Can multi-objective calibration of streamflow guarantee better hydrological model accuracy?

Hydrological models often require calibration. Multi-objective calibration has been more widely used than single-objective calibration. However, it has not been fully ascertained that multi-objective calibration will necessarily guarantee better model accuracy. To test whether multi-calibration was effective in comparison to single-calibration in terms of model accuracy, two strategies were tested out. For these strategies, the objective functions used included the Nash–Sutcliffe efficiency and its logarithmic form, which highlight high flow and low flow, respectively. These two indexes were first used for multi-objective calibration, and then they were separately employed for single-objective calibration. To assess the calibration strategies’ accuracy, the simulated streamflow was compared with observed streamflow, particularly high flow and low flow. This study was conducted in the upper stream of the Heihe River basin in northwest China using the FLEX-Topo model and MOSCEM-UA algorithm. The results show that the simulation based on the Nash–Sutcliffe efficiency performed best both in modelling the dynamics and simulating the high flow of the observed streamflow. Thus, it seems that multi-objective calibration does not necessarily lead to better model accuracy. This conclusion might provide useful information for hydrologists in calibrating their models, making their simulations more reliable. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/hydro.2018.131 s://iwaponline.com/jh/article-pdf/20/3/687/200057/jh0200687.pdf Ruqiang Zhang Junguo Liu (corresponding author) School of Nature Conservation, Beijing Forestry University, Beijing 100083, China E-mail: junguo.liu@gmail.com Junguo Liu Ganquan Mao School of Environmental Science and Engineering, South University of Science and Technology of China, Shenzhen 518055, China Hongkai Gao Julie Ann Wrigley Global Institute of Sustainability, Arizona State University, Tempe, AZ 85287, USA


INTRODUCTION
In order to understand hydrological processes and thus predict the likely influence of global climate change on hydrology, a means of extrapolating into the past and the future has been deemed necessary, mainly due to the limitations in space and time of hydrological measurement techniques and scope (Beven ).There are many types of models that can enable us to quantitatively extrapolate, predicting flooding, runoff, the availability of various water resources and nutrient transport (Mimikou et al. ; Molina-Navarro et al. ).However, these models are only simplified representations of the real world, and their accuracy cannot be taken for granted (Muleta ).In addition, some model parameters may not physically manifest and therefore cannot be determined through direct measurements.Thus, model calibration is always necessary (Kim & Lee ).Model calibration is the process of identifying model parameter values from the available parameter ranges to enable the maximization or minimization of the objective function (a function representing difference between simulated and observed values) (Muleta ).
There has been considerable research into various optimization algorithms used to identify optimal model parameter values.In the past, this particular research has mainly focused on the calibration of a single objective (Vrugt et al. a).For example, a widely used algorithm for identifying optimal parameter values with a single-objective function, the shuffled complex evolution, was developed at the University of Arizona (SCE-UA) (Kan et al. ).This type of calibration algorithm is primarily concentrated with matching one component of the hydrograph produced by the model to the observed data (Boyle et al. ).However, in regards to the observed data, it has been argued that any single-objective function, no matter how elaborately chosen, is usually inadequate to properly represent all of the characteristics (Vrugt et al. a; Sadeghi-Tabas et al. ).To circumvent this problem, multiple-objective calibration, which represents more than one aspect of a hydrological system and its behaviour, has been proposed as an alternative as it can incorporate more information from the available data (Zhang et al. ).
In the past, assumptions have been made that multi-objective calibration improves model accuracy (Kim & Lee ).
Nevertheless, little research has gone into testing this supposition prior to now, which this study undertakes.To carry out this test, the Nash-Sutcliffe efficiency and its logarithmic form were selected as the objective functions for both multi-

Study area
The Upper Heihe River Basin (UHRB) is the upper stream of the second largest inland river in Northwest China, the Heihe River (Figure 1 As it is the main runoff-producing region in the Heihe River basin, the UHRB is essential for an integrated water management practice, and so the hydrodynamics of the UHRB have garnered a great deal of research interest. One hydrological station and four meteorological stations are located in and around the UHRB (Figure 1(c)).
For this study, these meteorological stations provided input data for the hydrological model.In this model, Thiessen polygons were used to define the monitored area of these meteorological stations.Since the meteorological stations are all located at relatively low elevations, empirical formulas were used to adjust precipitation and temperature data.The streamflow discharge data for model calibration were obtained from the hydrological station (Yingluoxia Station) at the outlet of the UHRB to calibrate the model.All these input data were obtained from the Cold and Arid Regions Science Data Center (http://westdc.westgis.ac.cn/).

FLEX-Topo model
The FLEX-Topo model, a semi-distributed hydrological model, was used as the basis for different calibration strategies.Input data included daily precipitation and daily temperature, and the outputs included streamflow discharge and evapotranspiration.The FLEX-Topo model consists of four identically structured, parallel components representing four hydrological landscapes (hydrological upland, sunny-hillslope, shady-hillslope and hydrological lowland) which are classifed through topographic information that included height above the nearest drainage (HAND), elevation, slope and aspect (Gao et al. ).There are 25 parameters, shown in red in Figure 2. Table 1 shows the definition of the parameters and the ranges of their values determined by experience or references.The major runoff-producing mechanism of sunny-hillslope is assumed to be the same as that of shady-hillslope, but the parameters for this landscape take different values.
In hydrological lowland, the dominant hydrological pro- In line with these suggestions, these three parameters were Therefore, both indexes were included for multi-objective calibration in order to simultaneously consider both high flow and low flow.Meanwhile, these two indexes were also separately used for single-objective calibration.Since the MOSCEM-UA algorithm generally deals with a minimization procedure, the Nash-Sutcliffe efficiency and its logarithmic form were subtracted from one.Table 2 shows the mathematical formulation of the objective functions.
Comparison between different calibration strategies was made to assess the simulation accuracy in modelling observed streamflow, focusing on high flow and low flow.

RESULTS
Objective function values of single-and multi-objective calibrations For single-objective calibration, one set of parameters was obtained, and for multi-objective calibration the Pareto front consisting of 33 sets of parameters was obtained.
Note: O i is the observed discharge at time step i; S i is the simulated discharge; O ̄is the mean observed discharge over the entire simulation period of length N; S is the mean simulated discharge over the entire simulation period of length N.
based on NSE appeared slightly truer to the observed high flow than the other two resulting hydrographs.

DISCUSSION
This study aimed at testing whether multi-objective calibration would guarantee a better simulation of observed streamflow.Two widely used objective functions, NSE and lnNSE, were selected for model calibration.Since all the settings, including the input data, the hydrological model, the parameter ranges and the optimization algorithm were kept the same (except for the calibration strategies), it can reasonably be assumed that it was the objective functions that influenced model performance.
For high flow, the results show that simulation based on NSE performed slightly better.This may be because NSE weighs error on high flow more than error on low flow.
and single-objective calibration for the FLEX-Topo (Topography-driven FLux EXchange model) used in the upper stream of the Heihe River basin (UHRB) in northwest China.At the basin outlet, streamflow discharge was used for model calibration.Model accuracy was assessed by comparing the simulated streamflow with the observed streamflow data.
(a)).The river originates in the Qilian Mountains.The UHRB has an area of 10,009 km 2 and stretches for 303 km.The elevation of the UHRB ranges from 1,700 m to 5,000 m (Figure 1(b)).This mountainous region surrounding the UHRB is characterized by a cold desert climate, with an annual temperature of UHRB 2-3 C (Liu et al. ).The long-term average annual precipitation is ∼430 mm y À1 and potential evaporation is ∼520 mm y À1 .More than 80% of the annual precipitation occurs from May through September.Soil types in this region are predominantly mountain straw and grassland soil, chestnut-coloured soil, chernozemic soil and desert.The land cover includes forest, grassland, bare rock or bare soil, wetland and permanent snow (Figure 1(c)).On average, the UHRB produces ∼70% of the total river-borne runoff of the whole Heihe River Basin (Chen et al. ).

Figure 1
Figure 1 | (a) Location of the Upper Heihe River basin in China; (b) DEM of the Upper Heihe River basin; (c) land cover map of the Upper Heihe River basin and distribution of hydrology gauges and meteorology gauges in and around the Upper Heihe.

689R.Figure 2 |
Figure 2 | Structure of FLEX-Topo model (revised from Gao et al. 2014).Please refer to the online version of this paper to see this figure in colour: http://dx/doi:10.2166/hydro.2018.131.
which the actual evaporation is equal to potential evaporation S umaxFH [100,1,000] Maximum soil moisture capacity in the root zone of sunny hillslope generated surface runoff on hydrological upland into the splitter to separate preferential flow from recharge in sunny and shady capacity in the root zone of hydrological lowland β W [0.1,5] Parameter used to calculate runoff coefficient in hydrological lowland K W [1,9] Timescale of runoff from fast reservoir in hydrological lowland K s 90 Timescale of the runoff from slow reservoir C Rmax [0,5] Parameter indicating a constant amount of capillary rise The four landscapes are each characterized by various runoff-producing mechanisms, which are embodied in the parallel components of the FLEX-Topo model.The hydrological processes in each landscape are briefly described next.More details on the model parameters, the model structure and the water balance equations have been described by Gao et al. ().In the hydrological upland, the dominant hydrological processes are Hortonian overland flows (HOF) and deep percolation (DP).Precipitation (P) can be stored as snow cover (S wB ) if the daily temperature is below the threshold value T t .It is assumed that there is no interception due to a lack of significant vegetation.The sum (P eB ) of rainfall and the snowmelt, which is calculated by a degree-day model, flows towards the unsaturated zone reservoir (S uB ).When P eB is greater than the infiltration capacity (P t ), Hortonian overland flow (R HB ) occurs.Infiltration (R uB ) recharges the unsaturated reservoir (S uB ).Percolatation (R pB ) from S uB that flows into the slow-response reservoir (S s ) is calculated from the relative soil moisture (S uB /S umaxB ) and maximum percolation (P maxB ).Actual evapotranspiration (E aB ) from the unsaturated reservoir is estimated by the relative soil moisture (S uB /S umaxB ) and the potential evapotranspiration that is calculated by the Hamon equation (Hamon ).Saturation excess overland flow (R eB ) occurs if the amount of water in the unsaturated reservoir exceeds the maximum storage capacity (S umaxB ).R eB plus R HB is partitioned by a splitter parameter (D B ) into flow (R fB ) going into the fast-response reservoir (S fB ) and flow (R sB ) re-infiltrating into the slow-response reservoir (Ss).R fB turns into R LfB after convolution using the time lag parameter T lag , which represents the time interval between storm and fast runoff generation.Flow (Q fB ) from S fB is routed to the stream channel after time K fB .The major runoff-producing mechanism of shady-hillslope is the storage excess subsurface flow (SSF).The existence of vegetation indicates the necessity for the interception reservoir (S iFH ).Evapotranspiration (E iFH ) from the interception reservoir is assumed to be equal to potential evapotranspiration if the storage of the interception reservoir is nonzero.The sum (P eFH ) of the remainder of rainfall after interception and the snowmelt that is calculated from a degree-day model flow towards the unsaturated reservoir (S uFH ).P eFH is partitioned into runoff and flow that is routed to S uFH through the use of the runoff coefficient that is calculated from the parameter β FH representing the heterogeneity of soil properties.Runoff from P eFH and S uFH is separated by a splitter parameter (D) into flow (R fFH ) going into the fast-response reservoir (S fFH ) and flow (R sFH ) re-infiltrating into S s .Actual evapotranspiration (E aFH ) from the S uFH is estimated by parameter C e and potential evapotranspiration, the latter of which is calculated by the Hamon equation.C e is a threshold value.If S uFH /S umaxFH is larger than C e , actual evapotranspiration is assumed to be equal to potential evapotranspiration.R fFH becomes R LfB after convolution using the time lag parameter T lag and flows into the fast-response reservoir (S fFH ).Water (Q fFH ) from S fFH is routed to the stream channel with timescale (K fH ).
cess is saturation excess overland flow (SOF).Interception and snowmelt are the same as they are in shady-hillslope, but soil routine is different.Runoff (R fW ) produced from P eW and S uW is directly routed to the fast-response reservoir (S fW ) without delay because of its proximity to the stream channel.Due to the shallow groundwater level and limited storage capacity, capillary rise (C R ) occurs.C R is represented by a parameter (C Rmax ) that indicates a constant amount of capillary rise.Optimization algorithm and objective functionsThe MOSCEM-UA (Multi-Objective Shuffled Complex Evolution Metropolis-University of Arizona) algorithm that was developed by Vrugt et al. (a) was proposed for multiobjective calibration because it maintains a uniform sampling density within the Pareto set of solutions and includes the single-criterion end points.The evolution strategy employed in the MOSCEM-UA algorithm is similar to that of the SCEM-UA algorithm (Vrugt et al. b), but the probability ratio concept in the SCEM-UA algorithm was replaced by a multi-objective fitness assignment concept in order to develop the initial population of points toward a set of solutions resulting from a stable distribution.The MOSCEM-UA algorithm has been successfully applied in a wide range of hydrological and environmental models, demonstrating its reliability and effectiveness (Efstratiadis & Koutsoyiannis ).In this study, the MOSCEM-UA algorithm (Vrugt et al. a) was adopted to identify the parameters in the model (Figure 3).With these parameters, simulated streamflow is generated.Using the simulated and observed streamflow, objective function values were calculated by a module within the FLEX-Topo model.Three basic parameters had to be set in order to control the operation of the algorithm: the number of iterations, the number of parallel sequences, and the number of random samples.Kuczera () suggests that the number of parallel sequences be set to be equal to the number of the calibration parameters.The other two algorithmic parameters were set according to the recommended values in Vrugt et al. (b).

Figure 4
Figure 4 shows the results of different calibration strategies.It is clear that several tradeoffs exist in multi-objective calibration, indicating that no single solution can optimize

Figure 6
Figure 6 shows a scatterplot of the residuals in regards to observed flow.For low flows, these three simulations all

Figure 4 |
Figure 4 | Objective function values of single-and multi-objective calibration solutions.Please refer to the online version of this paper to see this figure in colour: http://dx/doi:10.2166/hydro.2018.131.
Figure 6, in which the centred scatter illustrates a nearly symmetrical distribution around the line whose ordinate value is equal to zero.It can be argued that a great deal of attention should be paid to objective function selection for multi-objective calibration as objective function has impact on model performance (Muleta ).It is crucial that performance of objective function be assessed before application in multi-objective calibration.

Figure 6 |
Figure 6 | Residuals plot of the different simulations corresponding to the multiple-and single-objective calibration.

Table 1 |
Parameters and ranges of values used in the FLEX-Topo model Parameter Range Description

Table 2 |
Mathematical formulations of the objective functions and evaluation index