Development and Application of a Distributed

Development and Application of a Distributed Hydrological Model: EasyDHM

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Xiaohui Lei 1; Weihong Liao 2; Yuhui Wang 3; Yunzhong Jiang 4; Hao Wang 5; and Yu Tian 6

Abstract: Distributed hydrological models have been commonly used in research involving water management because of their consideration of spatial variability. However, practical applications still encounter technical challenges such as complicated modeling, low computational efficiency, and parameter equifinality. A user-friendly model, EasyDHM, was developed and was shown effective over the years. In this paper, the essential parts of this model, namely, discretization of the spatial units, preparation and initiation of data and parameters, and the main physical processes are briefly introduced. In particular, the roles of the parameter sensitivity analysis and optimization for this model, which have considerably improved the prediction accuracy, are highlighted in this study. From the application to the upstream basin of Han River in China, the simulation and parameter estimation by EasyDHM turned out to be effective and easy to operate. EasyDHM can, therefore, be widely used for practical water management applications. DOI: 10.1061/(ASCE)HE.1943-5584.0000745. © 2014 American Society of Civil Engineers. Author keywords: Distributed hydrological model; Sensitivity analysis; Parameter optimization; Spatial discretization; EasyDHM model.

Introduction Distributed hydrological models (DHMs) were first developed in 1970s since the physical-based DHM was firstly proposed in “Blueprint for a Physically-based, Digitally-simulated Hydrologic Response Model” by Freeze and Harlan in 1969. DHMs, which enable the representation of the spatial variability of flow characteristics within a basin, help assess the impact of natural and human-induced changes and provide detailed descriptions of the hydrological processes in watersheds (Abbott and Refsgaard 1996). Study areas are divided into grids or small subbasins as basic computational units in DHMs. Conceptual or physical equations are used to simulate the hydrologic process in these computational units, which will be accumulated later to predict the discharge process at catchment outlets. Simulations require data and parameter values for each unit. Thus, the preparation of the spatial units, parameters, and data, i.e., preprocessing, is complex but essential for DHMs and is a major challenge for model development and application. 1 Professor, State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China. 2 State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China (corresponding author). E-mail: [email protected] 3 School of Environmental Science and Engineering, Donghua Univ., Shanghai 201620, China. 4 Professor, State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China. 5 Academician, State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China. 6 State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China. Note. This manuscript was submitted on December 6, 2011; approved on November 9, 2012; published online on November 12, 2012. Discussion period open until June 1, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydrologic Engineering, Vol. 19, No. 1, January 1, 2014. © ASCE, ISSN 1084-0699/2014/ 1-44-59/$25.00.

By taking advantage of the geographic information system (GIS) and computer techniques, the DHM preprocessing function has been streamlined and the data management and analysis ability has been improved (Fedra 1996; Singh and Woolhiser 2002). To this end, many DHMs have been developed and improved continuously, such as Systeme Hydrologique Europeen (SHE) (Abbott et al. 1986), TOPMODEL (Beven 1997), SWAT (Neitsch et al. 2005), VIC (Liang et al. 1994), TOPKAPI (Todini and Ciarapica 2001), and WEP (Jia et al. 2001). These models have been successfully used to characterize hydrological processes and solve practical hydrological and water resource problems. In addition, DHMs can also be incorporated into real-time flood forecasting systems for flood management, such as WATFLOOD (Kouwen 2000), DHSVM (Wigmosta et al. 1994), and LISFLOOD (De Roo et al. 2000), which greatly broaden the range of applications of DHMs. As a result, the computational efficiency and extended functions have increased the popularity of these DHMs. The core simulation of DHMs is based on physical equations and conceptual relationships with some simplifications. Research on these simulations is relatively mature. However, auxiliary parts have gradually become the focus of research on DHMs. Together with data preprocessing and the computational efficiency mentioned earlier, challenges have surfaced in DHM development and application. These challenges include the following: (a) choosing spatial and temporal resolutions, which should be appropriate for both data availability and the physical/conceptual assumptions of the model structure; (b) parameter problems, including overparameterization that leads to tedious calibrations and parameter equifinality, which means different parameter combinations within a chosen model structure can give similar model performance (Beven and Freer 2001); and (c) data problems. The data requirements of DHMs are huge and difficult to collect. Meteorologic and hydrologic data are usually observed at gauges. These data cannot interpret the spatial variation. Other data such as spatial fields of soil moisture, groundwater level, and flow at interior points should also be collected for assessing the capability of DHMs (Moreda et al. 2006). However, they are not easy to obtain, which also restricts the application of DHMs. For the same reason, lumped models may occasionally outperform DHMs in outlet flow simulations (Reed et al. 2004).

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As previously mentioned, the shortage of auxiliary modeling frameworks for the preprocessing and parameter estimation functions of DHMs is an obvious obstacle for model development and the extensive application of new DHMs. The development of DHMs with integrated auxiliary tools has shown its significance in their applications. In this paper, we introduce and validate a DHM called EasyDHM (Easy Distributed Hydrological Model). We independently developed EasyDHM as a convenient, user-friendly, efficient, and noncommercial model for hydrologic simulation. The core simulation in EasyDHM was developed based on some opensource DHM codes and the application experience of well-known DHMs. The corresponding modeling system called MWEasyDHM (MapWindow-Based Easy Distributed Hydrological Model) was developed based on the open-source GIS tool MapWindow (Lei et al. 2011) for the convenient use of this model. MWEasyDHM was built as a plug-in for MapWindow GIS, and it includes three main parts: a preprocessing module for hydrologic analysis, a simulation module, and a postprocessing module. MWEasyDHM was introduced and described by Lei et al. (2011). Spatial discretization, core simulation, and parameter estimation of EasyDHM are mainly introduced and validated in this paper. This paper is organized as follows. The spatial discretization pattern, data, and parameters for EasyDHM are presented in the next section, followed by a detailed description and explanation of its methodology within a parameter estimation module. Then, an application is presented to demonstrate the simulation process and the effect of this model in the case study section. Finally, the analysis of the parameterization of EasyDHM is summarized.

Parameters and Data Spatial Discretization The first step in EasyDHM is spatial discretization. MWEasyDHMs help complete this task for EasyDHM. Using this tool, the study area

is divided into several partitions according to the catchment topology of hydrologic stations and reservoirs along rivers. Each partition is later divided into several subbasins according to the digital river network extracted from the digital elevation model (DEM) of the study area. And each subbasin was refined into internal units according to respective rules. Fig. 1 shows the three internal units of an EasyDHM subbasin, with each containing only one reach. As indicated in Fig. 1(a), the subbasin border and main river channel can be determined. For each subbasin, the internal units can be divided into equal flowinterval bands [(EFBs), Fig. 1(b)]; equal elevation bands [(EEBs), Fig. 1(c)]; and hydrological response units [(HRUs), Fig. 1(d)]. The EEBs, encoded from 1 to 10 following the elevation gradient, are derived according to the elevation, whereas the subbasins in the plains are required as a single EEB. The EFBs are derived from the flow length of the net rain that reaches the outlet of the subbasins, which indicates that runoff in different grids within each EFB reaches the outlet with the same travel time. The HRUs are derived according to the hydrologic response mechanisms. The EEBs and EFBs are spatially linked, whereas the grids in each HRU are relatively independent. For EasyDHM, the simulation and parameter estimation are conducted one partition at a time. In each partition, the internal units are the basic computational elements for the runoff-generation simulation; subbasins are the basic elements for flow-routing simulation. The flow that passes through the outlet of a partition will be the discharge of the hydrologic station at that outlet or the inflow of the reservoir. With MWEasyDHM, the digital network of a study area can be derived automatically from the DEM (Lei et al. 2011). An accumulation threshold value is set to discriminate the dry/wet grid, and the improved Pfafstetter Coding System (O. Pfafstetter, Classification of hydrographic basins: coding methodology, unpublished manuscript) is used to rank the generated river network (Lei et al. 2010). Users can also choose the number of river ranks to divide the subbasins. Hence, the users using the accumulation threshold and the

(a)

(b)

(c)

(d)

Fig. 1. Three horizontal structures supported by EasyDHM model: (a) grids (arrows represent the flow direction based on the DEM elevation); (b) EFBs of a subbasin; (c) EEBs of a subbasin; (d) HRUs of a subbasin JOURNAL OF HYDROLOGIC ENGINEERING © ASCE / JANUARY 2014 / 45

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rank threshold can control the number of generated reaches. Considering subbasins are divided from reaches, the number of generated subbasins can also be controlled (Lei et al. 2010). This function greatly improves the generalization of the model because the number of basic computational elements can be controlled for both large and small basins by setting these thresholds.


Parameters The values of DHM parameters are usually difficult to determine because these models always have numerous kinds of parameters and computational units. In addition, the parameters cannot be measured for each unit. Thus, the parameters are usually derived from the underlying data by taking advantage of GIS and RS technology. In EasyDHM, the values of most parameters in each unit can be calculated from topographical characteristics of DEM, soil type, and land-use type due to their relationships. Thus, these parameters all have specific physical meaning. We named them as physical parameters in EasyDHM. Some other parameters in EasyDHM cannot be derived directly from the underlying data. For example, the parameter Basic Snowmelt Temperature is functionally related to topography, soil type, and type of land use in each unit. Other parameters such as Groundwater Parameters show little relationship with the aforementioned underlying data. All these parameters were assigned default values according to experience or the literature, with each parameter in one partition given the same value. These parameters are called global parameters in EasyDHM. Correction coefficients were set up especially in EasyDHM for convenience and to improve the efficiency of the parameter identification. The correction coefficients, also regarded as the same in one partition, are used to correct the physical parameters by multiplying the physical parameters with their relative correction coefficients. Thus, during parameter identification, the correction coefficients were adjusted aside from physical parameters themselves. However, not all physical parameters have relative correction coefficients. Only those parameters with high uncertainty in their initial values from underlying data are given correction coefficients. Other physical parameters were assigned fixed values for all simulations. In conclusion, the parameters of EasyDHM were categorized into three classes: physical parameters, global parameters, and correction coefficients. The global parameters and correction coefficients are also called adjustable parameters, which can be optimized for more effective simulation.

conflux simulations. Thus, in accordance with spatial discretization of the study areas, these data should be interpolated spatially for all computational units before simulation. Many spatial interpolation methods are available in EasyDHM, including the Thiessen polygon method (Boots 1980), the inverse distance weighted method (Bartier and Keller 1996), the Kriging method (Borga and Vizzaccaro 1997), and the Thiessen polygon and inverse distance weighted methods for considering elevation correction (Lu and Wong 2008), which were also seen in the paper that introduced MWEasyDHM (Lei et al. 2011).

Methodology Generally, the entire simulation for a selected partition contains two major parts: the runoff generation simulation of all internal units and the flow-routing simulation of all reaches within this partition. The flow chart is shown in Fig. 2. tEnd is the total number of time steps, and NSub represents the number of subbasins (reaches) within the calculated partition. As previously mentioned, the parameters were first determined from underlying data or set default values, and correction coefficients and global parameters should first be adjusted before simulation. Moreover, since EasyDHM is a physically-based model for continuous simulation, state variables such as soil moisture and snow coverage should be initialized before calculation at each time step. However, users should set only the initial conditions for state variables during

Hydrologic–Meteorologic Data Calibrating and evaluating the model requires observed discharge data from the hydrologic stations and reservoirs. Actually, discharge data at any particular time step is generally the average discharge at that time step in EasyDHM. Depending on the time step of a simulation, conversion between time scales of hydrologic data is usually necessary, similar to meteorologic data. Precipitation is the fundamental driving force for most hydrologic processes. Thus, precipitation data observed from rain gauges were required. Considering the Penman–Monteith equation (Monteith 1965) was chosen to calculate potential evapotranspiration (PET), the air temperature, shortwave radiation, relative humidity, and wind speed obtained from the routine meteorological stations were also required. Moreover, temperature data (maxima, minima, and means) were also required when snow accumulation and snowmelt occurred in a study area. These meteorologic observations are the major input data for runoff generation and flow

Fig. 2. Flow chart of the hydrological simulation by EasyDHM in a partition


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the first time step. In the subsequent time steps, the variables are internally managed using the values of the previous time step, as shown in Fig. 2.

during runoff generation, such as the EasyDHM method. Its simulation process is introduced in the following context. Snow Process


Runoff Generation Four different runoff generation methods are integrated in EasyDHM models, namely, EasyDHM, WetSpa (Wang et al. 1996), Xin’anjiang (Zhao 1984), and Hymod (Boyle et al. 2001). The latter three methods are all widely accepted models, which were reprogrammed in FORTRAN with some improvements by our research team. The EasyDHM method was developed independently and it is the default runoff generation simulation tool. In EasyDHM method, research areas are stratified into four vertical layers: vegetation canopy, surface layer, soil layer, and groundwater aquifer (Fig. 3). Precipitation goes first through vegetation canopy where canopy interception occurs, and then infiltrated water goes through the surface layer. Although the excessive infiltrating water fills the sinks, the rest infiltrates into the soil. Soil is divided into several layers, and soil water may move laterally or vertically in each layer. The soil water of the last layer goes vertically into groundwater aquifers as groundwater recharge. In these processes, surface sink-filling forms surface runoff, soil water discharged in lateral direction contributes to the interflow, and excessive subsurface water forms subsurface runoff. Together, they are called generated runoff. Evaporation occurs in the vegetation canopy, surface sink filling, soil water, and groundwater. Plant transpiration comes from soil water, as depicted in Fig. 3. The summary of evaporation and transpiration is called actual evapotranspiration. In addition, snow covering and melting are also considered in this method for better simulations in cold regions. For the three other methods for runoff generation simulation, the major hydrologic features for each internal unit, namely, actual evapotranspiration, surface runoff, soil water interflow, and groundwater drainage are also calculated, although using different equations. Thus, their values may differ even though the input data are the same. Any runoff generation methods for other DHMs can be easily incorporated in EasyDHM, if the same hydrologic features can be calculated. Considering different methods have different applicability, EasyDHM, with four runoff generations for now, is suitable for many regions of different locations, warm or cold, dry or wet. However, EasyDHM is also suitable for different regions using the same simulation method by changing the parameters, especially for those methods that consider more processes

Snow packs act as storage during the cold season and they are subsequently released as melt water during the warm season. Snow process is of great importance in the water cycle of river basins, especially those with cold climates. Therefore, the snow process is also simulated in EasyDHM method. When precipitation occurs, EasyDHM first classifies it as rainfall or snowfall based on the daily mean air temperature. The boundary temperature used to separate them as well as the snow melting temperature T mlt (°C) is defined by the user. Snow cover occurs at air temperatures less than the boundary temperature and no water infiltrates the soil surface. Once the air temperature exceeds this threshold, snowmelt occurs if snow cover is present. Melting water can be calculated using Eq. (1) and added as part of net rain in the same time step T snow þ T mx SNOmlt ¼ bmlt SNOcov ð1Þ − T mlt 2 where SNOmlt = the amount of water from the snowmelt (mm); SNOcov = the fraction of the area covered by snow in an internal unit; T snow = the snow pack temperature (°C); T mx = the maximum daily air temperature (°C); and bmlt = the melt factor for the day (mm=day=°C). The melt factor varies seasonally with the maximum and minimum values that occur during summer and winter solstices, respectively, and it forms a simple sine wave variation curve. Snow pack temperature is a function of the mean daily temperature during the preceding days (Anderson 1976). SNOcov is a function of the water content of the snow pack. The parameters involved in snow process simulation, including those boundary temperatures, are set as global parameters. PET and Potential Plant Transpiration In hydrologic processes, evapotranspiration is the main process for water loss, and it is an important component of the water cycle. PET is usually calculated first to obtain actual evapotranspiration. EasyDHM uses the Penman–Monteith equation (Monteith 1965) to calculate the PET. Potential transpiration (PT) is a part of the PET and is determined by the canopy coverage of the study area. If plants cover a large proportion of the canopy, the PT also occupies a large part of the PET. In EasyDHM, the leaf area index (LAI) is used to interpret canopy coverage. The PT is calculated using Eq. (2) ( PET·LAI 3.0 ; LAI ≤ 3:0 PT ¼ ð2Þ PET; LAI > 3:0 Canopy Process Interception first occurs in the canopy during rainfall. Storm characteristics, species of vegetation, percentage of canopy cover, growth stage, and season affect the interception amount. In EasyDHM, interception amount (I, mm) is calculated as a function of storage capacity (I 0 , mm), interception storage amount of the last time step [SIðt − 1Þ, mm], and precipitation amount (P, mm) I 0 − SIðt − 1Þ; P > I 0 − SIðt − 1Þ ð3Þ I¼ P; P ≤ I 0 − SIðt − 1Þ

Fig. 3. The structure of the runoff generation method, EasyDHM

where storage capacity I 0 = the main factor that influences the interception amount in a given internal unit. Considering I 0 varies JOURNAL OF HYDROLOGIC ENGINEERING © ASCE / JANUARY 2014 / 47

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continuously with time, a simple sine wave variation curve is introduced for convenient model programming. The empirical equation is similar to that used for estimating daily potential evaporation based on statistical analysis of long-term measurements (De Smedt 1997), which is given in Eq. (4) ðI − I min Þ d − 87 b I 0 ¼ I min þ max 1 þ sin 2π ð4Þ 2.55 365 where I min = the minimum interception storage capacity for a given internal unit (mm); I max = the maximum interception storage capacity (mm); and d = the Julian date. I min and I max are derived from the canopy coverage condition. The exponent b controls the shape of the variation curve of interception capacity, and is set to a default value of 1.35 in EasyDHM method. By subtracting the water intercepted from rainfall, the remaining water is called net rain, which reaches the ground and finallyforms runoff. The water from snowmelt is also added to the net rain. Water stored in the canopy eventually evaporates. The amount of evaporation in each time step is calculated from the amount of intercepted water stored in the canopy and the evaporation capacity. This calculating method is also suitable for calculating the amounts of evaporation from depression water, soil water, and groundwater. The evaporation capacity is first the PET amount before canopy process, and may later gradually decline by subtracting the actual amount of evaporation and transpiration in each layer. Although plant transpiration takes place in the canopy, its water still comes from soil moisture. Hence, plant transpiration is calculated as a soil process in EasyDHM. Surface Process In EasyDHM, surface runoff occurs whenever the rate of water application to the ground surface (net rain) exceeds the rate of infiltration. In the EasyDHM method, the Soil Conservation Service (SCS) curve method (Soil Conservation Service 1972) is introduced to estimate excess rainfall on surface [Eq. (5)] and the remaining one is regarded as infiltration for soil [Eq. (6)] Pn2 ðPn þ SÞ

ð5Þ

In ¼ Pn − PE

ð6Þ

PE ¼

where PE = the excess rain (mm); In = the infiltration amount (mm); Pn = the net rain for the day (mm); and S = the retention parameter (mm). The retention parameter varies spatially due to changes in soils, land use, management, and slope and is temporally due to changes in soil water content. The retention parameter is defined as in Eq. (7) 1000 S ¼ 25.4 − 10 ð7Þ CN where CN = the curve number for a given time. CN is dependent on soil permeability, land use, and antecedent soil water conditions. In the EasyDHM method, this relationship is simplified using a function made up of the parameter CN2, which is the curve number for the medium moisture condition and the water content of soil of the same internal unit. CN2 is set as a global parameter, with a default value of 31 days. Excess rain stays on the surface as a depression storage supplement or it flows laterally and contributes to surface runoff. Factors that affect depression storage include terrain feature, type of soil

surface, land use, antecedent rainfall, and soil moisture. Moreover, depression amount decreases with evaporation. In EasyDHM method, a simple empirical equation [Eq. (8)] suggested by Linsley et al. (1982) is used to estimate depression storage SDðt − 1Þ SD ¼ SD0 1 − exp PE þ SD0 ln − SD ð8Þ SD0 where SD = the depression storage of an internal unit (mm); and SD0 is the depression capacity (mm). The depression capacity of each internal unit is derived from the categories of average slope, land use, and soil type, and can be adjusted through a correction coefficient. From subtracting the depression storage amount from excess rain, the amount of remaining water forms the surface runoff RS Rs ¼ PE − SD

ð9Þ

Soil Process The EasyDHM method divides the soil profile into several soil layers to differentiate the vertical varieties. In each soil layer, the infilling water may be removed by percolation to the following layer, evaporation, or plant uptake. The remaining water amount may stay in soil or move laterally in the profile and contribute to stream flow. The soil layer processes are simulated layer by layer sequentially from surface to bottom.

Percolation Similarly, the excess soil water is calculated first for each soil layer using Eq. (10) ( SW 0;i ¼ θi − θfc;i θi > θfc;i ð10Þ SW 0;i ¼ 0 θi < θfc;i where SW 0;i = the excess soil water in the soil layer i (mm); θi = the water content of the soil layer i (mm) with the infilling water from precipitation on the upper layer; and θfc;i = the water content of the soil layer at field capacity (mm). Water is allowed to percolate when the excess soil water SW 0;I is greater than zero and the layer below i unsaturated. The percolation amount was calculated using Eq. (11) −Δt ð11Þ W p;i ¼ SW 0;i 1 − exp TT i where W p;i = the amount of water that percolates into the next lower soil layer (mm); Δt = the length of the time step (h); and TT i = the travel time for percolation (h). The travel time for percolation is unique for each layer, and it was calculated using a function of saturated hydraulic conductivity, field capacity amount, and saturated water content of the same layer.

Interflow The EasyDHM method introduces a kinematic storage model for soil interflow (lateral flow) calculation, which was developed by Sloan and Moore (1984). This model simulates a two-dimensional cross-section interflow moving along a downward flow path with a steep hillslope. The key shape parameters of the flow path can be represented simply by the slope (ω) and length (L, m) of a given internal unit. The interflow was calculated as follows:


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Ri ¼ K sin ω

2ðθ − θfc Þ 1000ϕd L

ð12Þ

where K = the saturated hydraulic conductivity (mm=h); ϕd = the drainable porosity of the soil (mm=mm); and 1,000 is a unit transfer multiplier for plant uptake and evaporation.

the flow routing of reaches, but instead directly goes into the outlet of a subbasin. Evaporation also occurs in groundwater aquifers, and groundwater storage is finally updated according to water balance as well for each time step.

Evapotranspiration and Generated Runoff


Actual Evapotranspiration from Soil Water The EasyDHM method treats plant uptake in soil as plant transpiration directly. Hence, for each soil layer, the water loss of plant transpiration and water evaporation should also be calculated. These two kinds of water loss are affected by soil depth. For instance, the actual water evaporation at a depth of z is written as follows: Esoil;z ¼ Es ·

z z þ expð2.347 − 0.00713zÞ

ð13Þ

where Es = soil evaporation capacity for soil water (mm). The depths of the soil layer are represented by the average values. The actual plant transpiration of each soil layer is also calculated similar to this. Soil evaporation capacity and the plant transpiration capacity are influenced by water condition, PET, and the amount of evaporation from interception and depression water because the evapotranspiration from soil water cannot be greater than soil water and the total evapotranspiration of a unit cannot be greater than the PET. Furthermore, the plant transpiration capacity cannot exceed the PT as well. Actual plant transpiration is also related to plant growth, and it is simplified using an equation with the root depth and LAI. Finally, the water content of each layer is updated according to water balance in preparation for the simulation of the following time step. Groundwater Process Percolation that moves past the lowest soil layer recharges for groundwater aquifer. Considering the recharge from the soil zone to the aquifer is not instantaneous; a time delay exists between the bottom percolation of soil and recharge of groundwater. The delay is determined by the hydraulic properties and geologic formations of aquifers, which can be calculated using the exponential decay weighting function proposed by Venetis (1969). In this function, the recharge to both aquifers on a given day is calculated as follows: W re ¼ ð1 − e−1=δ Þ · W p;n þ e−1=δ W re ðt − 1Þ

ð14Þ

where W re = the amount of recharge entering the aquifers (mm); δ = the delay time (day); and W p;n = the percolation water amount of the bottom soil layer (mm). The recharge directly contributes to the water storage in aquifers. Once the water stored exceeds the threshold, the base flow begins to enter the reach, which is calculated as follows: Rg ¼ ð1 − e−αΔt Þ · W re þ e−αΔt Rg ðt − 1Þ

For an internal unit, the runoff generation is simulated in the sequence mentioned in the brief introduction. The total evapotranspiration E and generated runoff R of an internal unit can be derived as follows: E ¼ EI þ ED þ Es þ EP þ EG

ð16Þ

R ¼ Rs þ R i þ R g

ð17Þ

where EI , ED , ES , and EG = the evaporation for water in the interception, depression, soil, and groundwater aquifer, respectively (mm); and EP = the plant transpiration in a given internal unit (mm), which comes from the soil water. The total amount of daily evapotranspiration E should not exceed the PET. The surface runoff Rs , soil interflow Ri, and the groundwater flow Rg form the total generated runoff of an internal unit. The surface runoff and soil interflow in all the internal units of a subbasin are added, which rout along the river in each subbasin until it reaches its outlet. This process is called flow routing. Flow Routing In EasyDHM, establishing the spatial relationship between each internal unit and the main reach of a subbasin is difficult, especially for HRUs, which do not comprise continuous grids (Fig. 1). Thus, the amount of generated runoff from all internal units was supposed to converge and flow into the main reach as a point source. For the reach in one subbasin, the summation of surface runoff, soil interflow generated from all internal units, and the discharge form its upstream reaches route along the rivers (Fig. 4). The total reach outflow and total groundwater flow form the discharge of the outlet. An equivalent reach is suggested for flow-routing simulation; the length of which is calculated according to the shape of this subbasin. EasyDHM also provides three routing algorithms, namely, Muskingum (McCarthy 1938), Variable Storage (Williams 1969), and Manning methods (Neitsch et al. 2005). These methods are all variations of the kinematic wave model (Chow et al. 1988). In the flow-routing simulation using these methods, a trapezoid shape is assumed for the sections in all reaches, whereas the

ð15Þ

where Rg = the groundwater flow into the main channel (mm); α = the base flow recession constant; and Δt = the calculation time step. Both α and δ are set as global parameters in EasyDHM method. In Eq. (15), the calculation of groundwater flow has already considered the effect of delay time, because the recharge water does not immediately form the base flow. Hence, in the EasyDHM method, groundwater flow in a subbasin does not participate in

Fig. 4. The flow-routing process of a given subbasin

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EasyDHM. This method, created by Van Griensven et al. in 2006, was successfully applied to the sensitivity analysis for the SWAT model (Neitsch et al. 2005). The LH-OAT algorithm combines the robustness of LH sampling algorithm (McKay et al. 1979) and the accuracy of the OAT [algorithm (Morris 1991)]. This method ensures accurate sampling throughout the entire possible parameter space based on the LH design, but also a robust and effective method of parameter sensitivity analysis by ascribing changes in each sampling value of the parameters. For LH-OAT sampling, the value space of each parameter is first stratified into m layers. In each stratum of a parameter, one value is sampled. Thus, each parameter can obtain m sampling points. The sampling points of all p parameters form the m sets of parameters. For one set of parameters, the value of each parameter changes once, whereas, the others remain the same based on the OAT method. This one set of parameters evolves into (p þ 1) sets. Therefore, the model will run mðp þ 1Þ times during the sensitivity analysis. The sensitivity analysis has two objective functions: the simulated average flow Qavg and the sum of squared residuals between the discharge value of a hydrologic station and its simulated discharge (SSQ). Using the average flow as the objective function describes the sensitivity of each parameter for the simulation results, whereas, using SSQ as the objective function helps determine the sensitivity of different parameters on simulation precision. The two objective functions are calculated according to the following equations:

longitudinal shape features (slope and equivalent length) are derived from the DEM. Parameter Estimation Functions


The default EasyDHM parameters may not produce a satisfactory simulation. Thus, adjustable parameters were included, and the parameter estimation module was developed. The sensitivity of the adjustable parameters will be first analyzed. Based on this analysis, the sensitive parameters can be optimized using an autocalibration algorithm. These parameters could be adjusted to their optimal values for better simulations. Adjustable Parameters The calculation processes are different for various runoff generation simulation methods. Thus, the parameters are also different. For the runoff generation method EasyDHM, 48 physical parameters (the number of soil layer is set to 2) and 10 global parameters were used. Eleven physical parameters were selected to adjust using correction coefficients (Table 1). The adjustable parameters are separated into four groups based on their functions in different processes. In Table 1, the canopy process is incorporated into the surface process. The parameters needed in two or more processes are categorized only in the major group. For instance, ItcmaxM and LaimaxM both affect the interception process and plant transpiration calculation in the soil process, but they are only listed in the surface category. Unlike runoff generation, the reach parameters for the flowrouting simulation mainly include the shape parameters for the reaches. Hence, in the three different methods for flow-routing simulation, the reach parameters are the same. Of the 15 reach parameters, 4 are adjusted by setting correction coefficients. The adjustable parameters are listed in Table 2.

Qavg ¼

n X

Qsim;i

n

ð18Þ

i¼1

SSQ ¼

n X

ðQsim;i − Qobs;i Þ2

ð19Þ

i¼1

Sensitivity Analysis

where Qsim;i = the simulated discharge during the ith period of a hydrologic station; and Qobs;i = the observed discharge during the ith period. The sensitivity of different parameters can be ranked by their relative sensitivity (RS), which represents the relative change in

To analyze the parameters that influence the simulation, a sensitivity analysis of these adjustable parameters should be conducted. The global parameter sensitivity analysis algorithm Latin Hypercube One Factor At a Time (LH-OAT) was introduced into

Table 1. Adjustable Parameters for Runoff-Generation Method EasyDHM Process Snow

Surface

Soil

Groundwater

Name

Meaning

Lower limit

Upper limit

Timp Snocovmx Sno50cov Smfmx Smfmn CN2 DepressM ItcmaxM LaimaxM ImpM UnitslopeM CondlyM (i) PorosityM Tdrain Solzcoe (i) RootdpthM FieldcapM Gwdelay Alphabf Dep_ImpM

Snow temperature lag factor Threshold depth of snow, above which there is 100% cover Fraction of SNOCOVMX that provides 50% cover Melt factor on June 21 Melt factor on December 21 Curve number at average moisture Correction coefficient of surface sink filling capacity Correction coefficient of maximum canopy interception capacity Correction coefficient of maximum leaf area index Correction coefficient of impermeable fraction Correction coefficient of slope of computational units Correction coefficient of saturated hydraulic Conductivity in the ith soil layer Correction coefficient of soil porosity Travel time for soil water percolation Depth fraction of the ith soil layer Correction coefficient of root depth Correction coefficient of soil field capacity Delay time of groundwater The base flow recession constant Correction coefficient of depth of impervious layer

0.5 0.8 0.3 4 1.4 1 0.5 0.5 0.5 0 0.1 0.8 0.5 10 0 0.5 0.5 0 0 0.4

1.5 1.2 0.7 8 4 100 3 3 3 2 10 100 1.5 50 1 1.5 1.2 200 1 0.83


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Pn ðQobs;i − Qsim;i Þ NS ¼ 1 − Pi¼1 n ðQ obs;i − Qobs Þ i¼1

Table 2. Adjustable Parameters for Flow-Routing Simulation Name

Meaning

CH_S2M CH_L2M CH_N2M CH_K2M


Lower limit

Correction coefficient of slope of main reaches Correction coefficient of length of main reaches Correction coefficient of Manning roughness of main reaches Correction coefficient of conductivity of riverbed bottom of main reaches

0.1 0.5

Upper limit 10 1.5

0.1

10

0.1

10

ð21Þ

The NS coefficient was used to assess the predictive power of the hydrologic model. The NS values ranged from −∞ to 1. The closer the value is to 1, the more accurate is the simulation effect of the model.

Case Study Site Description

the objective function [Eq. (1) or (2)] caused by the changes in the value of a certain parameter jMðe ; · · · ;e ·ð1þf Þ; · · · ;e Þ−Mðe ; · · · ;e ; · · · ;e Þj

RSi ¼

i i p 1 i p X ½Mðe1 ;1· · · ;ei ·ð1þf i Þ; · · · ;ep ÞþMðe1 ; · · · ;ei ; · · · ;ep Þ=2

jf i j

ð20Þ

where RSi = the RS of the parameter ei ; MðÞ = the objective function; and fi = the slight disturbance for parameter ei via the OAT method. The RS was summed up from all sample groups of the parameters via the LH method. Based on the RS values, the parameters were classified into four classes: extremely high sensitivity (RS greater than or equal to 1.0), high sensitivity (0.2 less than or equal to RS less than 1), medium sensitivity (0.05 less than or equal to RS less than 0.2), and low sensitivity (the remainder). Those parameters of high or extremely high sensitivity under the objective SSQ are selected for parameter optimization because accuracy is most important parameter for optimization. Furthermore, the sensitivity analysis of different parameters helps in determining the accuracy required for measuring parameters. Parameter Optimization In order to automatically implement the parameter optimization function of the EasyDHM model, we introduce the SCE-UA global parameter optimization algorithm, which is found to be robust, effective, and efficient. The SCE-UA algorithm, proposed by Duan et al. (1992), is a global parameter optimization algorithm integrating advantages of some controlled random searching methods like downhill simplex method (Nelder and Mead 1965) and biological competitive evolution (Holland 1975). The algorithm can uniformly, effectively, and quickly seek out the global optimum parameters, and is, thus, widely used in many continual hydrological models (Sorooshian et al. 1993). Its first step (Cycle 0) is to choose one initial population group of parameters from the possible parameter space randomly, then this initial group is divided into several complexes and every complex evolves separately by using the downhill simplex method. After some evolution, new groups are created by crossing over into different complexes, which allows new information to be obtained and optimum parameters to be discovered. The goal of parameter optimization is to seek out the parameters that improve the accuracy of the model simulation. Therefore, the chosen objective function could be SSQ as stated earlier. Generally, the Nash–Sutcliffe (NS) efficiency coefficient is introduced to estimate the precision of the simulation model (Duan et al. 1992) in EasyDHM

The Han River is the largest tributary in the middle reach of the Yangtze River in China. Its river basin covers an area of about 159,000 km2 and is located in the region of 30°10′N–34°20′N, 106°15′E–114°20′E. The main riverway was 1,577 km long. Up to 21 primary tributaries contribute to the Han River, each covering an area of over 1,000 km2 (Fig. 5). The Danjiangkou Reservoir along the Han River is the source of the Middle Route of the South-to-North Water Diversion Project in China. The runoff region of this reservoir is the whole upstream reach of the Han River. Therefore, the simulation of the hydrologic process of the upstream Han River is of great importance. This site is set as the study area for this paper to verify the performance and capabilities of EasyDHM. Data DEM Data For this research, the DEM data of the research region for the hydrologic analysis were obtained from the U.S. Geological Survey (USGS) HYDRO1K (website: http://edcdaac.usgs.gov/gtopo30/ hydro/) in the form of a 1-km × 1-km grid. DEM and the hydrological analysis module includes sink filling, flow direction generation, river network extraction, and the river network simulation were determined in the preprocessing module. Ensuring the consistency between the simulated river network and the actual river network is important. Thus, the initial DEM should first be modified and aligned in reference to the actual network. Land Use Data The land use data of the research region were obtained from the National County Land Coverage Vector Data, the product of the research, “Macro-Scale Survey and Dynamic Study of Natural Resources and Environment of China by Remote Sensing,” conducted by the Chinese Academy of Sciences (CAS). In the current research, the land use data from year 2000 with resolution at 1 km × 1 km are used. Soil Data The soil data from the research region were obtained from the soil database (SD) provided by the Nanjing Institute of Soil Science, CAS. At a grid resolution of 2 km × 2 km, the SD contains the percentages of soil particles with different sizes, including clay, sand grain, and silt in five soil layers at 0–10 cm, 10–20 cm, 20–30 cm, 30–70 cm, and more than 70 cm. According to the USGS soil triangle, the soil type in each grid was determined through the distribution of the three different soil particles. Hydrologic-Meteorologic Data The observed discharge data of all the 12 runoff stations and the observed precipitation data of the 37 rain gauges were collected from the China’s Ministry of Water Resources. The observed meteorologic elements including air temperature, short wave


J. Hydrol. Eng. 2014.19:44-59.


Fig. 5. Location of the study area—the upstream basin of Han River

radiation, relative humidity, and wind speed, as well as maximum and minimum daily temperature, were obtained from the weather stations within the research area. These data have the same time duration and time step as the hydrologic data. The meteorologic data were collected from the China Meteorological Administration. Division of Spatial Elements DEM, land use, soil type, and hydrologic-meteorologic data can be easily processed using MWEasyDHM, as well as the parameters of the whole simulation. Based on the locations of the hydrologic stations/reservoirs, 12 partitions are derived as shown in Fig. 6(a). The upstream-to-downstream spatial topology of these partitions is shown in Fig. 6(b). Fig. 7 shows the subbasins and internal units resulting from the model subdivision of the upstream Han River. The accumulation threshold value of river network was set to 500 km2 , which generated 118 subbasins (with 946 EEBs). To illustrate the effect of the three internal subbasin units, Fig. 7 also shows the two other kinds of internal units in the Number 52 subbasin. The upstream Han River is located in a mountainous

region. To simulate the runoff and conflux process in mountainous regions, the internal units of the EEBs were used in this study.

Results In this study, EasyDHM was used as the runoff generation method, and the Muskingum method was chosen for the flow-routing simulation. Up to 25 adjustable parameters were chosen for parameter estimation module (Tables 1 and 2). The calibration period was from January 1980 to December 1985 (1980 was preheat period), with a daily computational time step. The objective functions were also calculated in a daily time step, both in the sensitivity analysis and parameter optimization. The validation period was from January 1986 to December 1990. Parameter Sensitivity Analysis Results The results of the parameter sensitivity analysis of the catchment of the Xiangjiaping Station (the 5th partition) are shown in Table 3


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Fig. 6. Partitions and topology diagram: (a) scope of each partition; (b) spatial topology of all partitions

and Fig. 8. The low-sensitivity parameters were excluded. The RS of all parameters under the objective SSQ was higher than those under the objective average runoff. Therefore, the parameters under the objective function SSQ were more sensitive and should be analyzed more carefully. The parameters in the simulation of surface runoff and soil water were more sensitive than those in the groundwater simulation because of the relatively stable groundwater in this area. However, parameters for the snow process indicate low sensitivity. The results of the sensitivity analysis can be directly used as a selection reference for parameter optimization. To maximize the computational efficiency and effectiveness, only the extremely high and highly sensitive parameters (sensitive parameters) were optimized in this paper.

sub-basin river EEB

Legend of internal units EFB 10

1

HRU

Parameter Optimization Fig. 7. Division of upstream Han River basin and three different internal units in one subbasin

Based on the results of the sensitivity analysis of the 5th partition under the objective function SSQ, the first seven parameters in

Table 3. Result of Sensitivity Analysis at Xiangjiaping Station Objective: SSQ Parameter CN2 FieldCapM UnitSlopeM LaiMaxM PorosityM Dep_impM CondlyM(2) ItcmaxM CondlyM(1) CH_L2M CH_N2M Gwdelay Solzcoe(1) DepressM Sno50cov Alphabf CH_S2M ImpM

Objective: Average discharge

Rank

Relative sensitivity

Degree of sensitivity

Parameter

Rank


Degree of sensitivity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

2.010 1.040 0.851 0.489 0.380 0.315 0.302 0.174 0.119 0.104 0.065 0.051 0.036 0.029 0.020 0.008 0.006 0.001

Extremely high

FieldCapM CN2 LaiMaxM ItcmaxM UnitSlopeM PorosityM Solzcoe(1) Dep_impM CondlyM(2) Gwdelay Sno50cov DepressM CondlyM(1) Alphabf CH_N2M CH_L2M CH_S2M ImpM

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1.040 0.913 0.613 0.200 0.108 0.090 0.042 0.036 0.025 0.022 0.019 0.015 0.006 0.002 0.002 0.002 0.002 0.001

Extremely high High

High

Medium

Low

Medium

Low


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3.0 SSQ 2.0

Qavg

RS

A

B

C

D

E

1.0

Dep_impM

Alphabf

Gwdelay

Solzcoe(1)

CondlyM(2)

CondlyM(1)

PorosityM

UnitSlopeM

FieldCapM

DepressM

ImpM

ItcmaxM

LaiMaxM

CN2

Sno50cov

CH_N2M

CH_L2M

CH_S2M

Fig. 8. Relative sensitivity of various parameters of different objective functions: (a) parameters for flow routing; (b) parameters for snow process; (c) parameters for surface process; (d) parameters for soil process; (e) parameters for groundwater process

Preicipitaion

Observed discharge

With initial parameters

With optimal parameters

50 2000 100 1000

1984-12

1984-11

1984-10

1984-09

1984-08

1984-07

1984-06

1984-05

1984-04

1984-03

1984-02

0

1984-01

150

Precipitation (mm)

0

3000

Discharge (m3/s)


0.0

200

Fig. 9. Simulation results of the model at Xiangjiaping Station (comparing different parameters in 1984)

Table 3 were optimized. The other parameters retained their initial values. Function SSQ was also chosen as the objective function for the parameter optimization. The observed and simulated discharges in 1984, which is within the calibration period, at Xiangjiaping Station are shown in Fig. 9. The simulation results using the initial parameter values were acceptable when compared with the observation. However, the simulation can still be improved, especially for flood peak. After parameter optimization, the NS coefficient improved from 0.74 to 0.92, and the simulated flood peaks using the optimal parameters were also consistent with the observed flow. The optimal parameters for the 5th partition were directly used in the validation period. The NS coefficient of the simulation changed from 0.39 using the initial parameter values to 0.84 using the optimal parameter values. The simulation effect is shown in Fig. 10, which shows the simulated and observed discharges of Xiangjiaping Station in 1988. Thus, EasyDHM can be considered effective. Furthermore, its application is quite simple and convenient together with the MWEasyDHM tool. Validation by Other Methods For a hydrological model, the core objective is to simulate the discharge of rivers from precipitation within river basins. EasyDHM

has the same goal and offers different runoff generation and flowrouting methods for wider applications. Most of these methods are introduced from other mature and open-source hydrologic models. Our team developed only the runoff generation method EasyDHM. The EasyDHM method was validated using an observed discharge series. We also validated it by comparing its simulation results with those of other mature methods in EasyDHM. The observed and simulated discharges via different runoff generation methods at Xiangjiaping Station in 1984 are shown in Fig. 11. In these simulations, the same flow-routing method Muskingum was used, and both simulations used optimal parameter values. The simulated EasyDHM discharge process in 1984 is quite similar to that by the WetSpa method. However, differences were also observed between them. The EasyDHM simulation of large floods was slightly better than that by WetSpa. For small floods, the WetSpa method was better. In general, the EasyDHM method is effective upon validation via the WetSpa method. Thus, this runoff generation method and the entire EasyDHM are effective for hydrologic simulation and could contribute to this research field. Different DHMs derive different simulation results. EasyDHM offers different simulation results under different simulation methods. Thus, users can choose different simulation methods for different basins. Using the same method, the different


J. Hydrol. Eng. 2014.19:44-59.

Observed discharge

Preicipitaion

With optimal parameters 0

Discharge (m3/s)

2000

50

1500 100 1000 150

1988-12

1988-11

1988-10

1988-09

1988-08

1988-07

1988-06

1988-05

1988-04

1988-03

1988-02

1988-01

0

200

Fig. 10. Simulation results of the model at Xiangjiaping Station (comparing different parameters in 1988)

5000

4000

Discharge (m3/s)

Observed

WetSpa

EasyDHM

3000

2000

1000

198412

198411

198410

198409

198408

198407

198406

198405

198404

198403

198402

0 198401


500

Precipitation (mm)

2500

Fig. 11. Simulation results of the model at Xiangjiaping Station (comparing different methods in 1984)

parameters can also produce different simulation results. Thus, different parameters can also reflect spatial variability and even temporal variability.

Discussion For a DHM, EasyDHM is capable of interpreting and depicting spatial differences. Instead of using different simulation methods for different partitions, the same methods with different parameter values were used. The sensitivities of all parameters in all partitions are listed in Table 4. The grey cells indicate that these parameters are sensitive for those partitions based on their relative sensitivities. The sensitivity of the parameters differs with partitions, which shows the necessity of adjusting the parameters independently for each partition. In Table 4, the sensitivities of the different groups of parameters show almost the same pattern. The parameters for the surface process and the soil process were generally highly sensitive. The parameters for groundwater processes had low sensitivity. The snow parameters were insensitive in the whole research area. As analyzed in the 5th partition, these phenomena were probably caused by the spatial location and climate conditions of the

upstream basin of the Han River, which is warm and has a stable groundwater table. The parameter sensitivity for the flow-routing process was quite variable. In the downstream partitions, these reach parameters were highly sensitive. The 9th partition is a downstream partition, and its flow-routing parameters have low sensitivity (Fig. 6). The main reach of the 9th partition (catchment of Jingziguan Station) is relatively short, considering its shape. The upstream partition [catchment of Danfeng (II) Station] is smaller than that of the 9th partition, resulting in a less-dominant hydrologic process than the runoff generation process. For the other downstream partitions, the flow-routing processes were dominant for the formation of the discharge through the outlet, considering their shapes and upstream partitions. The reach parameters of the downstream partitions were the most sensitive parameters, particularly the 4th and 12th partitions. The comparison of the NS coefficients in different partitions before and after parameter optimization was shown in Table 5. Parameter optimization can greatly improve the NS coefficients in most partitions. The accuracy of the hydrological simulation of EasyDHM during the verification period is as precise as that in the calibration period after the parameter optimization.


J. Hydrol. Eng. 2014.19:44-59.

Table 4. Ranks of Each Parameter’s Sensitivity in all Partitions (Objective Function: SSQ With a Daily Time Step) Partitions

1

2

3

4

5

6

7

8

9

10

11

12

Upstream partitions For flow routing

— 26 16 14 15 10 13 8 2 26 1 4 7 9 5 12 26 26 3 6 11 26 26 26 26 26

— 26 12 16 26 7 14 4 2 17 1 3 5 10 11 8 26 26 6 9 13 15 26 26 26 26

1,2 26 4 11 14 7 15 6 1 19 2 3 5 8 13 12 26 26 10 9 16 18 17 26 20 26

3 26 1 2 3 14 17 13 4 19 10 5 9 11 6 15 26 26 12 16 7 8 26 26 18 26

— 21 10 11 17 8 14 4 1 18 2 3 5 13 7 9 26 20 6 12 16 15 26 19 26 26

4,5 26 3 4 9 8 16 5 1 26 2 7 6 11 10 14 26 26 12 13 15 17 26 26 26 26

— 26 4 10 12 6 15 8 1 17 2 3 9 7 13 14 26 26 5 11 16 19 26 18 20 26

— 26 17 15 16 8 13 3 1 26 2 4 7 10 9 12 26 26 5 6 11 14 18 19 26 26

8 26 14 16 15 6 12 4 1 26 2 3 5 9 10 11 26 26 7 8 13 17 26 26 26 26

— 26 14 16 26 4 13 5 2 15 1 3 8 9 10 11 26 26 7 6 12 26 26 26 26 26

— 26 14 15 16 8 13 4 2 26 1 3 6 9 11 10 26 26 7 5 12 17 26 26 26 26

6,7,9, 10,11 26 1 3 7 8 15 10 2 17 4 6 5 11 13 14 26 26 12 9 16 26 26 26 26 26


For surface process

For soil process

For groundwater process

For snow process

CH_K2M CH_L2M CH_N2M CH_S2M ItcmaxM DepressM LaimaxM CN2 ImpM FieldcapM UnitslopeM PorosityM Solzcoe(1) CondlyM(2) CondlyM(1) Tdrain RootdpthM Dep_ImpM Gwdelay Alphabf Sno50cov Snocovmx Timp Smfmn Smfmx

Note: Sensitivity rank number of 26 means the calculated relative sensitivity of this parameter is zero.

Table 5. Comparison of NS Coefficients Before and After Parameter Optimization NS coefficient (calibration period) Name of control stations Wuhou Town Shengxian Shiquan (II) Ankang Xiangjiaping Baihe Huanglongtan Danfeng (II) Jingziguan Xiping Xixia Danjiangkou

NS coefficient (verification period)

Next downstream control station

Initial parameters

Optimal parameters

Initial parameters

Optimal parameters

Shiquan (II) Shiquan (II) Ankang Baihe Baihe Danjiangkou Danjiangkou Jingziguan Danjiangkou Danjiangkou Danjiangkou Huangzhuang

0.4456 0.8454 0.7385 0.9180 0.7420 0.977 0.3838 0.6072 0.7644 0.5703 0.6868 0.9477

0.7075 0.9521 0.9117 — 0.9233 — 0.9015 0.9457 0.9059 0.9082 0.879 —

0.2819 0.4518 0.5374 0.9010 0.3869 0.9841 0.3576 0.3601 0.7152 — 0.6233 0.9783

0.6094 0.8807 0.6078 — 0.8390 — 0.7553 0.7665 0.7164 — 0.8332 —

The NS values for some hydrologic stations in Table 5, such as the Ankang Station, the Baihe Station, and the Danjiangkou Reservoir, exceeded 0.9 using the initial values for the adjusted parameters. Thus, optimizing the parameter in these partitions is unnecessary. The three stations are located in downstream partitions (refer to the topology of the hydrologic stations in Fig. 6). The discharge of the upstream hydrologic stations flows into the downstream hydrologic stations toward downstream partitions through river channels. Thus, the discharge of a downstream station comes from both the runoff from the linked upstream stations and the runoff generated in its own partition. The discharge of the upstream stations may contribute a large proportion. The Shiquan (II) and Jingziguan Stations also control downstream partitions. These partitions have low NS coefficients under

Table 6. Result of Sensitivity Analysis at Xiangjiaping Station Objective: SSQ Parameter ConductM Sno50cov CN2 Sftmp UnitSlopeM Smfmn Smtmp Timp Snocovmx PorosityM


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Objective: Average discharge

Rank


Parameter

Rank


1 2 3 4 5 6 7 8 9 10

0.326 0.118 0.072 0.022 0.016 0.008 0.005 0.005 0.004 0.004

ConductM Sno50cov CN2 UnitSlopeM Sftmp Smtmp Timp Smfmn Snocovmx PorosityM

1 2 3 4 5 6 7 8 9 10

0.058 0.015 0.014 0.005 0.004 0.003 0.003 0.001 0.001 0.001

Preicipitaion

Monthly optimal parameters

Daily optimal parameters

50 2000 100 1000 150

1984-12

1984-11

1984-10

1984-09

1984-08

1984-07

1984-06

1984-05

1984-04

1984-03

200 1984-02

0

Precipitation (mm)

0

1984-01

Fig. 12. Daily simulation results of Xiangjiaping Station (comparing different methods in 1984)

the initial parameter values; thus, they require parameter optimization. The NS coefficients can be above 0.9 after parameter optimization. Analyses of the topology of the hydrologic stations and areas of the upstream partitions show that the upstream partitions of Shiquan (II) and Jingziguan Stations cover a relatively small catchment. Therefore, larger upstream partitions greatly influence the simulated discharge of downstream stations, which imply that the parameter optimizations of downstream partitions are not required. When smaller upstream partition has less influence, the downstream partitions still require parameter optimization. In some practical applications, monthly average discharges are the simulation objective. The EasyDHM model can also be set to a monthly time step or simulated in a daily time step with a monthly time step output. The objective functions should also be calculated monthly. Using the 5th partition as an example, the sensitivity analysis was operated within the same calibration period. The simulation time step was maintained at 1 day and the analysis and output time step was changed to 1 month. The resulting relative sensitivities (greater than 0) of the adjustable parameters were shown in Table 6. Interestingly, the sensitivity of several parameters to the new objective functions decreased. Given that the simulation precision of the total monthly amounts of water were set as the objective, these parameters strongly controlling the daily variation in the discharge process were no longer significant. These parameters included those for flow routing and groundwater delay. The parameters for snow simulation became slightly more sensitive. Although nearly all parameters had low sensitivity, the five most sensitive parameters in Table 6 were chosen for parameter optimization in a monthly time step. The daily and monthly discharge processes of the Xiangjiaping Station are shown in Figs. 12 and 13 (the values used were from the year 1984). The daily simulation results from the optimal parameters under the objective function calculated from the monthly step were unsatisfactory, similar to the simulation results using the initial parameters in Fig. 9. This result is reasonable given that most of the sensitive parameters under the daily objective function were not optimized. However, the optimization under the monthly objective function was better than the monthly results, especially during the cold months when the discharge rate was relatively low. The snow parameters were more sensitive and were, thus, optimized, which improves the simulation of the snow process. The different behaviors of the sensitivity analysis and optimization under the different objective functions during different time

1000

Discharge (m3 /s)


Discharge (m3/s)

3000

Observed

800

Daily optimal parameters

600

Monthly optimal parameters

400 200 0 1

2

3

4

5

6

7

8

9

10

11

12

Fig. 13. Monthly simulation results of Xiangjiaping Station (comparing different methods in 1984)

steps may be caused by the seasonal validation during discharge because the discharges during flood events and dry months vary greatly. If SSQ was used as the objective function, the discharge during dry months represents only a very small proportion. These differences decreased when calculated using a monthly time step. Other functions that also reduce the differences between discharges were also set as objective functions such as in the following Eqs. (22)–(24): n X

ðlog Qsim;i − log Qobs;i Þ2

ð22Þ

n pffiffiffiffiffiffiffiffiffiffiffi X pffiffiffiffiffiffiffiffiffiffiffi 2 ¼ Qsim;i − Qobs;i

ð23Þ

OFlog ¼

i¼1

OFsqrt

i¼1

OFlog &sqrt ¼

n X

log

pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi Qsim;i − log Qobs;i

2

ð24Þ

i¼1

These objective functions are all transformations of SSQ. Different objective functions produce different sets of optimal parameters. Thus, in practical applications, users should choose objective functions based on the different patterns of the discharge processes. Parameters can reflect the differences among locations and time scales. Hence, the hydrologic simulations of various regions using various time steps perform quite well using EasyDHM. Although the parameters may lose their physical characteristics in this way, using parameters to represent the different simulation conditions


J. Hydrol. Eng. 2014.19:44-59.

rather than using different simulation methods is obviously more effective.


Conclusion Our research group developed independently the EasyDHM model, which integrates some of the newest technologies in hydrology and computer. The model has three main characteristics. (1) Easy manipulation—EasyDHM has a highly integrated system called MWEasyDHM, which provides general users with a friendly and convenient simulation environment. (2) Efficiency—the unique spatial structure of EasyDHM through the division of the partition/ subbasin/internal unit greatly improves the computational efficiency of model simulation and parameter calibration. Thus, this model is applicable to different basin scales (small, large, or superlarge watersheds) because the users can control the generated networks and basic spatial elements. (3) Generalization—EasyDHM is suitable for different regions, whether warm or cold and wet or dry, using different simulation methods or different parameters. In this paper, the hydrologic simulation and parameter calibration of the upstream basin of the Han River demonstrated the characteristics and effectiveness of EasyDHM. The parameter sensitivity analysis and parameter optimization showed that parameter sensitivity varies with spatial distribution. After parameter optimization, the precision and efficiency of the simulation were greatly improved. Moreover, larger upstream partitions greatly influence the discharge of downstream stations, thereby reducing the necessity of optimization on the downstream partition. Smaller upstream partitions have less influence and downstream partitions likely require parameter optimization. This phenomenon could be universal for other DHMs. The parameter estimation in this paper could also be applicable to other DHMs or other EasyDHM applications. The successful development of EasyDHM lays the foundation for extensive applications of DHMs in actual water resource management and flood forecast projects in China.

Acknowledgments This paper was jointly supported by funds from Hydrological Simulation & Regulation of Watersheds (Number 51021066) of the Funds for Creative Research Groups of China; Ministry of Water Resources’ Special Funds for Scientific Research on Public Causes (201001024, 201101026, and 201101024); and the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research (Grant Number IWHRSKL-201103).

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