Parameter uncertainty and identifiability of a conceptual semidistributed model to simulate hydrological processes in a small headwater catchment in Northwest China
 Shuai Ouyang^{1},
 Heike Puhlmann^{2},
 Shunli Wang^{3},
 Klaus von Wilpert^{4} and
 Osbert Jianxin Sun^{1}Email author
DOI: 10.1186/s1371701400149
© Ouyang et al.; licensee Springer 2014
Received: 21 March 2014
Accepted: 15 May 2014
Published: 20 June 2014
Abstract
Introduction
Conceptual hydrological models are useful tools to support catchment water management. However, the identifiability of parameters and structural uncertainties in conceptual rainfallrunoff modeling prove to be a difficult task. Here, we aim to evaluate the performance of a conceptual semidistributed rainfallrunoff model, HBVlight, with emphasis on parameter identifiability, uncertainty, and model structural validity.
Results
The results of a regional sensitivity analysis (RSA) show that most of the model parameters are highly sensitive when runoff signatures or combinations of different objective functions are used. Results based on the generalized likelihood uncertainty estimation (GLUE) method further show that most of the model parameters are well constrained, showing higher parameter identifiability and lower model uncertainty when runoff signatures or combined objective functions are used. Finally, the dynamic identifiability analysis (DYNIA) shows different types of parameter behavior and reveals that model parameters have a higher identifiability in periods where they play a crucial role in representing the predicted runoff.
Conclusions
The HBVlight model is generally able to simulate the runoff in the Pailugou catchment with an acceptable accuracy. Model parameter sensitivity is largely dependent upon the objective function used for the model evaluation in the sensitivity analysis. More frequent runoff observations would substantially increase the knowledge on the rainfallrunoff transformation in the catchment and, specifically, improve the distinction of fast surfacenear runoff and interflow components in their contribution to the total catchment runoff. Our results highlight the importance of identifying the periods when intensive monitoring is critical for deriving parameter values of reduced uncertainty.
Keywords
Dynamic identifiability analysis HBVlight model Hydrological modeling Sensitivity analysis Uncertainty analysisIntroduction
Hydrological models are important tools for water resource planning and management and in assessing the effects of climate and land use change on the hydrological cycles and runoff regimes (Pechlivanidis et al., [2011]; Zhang et al., [2012]). Conceptual hydrological models are widely used to simulate the land phase of hydrological cycles since they can capture the dominant catchment dynamics whilst remaining parsimonious and computationally efficient whilst requiring input data that are usually readily available and relatively simple and easy to use (Thyer et al., [2009]; Kavetski and Clark, [2010]).
Parameters in conceptual hydrological models need to be estimated through model calibrations because they cannot be directly determined from the physical characteristics of the catchment (Madsen, [2000]; Madsen et al., [2002]). However, when parameter calibration is employed, different parameter sets may simulate the observed system behavior equally well, which is termed “equifinality” (Beven and Freer, [2001]). Commonly, the calibrated model is tested against some independent (validation) dataset to ensure the applicability of the model to situations/periods not used in the model calibration. Typically, splitsampling or differential splitsampling are used to divide the entire dataset into two parts (Xevi et al., [1997]; Henriksen et al., [2003]; Moriasi et al., [2007]). Deteriorating model behavior for the validation dataset may hint at parameter identification problems. However, with regard to the relatively large number of free parameters in a rainfallrunoff model, a single measure of performance is a weak criterion to assess and declare (or refuse) modeling success against the background of omnipresent equifinality (Beven, [2001]). It is difficult to characterize the different aspects of model performance for a particular rainfallrunoff model with only one or two statistical criteria (Shakti et al., [2010]). There have been suggestions that the information from runoff data can be much better utilized and the information for model calibration is increased when using objective functions based on hydrological signatures rather than purely statistical measures (Shamir et al., [2005]; Gupta et al., [2008]; Wagener and Montanari, [2011]). Hydrological signatures are defined as hydrologic response characteristics that provide insight into the hydrologic functional behavior of catchments (Sawicz et al., [2011]). Such response characteristics are often indicative of a specific watershed and how its response differs from others; examples include common descriptors of the hydrograph shape such as the runoff duration curve and the time to peak flow (Shamir et al., [2005]). Moreover, different objective functions judge the goodness of a certain parameter set by different aspects and, hence, a model’s success at simulating runoff may be better quantified by using several evaluation measures (Dawson et al., [2007]) and the socalled Pareto optimality, which describes solutions in which an objective function cannot be improved without decreasing other objective functions.
It is therefore important for hydrologists to identify the dominant parameters controlling model behavior by using sensitivity analysis, which also helps to better understand the model structure, the main sources of model output uncertainty, and the identification issues (Ratto et al., [2007]). Among a variety of global sensitivity analysis methods currently available, the regional sensitivity analysis (RSA; Hornberger and Spear, [1981]), also known as the generalized sensitivity analysis, is very popular and widely used (Ratto et al., [2007]; Saltelli et al., [2008]).
Hydrological modeling involves multiple steps, each with uncertainties of different origins that render uncertainty in the final model predictions (Butts et al., [2004]). Realistic assessment of various sources of uncertainty is not only important for sciencebased decision making but also helps to improve model structure and to reduce model uncertainty. In recent years, quantification of uncertainties in hydrological modeling has received a surge of attention, and several methods have been developed to derive meaningful estimates of uncertainties bound on model predictions. Among these methods, the generalized likelihood uncertainty estimation (GLUE) method proposed by Beven and Binley ([1992]), and the Bayesian methods (Thiemann et al., [2001]; Engeland et al., [2005]) are widely used for simultaneous calibration and uncertainty assessment of different hydrological models (e.g., Freer et al., [1996]; Kuczera et al., [2006]; Blasone et al., [2008a]; Vrugt et al., [2009]; Dotto et al., [2012, 2014]). Both methods have been discussed with respect to their philosophies and the mathematical rigor they rely on (Gupta et al., [2003]; Kavetski et al., [2006]; Kuczera et al., [2006]; Blasone et al., [2008a]; Vrugt et al., [2009]; Jin et al., [2010]; Dotto et al., [2012, 2014]). The popularity of GLUE lies in its conceptual simplicity and relative ease of implementation, requiring no modifications to the existing source codes of simulation models (Vrugt et al., [2009]). Moreover, GLUE makes no assumption regarding the distribution of the model residuals, and it allows a flexible definition of the model performance (likelihood function), making it capable of including several variables in model calibration and uncertainty assessment (Blasone et al., [2008b]). The main critical point with GLUE is that the obtained confidence bounds are dependent on some subjective choices (e.g., the cutoff value between behavioral and nonbehavioral simulations; see the methods section), and therefore represent the empirical rather than the true distribution of model uncertainty.
Based on the RSA and the GLUE, Wagener et al. ([2003]) developed the socalled dynamic identifiability analysis (DYNIA), which is an approach to locating periods of high identifiability (i.e., low uncertainty) for individual parameters and to detect failures of model structure in an objective manner. The main motivation behind the DYNIA is an attempt to avoid the loss of information through aggregation of the model residual in time (Wagener et al., [2003]). This methodology can be applied to track the variation of parameter optima in time, to separate periods of information and noise, or to test whether model components (and therefore parameter values) represent those processes of intention (Wagener et al., [2003]).
The Qilian Mountains in northwestern China are the origin of several key inland rivers, including the Heihe, Shiyang, and Shule Rivers (He et al., [2012]), and are highly valued for their ecosystem services in conservation of water resources and biodiversity. Urban water supply and irrigation agriculture in the Heihe river basin depend largely on the steady water yield from the mostly nonperennial tributaries in the source regions in the Qilian Mountains. However, a declining forest cover in recent decades has imposed a potential risk of increased water runoff following heavy rainfall events because of reduced water conservation by vegetation, contributing to highly fluctuating water outputs. The lower altitudinal limit of the forest line retreated from 1,900 m a.s.l. in 1949 to around 2,300 m a.s.l. during the 1990s mainly because of overgrazing damage by goats and cattle and timber harvesting, and, as a consequence, the forest cover decreased from 22.4% to only 12.4% in the Qilian Mountains over the same period (Wang and Cheng, [1999]). This, together with the local impacts of global climate change, causes a great concern on declining water conservation capacity of the Qilian Mountains and thus the ecosafety of the region. As a result, great efforts are being directed at assessing the hydrological and ecological consequences of vegetation and climate change in the tributaries of the Qilian Mountains. Hydrological modeling is explored as an operational tool for effective assessment of changes in hydrological processes relating to modification of land cover and climate change.
In this study, we investigated the applicability of the HBVlight model (Seibert, [2005]) in simulating hydrological processes in the Pailugou catchment of Qilian Mountains, and determined sources and relative contributions of uncertainties in modeling procedures. The Pailugou catchment is a small headwater catchment in the Qilian Mountains, which drains into the Dayehekou basin and finally feeds into the Heihe River. The vegetation and partial attributes of hydrological processes in the catchment have been intensively investigated by the Academy of Water Resource Conservation Forests of Qilian Mountains in Zhangye, Gansu Province (AWRCFQM). The onsite investigations include a longterm meteorological observation, runoff monitoring, assessment on forest growth and health, and characterization of site conditions. Based on data from the monitoring program of the AWRCFQM and simulations with the HBVlight model, we aim to determine how runoff signatures would help with improving the model calibration, and to identify the periods when intensive monitoring is critically required for deriving parameter values of reduced uncertainty.
Methods
Study catchment
Data collection
HBVlight requires input forcing data consisting of daily precipitation and air temperature as well as monthly estimates of potential evapotranspiration. We obtained meteorological data for the full period 2000–2003 from a monitoring station near the catchment outlet at 2,570 m a.s.l. The meteorological data included air temperature, solar radiation, relative humidity, wind velocity, and precipitation. The daily mean air temperature was derived as the arithmetic average of temperatures recorded at 02:00, 08:00, 14:00, and 20:00 h Beijing Standard Time (BST). Monthly mean potential evapotranspiration was calculated from observed meteorological data using the FAO PenmanMonteith method described by Allen et al. ([1998]).
Annual rainfall, runoff, and potential evapotranspiration for the years 2000 to 2003 in the Pailugou catchment
Year  Rainfall(mm a^{−1})  Runoff(mm a^{−1})  Potential evapotranspiration(mm a^{−1}) 

2000  353  71  842 
2001  301  44  874 
2002  411  105  764 
2003  416  103  772 
Distribution of altitudinal ranges in the Pailugou catchment and corresponding percentage of cover by forest, shrubland, and grassland
Altitude(m a.s.l.)  Percentage of land area(%)  Forest(%)  Shrub(%)  Grass(%) 

2,660–2,750  5.04  44.84  8.33  46.83 
2,750–2,850  19.19  32.4  10.9  56.7 
2,850–2,950  26.99  43.57  8  48.43 
2,950–3,050  12.38  72.54  3.31  24.15 
3,050–3,150  7.94  67.13  26.2  6.68 
3,150–3,250  5.16  84.3  11.43  4.26 
3,250–3,350  4.8  46.05  51.87  2.08 
3,350–3,450  5.13  6.82  87.33  5.85 
3,450–3,550  5.49  92.71  7.29  0 
3,550–3,650  5.14  0  100  0 
3,650–3,788  2.74  0  100  0 
Model description
The HBVlight model (Seibert, [2005]) used in this study is a conceptual rainfallrunoff model modified from the original HBV model by Bergström ([1976]). There are two minor changes in the modified model corresponding in general to the original version described by Bergström ([1992]). The first is that, instead of starting the simulation with some userdefined initial state values, the HBVlight v3.0.0.1 uses a “warmingup” period during which state variables evolve from standard initial values to their correct values according to meteorological conditions and parameter values. Secondly, the restriction that only integer values are allowed for the routing parameter, MAXBAS, has been removed to allow the use of all real (noninteger) values.
In the routing routine, the total runoff at the catchment outlet (the sum of the outflows from two or three linear reservoirs depending on whether the water level in the upper groundwater box, SUZ, is above UZL) is computed using an equilateral triangular weighting function with the base MAXBAS.
With the designated model structure, there are a total of 34 parameters involved. We simplified the model structure by fixing the generally less sensitive parameter CWH at a value of 0.2, based on the suggestion by Uhlenbrook et al. ([1999]). The three vegetation zones were not differentiated for the other snow routine parameters (TT, CFMAX, SFCF, CFR), hence TT_{ forest } = TT_{ shrub } = TT_{ grass } = TT, etc. With this, the final model structure comprises 21 free parameters. We further constrained possible parameter values by defining the following bounds: FC_{ forest } > FC_{ grass } > FC_{ shrub } (taking into account the measurements by Wang et al., [2005]), BETA_{ forest } > BETA_{ shrub } > BETA_{ grass }, and LP_{ forest } < LP_{ shrub } < LP_{grass}.
Objective function definition
The “sensitivity factor” is 7 if the objective function OF (i.e., either R^{ 2 }, R_{ eff }, R_{eff,log}, S_{ VE }, S_{ FDC }, S_{ PQ }, S_{ PT }) is highly sensitive with respect to parameter p_{ i }. Similarly, c_{ OF }(p_{ i }) = 3 for moderately sensitive objective functions, c_{ OF }(p_{ i }) = 1 for slightly sensitive objective functions, and c_{ OF }(p_{ i }) = 0 for insensitive objective functions.
Regional sensitivity analysis
Model parameters and their value ranges (lower and upper limits) used in the Monte Carlo runs
Index  Parameter  Lower limit  Upper limit  Units 

Catchment  
1  PCALT  4.0  14.0  %/100 m 
2  TCALT  0  0.5  °C/100 m 
Snow routine  
3  TT  −2.5  2.5  °C 
4  CFMAX  1.0  9.0  mmd^{–1} °C^{−1} 
5  SFCF  0.2  0.65  – 
6  CFR  0  0.8  – 
Soil routine  
7  FC _{ forest }  200  580  mm 
8  FC _{ shrub }  25  300  mm 
9  FC _{ grass }  30  568  mm 
10  LP _{ forest }  0  0.60  – 
11  LPs _{ hrub }  0.50  0.89  – 
12  LP _{ grass }  0.70  0.90  – 
13  BETA _{ forest }  3.0  6.0  – 
14  BETA _{ shrub }  2.0  5.0  – 
15  BETA _{ grass }  1.0  3.0  – 
Response routine  
16  PERC  0.01  3.0  mm d^{−1} 
17  UZL  15  70  mm 
18  K _{ 0 }  0.4  1.0  d^{−1} 
19  K _{ 1 }  0.035  0.20  d^{−1} 
20  K _{ 2 }  0.020  0.035  d^{−1} 
Routing routine  
21  MAXBAS  6.0  11.0  d 
Uncertainty analysis
The uncertainty in the simulated runoff is assessed using the GLUE method (Beven and Binley, [1992]; Beven and Freer, [2001]), which is based on the concepts of RSA. Performance of the GLUE analysis includes the following steps, with steps i to iii being identical to the RSA procedure: i) a large number of model runs with randomly chosen parameter sets selected from a chosen probability distribution; ii) definition of the likelihood function (Eqs. 1 to 8) and calculation of likelihood values corresponding to the parameter sets; iii) selection of a cutoff threshold value or a fixed percentage of the number of sample parameter sets for the likelihood function to distinguish between the behavioral parameter sets and the nonbehavioral parameter sets (the runs yielding the 500 highest objective function values [i.e., 5% of the total runs] were classed as behavioral runs, similar to the cutoff used in the RSA analyses); iv) rescaling of the cumulative likelihood values of all behavioral models to unity; and v) calculation of the percentiles of the cumulative distribution of the likelihood measure. GLUE integrates the outputs of all behavioral models in an ensemble prediction. For each time step of the simulation, the output prediction is obtained as the median of the distribution of all ensemble members, and its uncertainty bounds are estimated as 2.5% and 97.5% percentiles of the distribution.
Dynamic identifiability analysis (DYNIA)
Taking into account considerations of Wagener et al. ([2003]) and based on previous experiences in other applications, we used a window size of 5 days (i.e., n = 2) for all parameters.
Results and discussion
Parameter sensitivity
RSA parameter sensitivities for various objective functions
Parameters  Statistical measures  Runoff signatures  Combined objective functions  

R ^{ 2 }  R _{ eff }  R _{ eff, log }  S _{ VE }  S _{ FDC }  S _{ PQ }  S _{ PT }  C_{ OF }  
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8–28)  
Catchment  
PCALT  ***  ***  ***  **  ***  ***  ***  (8)  *** 
TCALT  ***  *  –  *  *  –  –  (9)  ** 
Snow routine  
TT  ***  ***  *  **  **  *  *  (10)  ** 
CFMAX  *  **  *  *  –  –  –  (11)  ** 
SFCF  ***  ***  **  ***  –  **  **  (12)  *** 
CFR  –  –  –  –  –  *  –  (13)  * 
Soil routine  
FC _{ forest }  *  *  *  –  *  –  –  (14)  –– 
FC _{ shrub }  ***  **  **  *  ***  ***  **  (15)  *** 
FC _{ grass }  *  –  **  –  **  **  *  (16)  * 
LP _{ forest }  –  –  *  *  –  –  –  (17)  * 
LP _{ shrub }  **  *  *  –  –  **  **  (18)  – 
LP _{ grass }  –  –  –  –  –  –  **  (19)  ** 
BETA _{ forest }  –  *  (20)  *  
BETA _{ shrub }  *  *  *  –  –  **  **  (21)  ** 
BETA _{ grass }  **  –  *  *  *  ***  **  (22)  *** 
Response routine  
PERC  ***  **  **  ***  ***  ***  ***  (23)  * 
UZL  *  **  –  –  ***  –  –  (24)  *** 
K _{ 0 }  (25)  
K _{ 1 }  ***  ***  *  **  **  *  ***  (26)  ** 
K _{ 2 }  **  **  **  **  –  *  *  (27)  ** 
Routing routine  
MAXBAS  –  **  –  **  ***  **  ***  (28)  *** 
Among the different model routine parameters, the catchment parameter PCALT is the most sensitive, with moderate or high sensitivities for all objective functions. PCALT describes the linear gradient of precipitation with altitude. Since the climate data for the modeling are derived from a monitoring station just below the catchment outlet, the linear extrapolation of the precipitation to the catchment area by means of PCALT highly influences the assumed areal precipitation input and, hence, the potential recharge water and the catchment runoff. The second catchment parameter, the temperature gradient TCALT, is less sensitive (high sensitivity with respect to R^{ 2 }, and moderate sensitivity for C_{ OF }). All snow routine parameters are sensitive with respect to most of the objective functions, with the only exception being CFR, which is sensitive only with respect to S_{ PQ }. The Pailugou catchment experiences long periods of snow cover; runoff almost ceases in winter, and is highly influenced by snow melt and refreezing processes during late spring and summer as well as the start of snow accumulation in fall. Therefore, the dominant role of the snow routine parameters for the model performance is not astonishing.
The soil moisture routine parameters are generally more sensitive with respect to the runoff signatures, especially with those focusing on runoff peaks (S_{ PT }, S_{ PQ }). The storage capacity of the soil moisture reservoir, FC, has a larger impact on the model performance than BETA, which influences the amount of percolation from the soil moisture storage to the groundwater in times when the soil is not saturated. LP, which describes the reduction of the potential evapotranspiration in drier soils, has the least sensitivity. The sensitivities of BETA, LP, and FC vary between different vegetation classes. Although forests cover almost half of the catchment, the parameters of this vegetation class influence the model performance less than the parameters of the two other classes do.
The response routine parameters are generally sensitive with respect to most of the objective functions, except K_{0}. The parameter PERC, which represents the maximum percolation rate from the upper groundwater box to the lower groundwater box, is the most sensitive parameter of the response routine. The large influence of PERC on the model fit indicates the importance of slow groundwater runoff in the catchment. K_{0} is the least sensitive model parameter, and no objective function under consideration identified K_{0}. K_{0} controls the fast runoff when the filling in the upper groundwater box exceeds the threshold UZL (Figure 2). Precipitation in the Pailugou catchment is generally very low and it is realistic to assume that fast surface or nearsurface runoff is a rare event, occurring only after exceptionally high rain storms. However, the main reason for the low sensitivity of K_{0} is most likely the low time resolution of the outflow data and the model, which is larger than the reaction time of fast runoff in this small and very reactive headwater catchment. Contrary to the fast outflow coefficient, K_{0}, the second outflow coefficient of the upper groundwater box, K_{1}, proves to be highly sensitive, which indicates the importance of fast interflow for the runoff generation in the catchment. K_{2}, the recession coefficient of the lower groundwater box, is moderately sensitive to most objective functions and plays a lesser role for the objective functions focusing on runoff peaks (S_{ PQ }, S_{ PT }). The threshold level, UZL, above which fast runoff from the upper groundwater box occurs, is generally not very sensitive. However, its sensitivity is much increased when considering the flow duration curve as efficiency criteria.
The routing parameter MAXBAS shows a higher sensitivity with respect to the objective functions based on runoff signatures and the combined objective functions than to the more statistical measures.
Uncertainty analysis
As clearly illustrated in Figure 3, some parameters are constrained in different value ranges depending on which objective function is used to assess the model behavior. For example, values of PCALT in the behavioral runs are relatively large when considering R^{ 2 }, R_{ eff }, or C_{ OF } as the objective function, and are significantly lower when using S_{ PQ } or S_{ PT }. The snow correction factor, SFCF, attains higher values in the behavioral runs when considering R_{eff,log} as the objective function. Values of the response routine PERC are particularly low when based on S_{ PQ } and S_{ PT }. The values of the routing routine MAXBAS are especially low when based on S_{ FDC }, but much higher values are attained when based on other objective functions.
It should be noted that the estimated model uncertainties are sensitive to the choice of threshold values which distinguish behavioral and nonbehavioral model runs, which has been often considered as one of the main drawbacks of the GLUE technique (e.g., Montanari, [2005]; Blasone et al., [2008b]). However, in this study, we did not investigate how sensitive the model simulation results are to the cut off threshold values, therefore, further studies need to investigate how the threshold value should be chosen in order to provide stabilization (may be difficult) in the application of the GLUE method.
Temporal changes of parameter sensitivity
Figure 7a displays the development of the IC (Eq. 13) over time for the catchment parameters (PCALT, TCALT) and the parameters of the snow routine (TT, CFMAX, SFCF, CFR). The IC of PCALT varies largely over the simulated time period; it is highest during the rainy season, when the soil moisture storage and the groundwater storages are filled and additional precipitation produces runoff, and it decreases continuously during recession periods. The IC for TCALT is significantly higher in periods with active vegetation, when the soil moisture is high. The parameters of the snow routine – with exception of CFR which has a low IC over the entire simulation time – are generally better identifiable during the snow melt period, especially during the first main melt events in spring.
Figure 7b displays the development of the IC over time for the parameters of the soil moisture routine. FC_{ shrub } shows a pronounced temporal dependency of the IC; it is more identifiable during the early vegetation period when the soil moisture storage is replenished by melt water. The IC s for FC_{ forest } and FC_{ grass } show similar patterns, both exhibiting a somewhat higher identifiability during the periods when the catchment is already relatively wet and further precipitation increases the proportion of faster runoff components in the total catchment runoff. The IC s of LP and BETA of the same vegetation class show similar patterns; LP and BETA are generally better identifiable prior to runoff peaks, in times when the catchment’s storages are filling.
The IC for the parameters of the response routine and the routing routine (Figure 7c) is directly linked to the dynamics of the runoff peaks. The IC for PERC is higher in early winter, in the course of declining percolation from the upper groundwater box to the lower groundwater box. The three recession constants, K_{0}, K_{1} and K_{2}, show very distinct patterns of IC. While the IC of the fast runoff component (K_{0}) is always very low, that of K_{1} is markedly increased in the falling limbs of runoff peaks and decreases with very high runoff events. The dominant role of the parameter K_{1} for controlling recession after peak runoffs underlines the importance of fast subsurface flow in the catchment. The IC of K_{2}, which influences the dynamics of the slow groundwater runoff, continuously increases during low flow periods, when recharge from the soil zone ceases and the baseflow from the lower groundwater box becomes the main runoff source. UZL becomes somewhat better identifiable in late summer when the catchment is already relatively wet from the summer rains, and additional precipitation causes the upper groundwater box to exceed the threshold filling UZL and initiates fast runoff. Not surprisingly, the routing parameter MAXBAS is more identifiable during pronounced runoff peaks following snow melt and in the wet season, especially in the rising limbs of the runoff peaks.
Temporal changes of optimal parameter values
The DYNIA analysis reveals different types of parameter behavior. The optimum values (i.e., red dots in Figure 8) of 11 model parameters (i.e., PCALT, TCALT, CFMAX, SFCF, FC_{ shrub }, LP_{ shrub }, LP_{ grass }, PERC, UZL, K_{2}, and MAXBAS) are constant over time (Figure 8). For these parameters, the same value would be identified, regardless of the time period used for the model conditioning/calibration. For five more parameters (i.e., TT, FC_{ forest }, BETA_{ shrub }, BETA_{ grass }, K_{1}), the variation of the optimum parameter values (i.e., red dots) is less than 10% of the original parameter range, also indicating the possibility of a relatively stable and timeinvariant parameter identification. For the other parameters (CFR, LP_{ forest }, BETAf_{ orest }, K_{0}, FC_{ grass }), the optimum values of these parameters shift over the time domain (Figure 8). This can be attributed to the very low sensitivities (Figure 7) of these parameters or inadequacies within the model structure. Our results indicate the importance of identifying the periods when intensive monitoring is critical for deriving parameter values of reduced uncertainty.
Conclusions
 1.
The results of RSA show that model parameter sensitivity is largely dependent upon the objective function used for the model evaluation in the sensitivity analysis. Most of the model parameters are sensitive when the runoff signatures and combined objective functions are used. The time resolution of the runoff observations and the HBVlight simulations is too coarse to satisfactorily describe the fast runoff processes in the catchment. More frequent runoff observations would substantially increase the knowledge on the rainfallrunoff transformation in the catchment and, specifically, improve the distinction of fast surfacenear runoff and interflow components in their contribution to the total catchment runoff.
 2.
The results of GLUE show that the HBVlight model is generally able to simulate the runoff in the Pailugou catchment with an acceptable accuracy. However, a distinct pattern of mismatch is found in some highintensity rainfall/snow melt events at a daily step. Most parameters are well constrained, showing higher parameter identifiability and lower model uncertainty when runoff signatures or the combined objective functions are used. The combined objective function focusing on the catchment parameter TCALT performed best in terms of model uncertainty and model precision.
 3.
The DYNIA analysis shows different types of parameter behavior. The optimum values of 11 model parameters are constant over time regardless of the time period used for the model conditioning/calibration. For 5 parameters, the variation of the optimum parameter values is less than 10% of the original parameter range, also indicating the possibility of relatively stable and timeinvariant parameter identification. For the other 5 parameters optima change over the time domain. All of these indicate that model parameters have specific periods where they are more sensitive, more identifiable, and where they play a clearer role than during other periods. The hydrological process of snow routine could be better described if monitoring is intensified during snow melt. Our results also highlight the importance of identifying the periods when intensive monitoring is critical to derive parameter values of reduced uncertainty.
Changes in climate and/or land cover have significant implications to rainfallrunoff dynamics at watershed or catchment scales, which in turn affect regional ecosystem processes. Hydrological models are important tools for evaluating the potential impacts of climate change and land cover change on the hydrological cycles and runoff regimes. However, uncertainty in model parameters due to a lack of identifiability may greatly limit the use of models for purposes such as parameter regionalization or the investigation of land use or climate. Sensitivity analysis and identification of parameters with significant implications to changes in landscape features are a critical step in studying regional ecosystem processes in response to natural or anthropogenic perturbations. A higher identifiable parameter can reduce model uncertainty and is critical for evaluating the effects of climate change and land use disturbance on the hydrological cycles.
It should be noted here that the generality of results and conclusions of this study need to be verified through the application of HBVlight in other regions.
Abbreviations
 AWRCFQM:

Academy of Water Resource Conservation Forests of Qilian Mountains in Zhangye:
 BETA :

An empirical shape parameter:
 BST:

Beijing Standard Time:
 CFMAX :

The degreeday factor:
 CFR :

The refreezing coefficient:
 DYNIA:

Dynamic Identifiability Analysis:
 FC :

Maximum soil moisture storage:
 GLUE:

Generalized Likelihood Uncertainty Estimation:
 IC :

Information content:
 K _{ 0 } :

Recession coefficients of fast runoff:
 K _{ 1 } :

Recession coefficients of delayed runoff:
 K _{ 2 } :

Recession coefficients of low baseflow runoff:
 LP :

Soil moisture value above which actual evapotranspiration above potential evapotranspiration:
 MAXBAS :

A variable of length of triangular weighting function:
 PCALT :

Change of precipitation with elevation:
 PERC :

Maximum percolation rate from upper to lower groundwater box:
 R ^{ 2 } :

Coefficient of determination:
 R _{ eff } :

NashSutcliffe efficiencies:
 RSA:

Regional Sensitivity Analysis:
 S _{ VE } :

Volumetric efficiency:
 S _{ FDC } :

Flow duration curve:
 S _{ PQ } :

Peak flow:
 S _{ PT } :

Time to peak:
 TCALT :

Change of temperature with elevation:
 TT :

Temperature threshold for rain or snow:
 UZL :

Threshold for the fast runoff:
Declarations
Acknowledgements
This research was jointly funded by Robert Bosch Foundation and Beijing Municipal Commission of Education (Key Laboratory for Silviculture and Conservation). Authors are grateful to the Academy of Water Resource Conservation Forest of Qilian Mountains (AWRCFQM), Zhangye, Gansu Province, China, for organizing the international joint project work and providing field data.
Authors’ Affiliations
References
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