Si-min QU*, Han LIU Yan-ping CUI Peng SHI Wei-min BAO Zhong-bo YU

1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, P. R. China

2. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China

3. Department of Forest Engineering, Resources and Management, Oregon State University, Corvallis, OR 97331, USA

Test of newly developed conceptual hydrological model for simulation of rain-on-snow events in forested watershed

Si-min QU*1,2,3, Han LIU1,2, Yan-ping CUI1,2, Peng SHI1,2, Wei-min BAO1,2, Zhong-bo YU1,2

1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, P. R. China

2. College of Hydrology and Water Resources, Hohai University, Nanjing 210098, P. R. China

3. Department of Forest Engineering, Resources and Management, Oregon State University, Corvallis, OR 97331, USA

A conceptual hydrological model that links the Xin’anjiang hydrological model and a physically based snow energy and mass balance model, described as the XINSNOBAL model, was developed in this study for simulating rain-on-snow events that commonly occur in the Pacific Northwest of the United States. The resultant model was applied to the Lookout Creek Watershed in the H. J. Andrews Experimental Forest in the western Cascade Mountains of Oregon, and its ability to simulate streamflow was evaluated. The simulation was conducted at 24-hour and one-hour time scales for the period of 1996 to 2005. The results indicated that runoff and peak discharge could be underestimated if snowpack accumulation and snowmelt under rain-on-snow conditions were not taken into account. The average deterministic coefficient of the hourly model in streamflow simulation in the calibration stage was 0.837, which was significantly improved over the value of 0.762 when the Xin’anjiang model was used alone. Good simulation performance of the XINSNOBAL model in the WS10 catchment, using the calibrated parameter of the Lookout Creek Watershed for proxy-basin testing, demonstrates that transplanting model parameters between similar watersheds can provide a useful tool for discharge forecasting in ungauged basins.

Xin’anjiang model; snow energy and mass balance model; rain-on-snow event; H. J. Andrews Experimental Forest

1 Introduction

In the Pacific Northwest (P NW) of the United States, rain-on-snow (ROS) events are a common driver of flooding. Harr (1981) has found that many of the highest peak flows of the Willamette River at Salem, Oregon were associated with ROS events. The importance of theseevents to peak discharges and flooding has been highlighted through many snow hydrology studies in the PNW (Harr 1981; Berris and Harr 1987; Marks et al. 1998). Experimental analysis of ROS events in the PNW (Berris and Harr 1987) and more recent model analysis of the same dataset (van Heesjwick et al. 1996) reveal that rainfall rates alone have little effect on snowmelt, and that snowmelt is more sensitive to wind speed. There have been several experimental studies focusing on energy balance (EB) dynamics of melting snow in the PNW. For example, Marks et al. (1998) reported that 60% to 90% of the snowmelt was driven by turbulent energy changes during one of the largest recorded ROS events in the region, which occurred in February of 1996. More recently, Mazurkiewicz et al. (2008) used a physically based snow energy and mass balance (SNOBAL) model to simulate snowpack accumulation and melt, addressing questions concerning the relative importance of various energy balance components at different time scales in different topographic settings. They reported the relative importance of EB components in causing melt changes at different time scales. At the event scale, net radiation was a substantial contributor to snowmelt.

In spite of these detailed studies, there has been little work on quantifying the difference between precipitation estimates with and without consideration of snowmelt. Accurate rainfall estimation from observations is an essential prerequisite for successful hydrological modeling, e.g., short-term flood forecasting. Meanwhile, the effects of ROS events on the simulation efficiency of hydrological models are poorly understood.

In this study, a conceptual hydrological model, the XINSNOBAL model, which links the Xin’anjiang model with the SNOBAL model, was developed and used to investigate the influence of snowmelt on runoff and peak flow of flood events. The main points explored in this paper are (1) testing the application of the XINSNOBAL model in the H. J. Andrews (HJA) Experimental Forest; (2) quantifying the difference between the simulation results with and without consideration of snowmelt; and (3) evaluating the efficiency of the model in the simulation of flood events in the WS10 catchment, with its parameters calibrated by use of the hydrological data in the Lookout Creek Watershed.

2 Methods

2.1 Xin’anjiang model

The Xin’anjiang model was developed on the basis of the analysis of hydrological data from the Xin’anjiang Reservoir located in Zhejiang Province, China. The model can be used for flood forecasting and for runoff and streamflow simulation, and has been improved incrementally since it was proposed in 1973 (Li et al. 1998, 2006, 2007; Wang et al. 2007; Wang and Zhou 1998). It is the most widely used model for forecasting flood disasters in China, and has been applied extensively in most humid regions of China, which are situated in the south and east of the country, where the climate is warm with little snow. The model has been applied in other ways, such as water resources estimation, design flood and field drainage calculation, water project programming, and hydrological station planning. However, very fewstudies have actually focused on its application to the simulation of ROS flood events in the PNW.

According to the model structure, runoff was originally separated into two components using the concept of the final constant infiltration rate. However, in 1980, the model was modified to represent three components: surface runoff, subsurface flow, and groundwater flow. The main feature of the model is the concept of runoff formation based on the depletion of storage, which means that runoff is not produced until the soil moisture content of the aeration zone reaches the field capacity, and thereafter runoff equals the rainfall excess without further loss. The validity of the model is limited to humid and semi- humid regions.

In the Xin’anjiang model, the basin is divided into a set of sub-basins for consideration of spatial heterogeneity of precipitation and underlying surfaces, and the Thiessen polygon method was used in this study. The simulation of the outflow from each sub-basin has four major components: evapotranspiration, runoff generation, runoff separation, and flow concentration. The flow chart of the model for calculating the outflow of each sub-basin and the functions, methods, and corresponding parameters of the model in different layers can be found in Zhao (1992). The inputs of the model are rainfall (P) and measured pan evaporation (EM), and the outputs are outlet discharge (Q) and actual evapotranspiration (E).

2.2 SNOBAL model

The SNOBAL model is a physically based snow energy and mass balance model developed by Marks and Dozier (1992) and described in detail by Marks et al. (1999). The model has been applied to different areas including Central Canada (Link and Marks 1999), Turkey (Sensoy et al. 2006), and the PNW (Marks et al. 1998; van Heesjwick et al. 1996; Mazurkiewicz et al. 2008). The required forcing data for the model are net solar radiation, incoming thermal radiation, air temperature, precipitation, wind speed, vapor pressure, and ground temperature. These forcing data were processed at three-hour intervals for model runs in this study.

2.3 XINSNOBAL model

The XINSNOBAL model is a conceptual hydrological system linking the Xin’anjiang hydrological model and the SNOBAL model. First, net solar radiation, incoming thermal radiation, air temperature, precipitation, wind speed, vapor pressure, and ground temperature are used as inputs of the SNOBAL model to calculate the equivalent rainfall from snowmelt, described asP, at three-hour intervals. Second,Pcalculated at three-hour intervals is distributed equally across one-hour intervals. Finally, the averagePandEMat one-hour intervals are used as the inputs of the Xin’anjiang model to simulate the discharge. The objective of the XINSNOBAL model is to simulate large ROS flood events. Also, the model is used as a learning tool to understand how snowpack accumulation and snowmelt influence the runoff and peak discharge under ROS conditions.

2.4 Multi-phase parameter calibration and validation

Traditional calibration methods of hydrological models with some particular structures have been aimed at finding an optimal set of parameter values to represent a watershed area. This produces, to some extent, uncertainty in the calibration process if there are many parameters in the model. As for the Xin’anjiang model, there are 15 parameters, as shown in Table 1. For the insensitive parameters (B,C,WUM,WLM, andEX), some empirical values were assigned (Zhao 1992). However, the sensitive parameters (K,WM,SM,KI,KG,CS,CI,CG,KE, andXE) need to be calibrated according to the calibration criteria. To reduce the uncertainty in the process of parameter calibration, a multi-phase parameter calibration method was developed in this study. According to the model calculation, all parameters in the model are separated into four phases: the evapotranspiration phase, runoff generation phase, water-source separation phase, and concentration phase. The role of the parameters in the first two phases is to assure a water balance between the volumes of the modeled and observed flows, which are more sensitive at the resolution of a 24-hour interval than at a one-hour interval. Therefore, a daily model (with a time interval of 24 hours) was developed based on the calibration of the model parameters in the evaportranspiration and runoff generation phases with the daily rainfall data, and then an hourly model (with a time interval of one hour) was developed based on the calibration of the model parameters in water-source separation and concentration phases with hourly rainfall data (Zhao 1992). The further adjustment of the parameters in the latter two phases provides for better performance of the Xin’anjiang model.

Table 1Parameters of Xin’anjiang model

The multi-phase parameter calibration method developed in this study has many advantages. It is relatively simple and can reduce the uncertainty in the process of parameter calibration. The introduction of the concept of multi-phase parameter calibration can reducethe dimensions of parameters, which means that different time-scale models and different objective functions are used to calibrate different parameters. This dimension reduction is particularly useful in guaranteeing reasonably unique parameter values.

Three goodness-of-fit measures were employed to assess the performance of the model: dR, dQmax, and DC.

dRis defined as

whereRCandROare the calculated and observed runoffs over an event, respectively.

dQmaxis defined as

where QCmaxand QOmaxare the calculated and observed peak discharges, respectively.

The deterministic coefficient (DC) is computed over n observations as

Furthermore, the percent bias (PBIAS), the deterministic coefficient, and the ratio of the root-mean-square error (ERMS) to standard deviation of observed data (DS), described asRSR, were employed as goodness-of-fit criteria for model calibration and validation (Santhi et al. 2001; Moriasi et al. 2007), which are defined as follows:

3 Study site and data

The developed XINSNOBAL model was applied to the Lookout Creek Watershed and the WS10 catchement in the HJA Experimental Forest. The forest is located on the western slope of the Cascade Mountains of Oregon, and encompasses the 62-km2drainage area of Lookout Creek, a tributary of the Blue River in the McKenzie River Basin. The locations ofthe study watershed and main gauging stations are shown in Fig. 1. The watershed spans elevations from 800 to 2 000 m and has slopes from 60% to 100%. It has been described in detail in previous publications (Jones and Grant 1996; Tague and Band 2001; Wemple and Jones 2003). The mean annual precipitation ranges from 1 800 mm at lower elevations to 3 000 mm at higher elevations. The Mediterranean climate produces approximately 80% of the annual precipitation in the months between November and March, whereas summers are typically warm and dry. Above an elevation of 1 000 m, winter precipitation falls mainly as snow. The transient snow zone lies roughly at the elevation between 500 and 1 000 m. At these elevations, snow and rain are frequent in the winter months, and ROS events commonly occur. The study area is underlain by Tertiary and Quaternary volcanic rocks, primarily andesites and basalts, with some glacial deposits. Over 75% of the watershed area is underlain by highly weathered and deeply dissected volcanics.

Fig. 1Lookout Creek Watershed and WS10 catchment in HJA Experimental Forest

Hydrological data from five permanent rain gauges from lower to higher elevations of the Lookout Creek Watershed were used. The rain gauges included PRIMET, H15MET, VANMET, CENMET, and UPLMET, with weighting coefficients of 0.217, 0.210, 0.078, 0.313, and 0.182, respectively (Mazurkiewicz et al. 2008). There are an evaporation station and a discharge station in the watershed. At each rain gauge, there are observations of air temperature, relative humidity, precipitation, incoming solar radiation, wind speed, ground temperature, and snow water equivalent. All the stations in the watershed have nearly complete records for the water years from 1996 to 2005 (for example, the water year of 1996 was from 8:00 a.m. on October 1, 1995 to 8:00 a.m. on September 30, 1996), providing a unique dataset for the XINSNOBAL model as it is applied to discharge simulation. Data for 20 flood events between 1995 and 2004 were used, comprising continuous hourly rainfall, evaporation, discharge, and other meteorological elements measured at the Lookout Creek Watershed. The data were split into two independent subsets for model calibration and validation. For the daily model, the data from 1996 to 2003 were used for parameter calibration, and the data from 2004 and 2005were used to model validation. For the hourly model, data of 15 floods from 1995 to 1999 were used for calibration, and data of five floods from 2002 to 2004 were used for model validation.

For proxy-basin testing, the hourly model, with the calibrated parameters of the Lookout Creek Watershed, was used to simulate the discharge of the WS10 catchment. The WS10 catchment, with an area of 0.101 km2, is very close to the Lookout Creek Watershed. The location of the catchment is shown in Fig. 1. The catchment has similar physical, geographical, and geological characteristics to the Lookout Creek Watershed. There is no rain gauge in the WS10 catchment. Some statistical analysis shows that the rainfall data at the PRIMET station correlate with the data collected in the WS10 catchment (Mazurkiewicz et al. 2008). Therefore, the rainfall data at the PRIMET gauging station were used to simulate the discharge of the WS10 catchment. Data of 11 flood events from 1996 to 2003 in the WS10 catchment were used to examine the simulation results.

4 Results and discussion

4.1 Lookout Creek Watershed simulation

Multi-phase parameter calibration was used to reduce the uncertainty in the process of parameter calibration. The objective of the daily model was to determine the evapotranspiration and runoff generation parameters. The calibrated parameters of the daily model for the Lookout Creek Watershed are listed in Table 2. The water-source separation and concentration parameters in the daily model were used as the initial values of the hourly model. In the hourly model, those parameters need further modification. The final results of calibrated parameters of the hourly model are also shown in Table 2.

Table 2Parameters of daily and hourly Xin’anjiang models of Lookout Creek Watershed

Table 3Simulation results of daily model in calibration stage

Table 4Simulation results of daily model in validation stage

The performance of the calibrated hourly model for the Lookout Creek Watershed is given for the cases with and without consideration of snowmelt in Tables 5 and 6, respectively. The validation results for both cases are shown in Tables 7 and 8, respectively.

Table 5Calibration results of hourly model with consideration of snowmelt

Table 6Calibration results of hourly model without consideration of snowmelt

Table 7Validation results of hourly model with consideration of snowmelt

Table 8Validation results of hourly model without consideration of snowmelt

Fig. 2Modeled and measured discharges in Lookout Creek Watershed in calibration stage

Fig. 3Modeled and measured discharges of Flood 020305 in Lookout Creek Watershed in validation stage

The Xin’anjiang model uses observed precipitation data as the inputs, and it does not induce large errors in those flood events without snow. However, in the situations when ROS events occurred, the observed precipitation was usually underestimated. Using the SNOBAL model to simulate large ROS flood events can improve precipitation estimation significantly. The statistics of the average rainfall, shown in Tables 5 through 8, reveal that using the SNOBAL model increases the precipitation from 421.3 mm to 449.8 mm in the calibration stage, and from 402.5 mm to 435.5 mm in the validation stage.

From Tables 5 through 8 and Figs. 2 and 3, it can be seen that the simulation performance of the XINSNOBAL model with consideration of snowmelt is better than that of theXin’anjiang model, which does not take snowmelt into account. In the calibration stage, the average deterministic coefficient of the XINSNOBAL model is 0.837. However, that of the Xin’anjiang model is only 0.762. Furthermore, the relative errors of the runoff and peak flow of the XINSNOBAL model are less than that of the Xin’anjiang model. The same results can be obtained in the validation stage.

From a hydrological perspective, the performances of different hydrological models are compared by using precipitation data as their inputs and then assessing the simulated discharges of different models against observations. It can be seen that the XINSNOBAL model performed better when the precipitation data with consideration of snowmelt were used as inputs, while the peak discharge of ROS flood events was usually underestimated when snowmelt was not taken into account. This supports the view that, in the PNW of the United States, the XINSNOBAL model often provides a reliable and robust flow simulation.

From Tables 9, we can also see that the daily and hourly models both show good performance in the Lookout Creek Watershed.

Table 9Performance of daily and hourly models

4.2 Proxy-basin testing in WS10 catchment

5 Conclusions

A conceptual hydrological model that links the Xin’anjiang hydrological model with the SNOBAL model was developed in this study. The resultant model was applied to the Lookout Creek Watershed in the HJA Experimental Forest in the western Cascade Mountains of Oregon, and its ability to simulate streamflow was evaluated.

Table 10Simulation results of hourly model in WS10 catchment

The simulation was conducted at 24-hour and one-hour time scales for the period from 1996 to 2005. The multi-phase parameter calibration method was adopted to reduce the uncertainty of parameter calibration. Results indicated that the runoff and peak discharge could be underestimated if snowpack accumulation and snowmelt under ROS conditions were not taken into account. The average deterministic coefficient of the hourly model in streamflow simulation in the calibration stage was 0.837, which was significantly improved over that of 0.762 when the Xin’anjiang model was used alone.

Good simulation performance of the XINSNOBAL model in the WS10 catchment, with the calibrated parameters of the Lookout Creek Watershed, shows that there is a definite link between model parameters, geographical characteristics, and underlying conditions of the two watersheds. The benefit of transplanting parameters between similar watersheds is very appealing in the flood prediction of ungauged basins.

Acknowledgements

We thank Jeffrey J. McDonnell for his constructive ideas and suggestions and Adam Mazurkiewicz for his support for the data and the SNOBAL model.

Berris, S. N., and Harr, R. D. 1987. Comparative snow accumulation and melt during rainfall in forested and clear-cut plots in the Western Cascades of Oregon.Water Resources Research, 23(1), 135-142. [doi:10.1029/WR023i001p00135]

Harr, R. D. 1981. Some characteristics and consequences of snowmelt during rainfall in western Oregon.Journal of Hydrology, 53(3-4), 277-304. [doi:10.1016/0022-1694(81)90006-8]

Jones, J. A., and Grant, G. E. 1996. Peak flow responses to clear-cutting and roads in small and large basins, western Cascades, Oregon.Water Resources Research, 32(4), 959-974. [doi:10.1029/95WR03493]

Li, Z. J., Kong, X. G., and Zhang, C. W. 1998. Improving Xin’anjiang model.Journal of China Hydrology, 18(4), 19-23. (in Chinese)

Li, Z. J., Zhang, K., and Yao, C. 2006. Comparison of distributed geological models based on GIS technology and DEM. Journal of Hydraulic Engineering, 37(8), 1022-1028. (in Chinese)

Li, Z. J., Yao, C., and Wang, Z. H. 2007. Development and application of grid-based Xin’anjiang model. Journal of Hohai University (Natural Science Edition), 35(2), 131-134. (in Chinese)

Link, T., and Marks, D. 1999. Distributed simulating of snowcover mass and energy balance in the Boreal Forest. Hydrological Processes, 13(14-15), 2439-2452. [doi:10.1002/(SICI)1099-1085(199910)13:14/ 15＜2439::AID-HYP866＞3.0.CO;2-1]

Marks, D., and Dozier, J. 1992. Climatic and energy exchanges at the snow surface in the alphine region of the Sierra Nevada, 2: Snow cover energy balance. Water Resources Research, 28(11), 3043-3054. [doi:10. 1029/92WR01483]

Marks, D., Kimball, J., Tingey, D., and Link, T. 1998. The sensitivity of snowmelt processes to climate conditions and forest cover during rain-on-snow: A case study of the 1996 Pacific Northwest flood. Hydrological Processes, 12(10-11), 1569-1587. [doi:10.1002/(SICI)1099-1085(199808/09)12:10/11＜1569::AID-HYP682＞3.0.CO;2-L]

Marks, D., Domingo, J., and Frew, J. 1999. Software Tools for Hydro-climatic Modeling and Analysis: Image Processing Workbench, ARS-USGS Version 2. Boise: Northwest Watershed Research Center, Agricultural Research Service. http://cirque.nwrc.ars.usda.gov/～ipw.

Mazurkiewicz, A. B., Callery, D. G., and McDonnell, J. J. 2008. Assessing the controls of the snow energy balance and water available for runoff in a rain-on-snow environment. Journal of Hydrology, 354(1), 1-14. [doi:10.1016/j.jhydrol.2007.12.027]

Moriasi, D. N., Arnold, J. G., van Liew, M. U., Binger, R. L., Harmel, R. D., and Veith, T. 2007. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Transactions of the ASABE, 50(3), 885-900.

Santhi, C., Arnold, J. G., Williams, J. R., Dugas, W. A., Srinivasn, R., and Hauck, L. M. 2001. Validation of the SWAT model on a large river basin with point and nonpoint sources. Journal of the American Water Resources Association, 37(5), 1169-1188.

Sensoy, A., Sorman, A. A., Tekeli, A. E., Sorman, A. U., and Garen, D. C. 2006. Point-scale energy and mass balance snowpack simulations in the upper Karasu Basin, Turkey. Hydrological Processes, 20(4), 899-922. [doi:10.1002/hyp.6120]

Tague, C. L., and Band, L. E. 2001. Evaluating explicit and implicit routing for watershed hydro-ecological models of forest hydrology at the small catchment scale. Hydrological Processes, 15(8), 1415-1439. [doi:10.1002/hyp.171]

van Heesjwick, M., Kimball, J. S., and Marks, D. 1996. Simulation of Water Available for Runoff in Clearcut Forest Openings During Rain-on-snow Events in the Western Cascade Range of Oregon and Washington. Tacoma: U.S. Geological Survey.

Wang, G. S., and Zhou, J. H. 1998. Improvement on Xin’anjiang model. Hydrology, 43(s1), 23-27. (in Chinese)

Wang, L. L., Li, Z. J., and Bao, H. J. 2007. Application of hydrological models based on DEM in the Yihe Basin. Journal of Hydraulic Engineering, 37(s1), 417-422. (in Chinese)

Wemple, B. C., and Jones, J. A. 2003. Runoff production on forest roads in a steep, mountain catchment. Water Resources Research, 39(8), 1220-1236. [doi:10.1029/2002WR001744]

Zhao, R. J. 1992. The Xin’anjiang model applied in China. Journal of Hydrology, 135(1-4), 371-381. [doi: 10.1016/0022-1694(92)90096-E]

(Edited by Ye SHI)

This work was supported by the National Natural Science Foundation of China (Grants No. 40901015 and 41001011), the Major Program of the National Natural Science Foundation of China (Grants No. 51190090 and 51190091), the Fundamental Research Funds for the Central Universities (Grants No. B1020062 and B1020072), the Ph. D. Programs Foundation of the Ministry of Education of China (Grant No. 20090094120008), the Special Fund of State Key Laboratories of China (Grants No. 2009586412 and 2009585412), and the Programme of Introducing Talents of Disciplines to Universities of the Ministry of Education and State Administration of the Foreign Experts Affairs of China (the 111 Project, Grant No. B08048).

*Corresponding author (e-mail: wanily@hhu.edu.cn)

Received Jul. 21, 2011; accepted Nov. 23, 2011