process as well, particularly at beginning of the rainy season from April to July when the correlation between the monthly discharge and the monthly rainfall was low as the result of a lag time in the hydrograph. With the size of the drainage area at Bak Trakuon Station, the elongated shape, the forested land cover with varying densities, and the textures of Dystric Leptosol and Cambisol may also contribute to this broad rising limb in the hydrograph (concentration curve of the hydrograph from April to September) owing to retardation of overland flow and the increase of infiltration and storage capacities of the soils [51
]. However, the sharp slope of the falling limb of the hydrograph (recession curve of the hydrograph from late October to December) is likely due to the hilly terrain topography of the drainage area that form a large stream and valley slopes, which result in quick depletion of storage [51
Compared to other land covers, a forested watershed has some unique features. Mature forests have relatively large aboveground (i.e., over-story and under-story layers) and belowground (i.e., roots) biomass [52
]. They generally have a higher canopy surface roughness, higher leaf area index, and deeper roots compared to crops and/or grass [54
], which result in a relatively high ET [55
] and soil infiltration capacity. Forest soil permeability would be maintained by defoliation and organic matter supply from the biomass and considerably reduce the potential for surface flow, lower the total stream flow, and lower the peak flow [56
]. Generally, forest stream flow originates from subsurface flow (lateral flow) or groundwater discharge at headwater streams.
Based on the hydrograph and physiographic characteristics of this study area, the NSE, RSR, and MNS objective functions in addition to their goodness of fits for simulating the discharge (Figure 3
and Figure 4
) were found to be among the better objective functions for estimating hydrological components, such as a higher ET, lower surface runoff, larger lateral flow, smaller groundwater flow, greater revap, and lower water yield (Figure 5
). Moreover, their performances in simulating hydrograph components were overall better than other objective functions, especially the NSE and RSR objective functions, when simulating the base flow, rising limb, and falling limb (Figure 8
, Figure 9
and Figure 11