DEVELOPMENT OF SIMPLE CATCHMENT HYDROLOGICAL MODEL BASED ON TOPMODEL

SHUFEN SUN

LASG, Institute of Atmospheric Physics, Beijing 100029, China

HUIPING DENG

Geography Department, Liao Cheng University, Liao Cheng 252059

Shandon Province, China

Abstract In this work, a simple catchment hydrological model based on TOPMODEL will be described. Then the model will be verified by using 40 years observation data in a Chinese catchment. Since the model includes several factors affecting the simulation results, several sensitivity studies for the factors such as channel initiation threshold (CIT), the number to differentiate whole catchment into sub-zones and the grid size dividing the catchment are conducted, and the results from the sensitivity studies are analyzed.

INTRODUCTION

Over the past 20 years, several soil-vegetation-atmosphere transfer (SVAT) schemes have been developed with different structure and complexity and they present direct role of vegetation in determining the surface energy and water balance as good as possible. However, Koster and Milly [6] examined the effective functional relationships among soil root zone moisture, evaporation and runoff and pointed out that annual evaporation rate is controlled as much by runoff as by its evaporation formulation. The upshot of their analysis is that, if the formulation of runoff in an SVAT is poor, the SVAT will give unrealistic soil moisture distribution and in turn unrealistic annual evaporation rate regardless of the quality of the evaporation formulation. As with the increased recognition of the importance of this kind of interaction, there have been sustained efforts to develop a more realistic large-scale hydrological model.

Since 1980s, a physical based and distributed model including detailed physics such as SHE model (Abbott et al, [1]) was developed. However, this kind of model includes many parameters difficult to obtain as well as consumes computer resources a lot，and thus not suitable for climate study.

In order to meet the requirement from land surface model study in GCM, TOPMODEL (Topographical-based hydrological model), a semi-distributed and partly physically based model, only uses a few parameters to describe the topographic controls on soil water spatial distribution, which is very essential to partition precipitation into surface evaporation and runoff in current SVAT. So, TOPMODEL can be extended to improve land surface model (Randal at al.[9]). However, there exist some uncertainties in the determination of several factors in TOPMODEL which will affect the model result.

In this paper, the TOPMODEL and a simple hydrological cycle model being integrated with TOPMODEL will be briefly described. Then, the integrated model will be evaluated by using the observation data of around 40 years (1960-1999) in a catchment in China. Finally, Some sensitivity studies for the factors will be conducted.

BASIC PRINCIPLE AND EQUATIONS FOR TOPMODEL

Both model and data have shown that substantial soil moisture heterogeneity always exists in a catchment at almost any scale (Bell et al. [2]；Owe et al.[8])and that one critical factor to control the distribution of soil moisture is topography (Beven and Kirkby, 1979 [3];Burt and Butcher [5]). TOPMODEL (Beven and Kirkby [3]; Beven, 2000 [4]) has the advantage of a few parameters and good physical meaning. By using topography index intrinsic by the catchment and average water storage deficit calculated in the catchment, TOPMODEL explicitly describe the influence of topography issue on the soil moisture distribution and horizontal variation of ground water table over the catchment. The model directly predicts the portion of saturation excess area and then can estimates the saturation excess runoff in the catchment.

According to the three assumptions from TOPMODEL (Beven and Kirkby [3] and 2000[4]) and other assumptions such as quasi steady condition of ground water table, uniform and constant local saturated transmisivity and rate of water recharge from un-saturation zone to ground water constantly being spatially uniform over the catchment, one have following equations to describe relations among mean of water storage deficit in un-saturation zone for the entire catchment() , local storage deficit of the un-saturation zone at location () the total base flow () :

(1)

(2)

= (3)

= and (4)

where is hydraulic gradient of ground water equal to the slope of catchment surface elevation at location , is the drainage area through the location in the catchment per unit contour length., is defined as local topography index and is average topography index of the catchment which reflect the control hydrological effects on the catchment, is a parameter to adjust the decreasing rate of local transmisivity with increasing water storageand and estimated with empirical formula (Beven and Kirkby [3] and [4]) by using long term river runoff recession data in the catchment, is base flow when is zero. Equation (1) to (4) clearly predicts the saturation area distribution where <0, its fraction and base flow rate in the catchment.

THE SIMPLE CATCHMENT HYDROLOGICAL CYCLE MODEL

One need a hydrological cycle model implemented into TOPMODEL to integrate the function of vegetation and other hydrological components in a catchment, which describes land surface processes among atmosphere, vegetation, root zone, un-saturation zone and unconfined aquifer. A simple hydrological cycle model is developed to integrate with TOPMODEL. The integrated model defines four layers in vertical direction: interception layer of canopy, root zone in soil, un-saturation zone and unconfined ground water zone. The precipitation is intercepted first by vegetation to meet its maximum storage capacity , and the remaining of the precipitation (called as effective precipitation) will pass through the canopy and reach the ground surface below. The effective precipitation will be first supplied to root zone until the water is full of the water storage in the zone, then to the un-saturation zone to fill its water storage deficit,, and final remaining will become surface excess runoff. The un-saturation zone constantly recharges water to ground water at rate The simple hydrological model is briefly described below (For detail, please refer to Beven [4] and Sun and Deng [11]). In the model, actual evaporation from ground surfaceis parameterized by:

(5)

where is residual potential evaporation, which equals to the difference between potential evaporation calculated by Penman’s equation and evaporation from canopy . and are local water storage and mean of maximum storage capacity of the root zone in the catchment. Local rate of water recharge is

(6)

where is local water storage in the un-saturation zone and parameter is a mean residence time constant of /per unit of the water storage deficit. Thus, the mean of local water storage deficit changes with time:

(7)

where is the mean of over the catchment. If represents the total saturation excess runoff over the catchment which can be estimated by the local water storage deficit distribution , total runoff = + . comes from Eq. (4). In the model, there are several parameters such as , and so on, which are basically estimated based on measured hydrological data in the catchment. The effective precipitation is obtained by following formula:

and

and (8)

where is the precipitation from input data, is current water storage of the canopy, and is initial water storage of canopy. The evaporation from canopy is estimated by

or (9)

where is potential evaporation calculated by Penman’s equation. Due to the evaporation, final water storage in canopyafter each time step should be adjusted by:

(10)

MODEL VARIATION BY USING DATA OF SOUMOU RIVER CATCHMENT

To evaluate the model developed, the model is used to simulate the long tern runoff data from 1960-1999 in Soumou River Catchment (a tributary of Yangtze River) in China. It is located in North West China. It is a mountain region with the area around 3015.6 km2. Woodland and pasture are two major land surface covers in it. In general speaking, the model simulates the observation records pretty well in both magnitude and change trend for either daily or monthly or seasonal mean of river runoff. The general quality of the model can refer to the table 2. Here, only the results shown in Fig. 1 and Fig. 2 (which are ones based on the CIT equal to 0.5 ) are exemplified. The figures show the comparison of simulated daily and monthly means of river runoff with observation data for two years. It can be found that the simulated result of runoffs is in good agreement with the observation data in either magnitude or change trend.

SENSITIVITY STUDY

Sensitivity of TOPMODEL to CIT

Estimation of the topography index distribution is a key problem (Beven and Kirkby [4], Sun & Deng[11]) for TOPMODEL performance. Currently, digital elevation model (DEM) is extensively used to calculate the spatial distribution of topography index for a catchment (Quinn et al.[7]; Wolock and Price[12]; Saulnier et al.[10]). But there are two factors to affect estimation of the topography index distribution. One is how to decide whether a grid is one with or without river channel inside. Another one is grid size scale in the model which is defined by the resolution of digital elevation data. If a grid with realistic river channel inside is misinterpreted as one of water collection area without river channel, the number of grid with high topography index will increase, and the distribution of topography index in a catchment will lean to the end of high value and in turn the average topography index of the catchment will enlarge. In order to control the effect from the grid define, the Channel Initiation Threshold (CIT, km2) for a catchment is assigned in the model. A grid, having water-collecting area (drainage area) greater than CIT, is considered as one with water channel; otherwise, the grid is considered as area without water channel and only serves as one collecting water flow from upstream.

Table 1 shows the distribution of Probability density function () of topographic index of Soumou River Catchment for five CITs (in the figure and table, upper case CIT is lowcased as cit, cit1=0.01 km2, cit2= 0.1 km2, cit3=0.5 km2, cit4=1 km2 and cit5=5 km2). From the table, it can be found that both maximum topography index and average topography index for the catchment will increase with CIT increase. But, difference between the curves of with cit greater than 0.5(km2) is small. In order to demonstrate the effect of CIT on the model result, Table 2 shows the percentage of efficiency of each year from 1960 to 1999 for 5 CITs. can represents the degree of the model precision (also was used to evaluate general quality of the model mentioned in previous section ) and is defined as

(11)

where is the annual variation of the daily runoff mean of observation data and is the annual variation of the difference between the daily means of observation and model result. You can find that the coefficient does not show big difference from each other with different CIT except of very small CIT. For CITs greater than 0.5 km2, are almost the same，which is consistent with the fact that curves with CIT greater than 5km2 are almost same., value for most of years being greater means TOPMDEL model can works well in simulating the runoff in the Catchment. Fig. 3a and 3b show Comparison between annual means of total runoff and surface runoff depths over 40 years due to different CIT (cit1=0.01 km2, cit2=0.1 km2, cit3=0.5 km2, cit3=1 km2 and cit5=5 km2). The maximum differences between means of surface runoff and between means of total runoff depth are around 10-15mm/year and 40-50mm/year. The results predicted with smaller CITs of 0.01 and 0.1are quite different from those with bigger CITs. But, the results predicted with CITs greater than 0.5 km2 show minor variation.

Table 1. The properties of topography index change with grid size

Grid size (m) / Cit (km2) / Average topography index / Variation range of topography index
100 / Cit1=0.01 / 11.1 / 8-20
100 / Cit2=0.1 / 12.2 / 8-22
100 / Cit3=0.5 / 12.4 / 8-23
100 / Cit4=1.0 / 12.4 / 8-23
100 / Cit5=5.0 / 12.5 / 8-25
200 / Cit1=0.04 / 12.5 / 11-21
200 / Cit2=0.48 / 13.2 / 11-22
200 / Cit3=1.0 / 13.3 / 11-23
200 / Cit4=5.0 / 13.4 / 11-25
200 / Cit5=10.0 / 13.4 / 11-25
400 / Cit1=0.16 / 13.9 / 13-22
400 / Cit2=0.48 / 14.3 / 13-23
400 / Cit3=0.96 / 14.4 / 13-24
400 / Cit4=5.12 / 14.7 / 13-25
400 / Cit5=10.24 / 14.7 / 13.25
800 / Cit1=0.64 / 15.7 / 14-23
800 / Cit2=1.28 / 15.9 / 14-23
800 / Cit3=5.12 / 15.9 / 14-25
800 / Cit4=10.24 / 16.2 / 14-25
800 / Cit5=19.84 / 16.3 / 14-25

Table 2. Percentage efficiency at different CIT values (km2)

CIT
Year / 0.01 / 0.1 / 0.5 / 1 / 5 / CIT
Year / 0.01 / 0.1 / 0.5 / 1 / 5
1960 / 0.53 / 0.66 / 0.70 / 0.72 / 0.72 / 1980 / 0.82 / 0.83 / 0.83 / 0.83 / 0.83
1961 / 0.43 / 0.46 / 0.52 / 0.53 / 0.54 / 1981 / 0.84 / 0.86 / 0.85 / 0.85 / 0.86
1962 / 0.69 / 0.73 / 0.73 / 0.72 / 0.72 / 1982 / 0.86 / 0.85 / 0.84 / 0.83 / 0.83
1963 / 0.64 / 0.67 / 0.71 / 0.72 / 0.73 / 1983 / 0.80 / 0.83 / 0.85 / 0.85 / 0.86
1964 / 0.66 / 0.66 / 0.66 / 0.65 / 0.65 / 1984 / 0.68 / 0.72 / 0.76 / 0.76 / 0.77
1965 / 0.77 / 0.77 / 0.72 / 0.71 / 0.71 / 1985 / 0.52 / 0.52 / 0.53 / 0.53 / 0.55
1966 / 0.54 / 0.58 / 0.63 / 0.64 / 0.65 / 1986 / 0.72 / 0.72 / 0.74 / 0.74 / 0.74
1967 / 0.68 / 0.68 / 0.68 / 0.67 / 0.67 / 1987 / 0.65 / 0.67 / 0.69 / 0.70 / 0.70
1968 / 0.62 / 0.62 / 0.64 / 0.64 / 0.65 / 1988 / 0.74 / 0.75 / 0.72 / 0.71 / 0.71
1969 / 0.80 / 0.80 / 0.81 / 0.81 / 0.81 / 1989 / 0.78 / 0.75 / 0.72 / 0.72 / 0.72
1970 / 0.29 / 0.29 / 0.33 / 0.33 / 0.36 / 1990 / 0.77 / 0.77 / 0.77 / 0.77 / 0.77
1971 / 0.68 / 0.68 / 0.68 / 0.68 / 0.68 / 1991 / 0.52 / 0.52 / 0.57 / 0.58 / 0.59
1972 / 0.71 / 0.72 / 0.71 / 0.71 / 0.72 / 1992 / 0.76 / 0.74 / 0.75 / 0.75 / 0.76
1973 / 0.69 / 0.69 / 0.70 / 0.69 / 0.68 / 1993 / 0.82 / 0.81 / 0.82 / 0.82 / 0.83
1974 / 0.79 / 0.79 / 0.79 / 0.79 / 0.78 / 1994 / 0.63 / 0.64 / 0.66 / 0.67 / 0.69
1975 / 0.57 / 0.61 / 0.64 / 0.65 / 0.67 / 1995 / 0.64 / 0.63 / 0.59 / 0.59 / 0.59
1976 / 0.76 / 0.75 / 0.73 / 0.73 / 0.74 / 1996 / 0.50 / 0.50 / 0.52 / 0.51 / 0.52
1977 / 0.70 / 0.67 / 0.65 / 0.64 / 0.63 / 1997 / 0.74 / 0.72 / 0.70 / 0.70 / 0.71
1978 / 0.28 / 0.33 / 0.38 / 0.38 / 0.38 / 1998 / 0.62 / 0.64 / 0.67 / 0.68 / 0.70
1979 / 0.53 / 0.56 / 0.60 / 0.60 / 0.60 / 1999 / 0.85 / 0.81 / 0.82 / 0.82 / 0.82

Sensitivity of TOPMODEL to grid size in catchment