2Former Graduate Student, Dept. of Civil Engineering,

National Taiwan University, Taipei, Taiwan, China

Abstract: This research developed methods to estimate the total phosphorus flux into a reservoir. Chiu’s models for calculating the distribution of velocity and sediments over a channel cross-section were combined in this study. Models were applied to estimate the total phosphorus flux in inflows of Te-Chi Reservoir and Feitsui Reservoir in Taiwan. The model results compare favorably to the vertical distribution of observed data in velocity, sediments, and dissolved and particulate phosphorus concentrations. Using long-term streamflow data (hourly or daily), the annual total phosphorus loading rates can be estimated by the models developed herein. Those loading rates are essential for water quality and eutrophication modeling in the reservoir.

 

Keywords: dissolved phosphorus, particulate phosphorus, reservoir inflow, phosphorus loading, sediment concentration, efficient measurement, annual loading rate

Phosphorus is a limiting nutrient for most eutrophic reservoirs. High percentage of annual total phosphorus loading into a reservoir is transported by high flows. They are classified as nonpoint sources pollution which occurs during storm periods. During high flows, measurements on velocity, sediment concentration and water quality are very difficult. Thus efficient measurements are needed for estimating flow, sediment and water quality flux into a reservoir.

This paper develops methods combing with efficient measurements to more accurately estimate the phosphorus flux over a cross-sectional area. The methods are also applicable to a chemical or toxic substance which adsorbs to the sediments in a water column.

Chemicals or phosphorus exit in two forms, dissolved form and particulate form. The total concentration C_T can be expressed as (Thomann and Mueller, 1987):

C_T = Cp + Cd = Cd ( 1 + Km )                             (1)

where C_p = particulate concentration, C_d = dissolved concentration, m = suspended solid concentration, and K = partition coefficient.

The flux of chemicals a across across-section over a storm of period T can be expressed as:

                      (2)

where F = flux, u(y,z) = velocity which varies with depth z and width y, W = total width of the river, and D = total depth of the river.

K can be different due to different particle size and organic fraction of suspended solids. Hence

                                         (3)

When K_i = the K value for suspend solids i and f_i = the fraction of suspend solids i.

Chiu(1989) developed a method for efficient measurement of discharge in a river. Cross-sectional average velocity can be written as:

                                         (4)

Where u_max = maximum velocity, = e^M / (e^M–1) – 1/M, and M = parameter. and M can be obtained from field data.

Furthermore the distribution of u can be represented by:

                                                         (5)

When = dimensionless variable with which u develops, = maximum value of . is express by :

                                                           (6)

Where D = total water depth and h = parameter.

The above models suggest an efficient method of discharge measurement in which, to determine the mean velocity at a channel cross-section, only u_max is needed since is constant and hence mean velocity can be obtained using equation (5). U_max occurs within a small region in a channel cross-section and hence can be estimated by a quick velocity sampling on the z axis (Chiu and Chen, 1999).

An efficient measurement of sediment inflow is possible using the methods developed by Chiu, et al. (2000). During high flows, strong currents and rapid change in flow conditions make sediment sampling unpractical. A good alternative is to conduct a quick, point sampling, which in turn requires a mathematical model to estimate the mean concentration from point sampling. The models developed by Chiu et al. (2000) can be used to satisfy this need since they can describe distribution of sediment concentration over the entire vertical, from the channel bed to the water surface (Chiu and Chen, 1999).

Te-Chi reservoir is the fourth largest reservoir in Taiwan. Main purposes of the reservoir are hydropower generation and water use in central Taiwan. Water quality in Te-Chi reservoir is under eutrophic condition due to significant nutrient loading from agricultural activities in the watershed. One of the major purposes of this study is to more accurately estimate nutrient (phosphorus) and sediment loading for management of the reservoir.

Field measurements of velocity, sediment concentration and water quality variables were carried out in 1997 to 1999 at Sung-Mao station which controls main inflow to the reservoir. Figure 1 shows the measured velocity distribution in vertical direction and its comparison to the model developed by Chiu (1989) as described in section 2. The agreement is quite good. Figure 2 shows an example set of vertical distribution of measured particulate phosphorus concentrations and its comparison to the model result obtained by the methods developed herein combining with the sediment distribution model from Chiu, et al. (2000). The comparison is favorable.

Figure 3 shows the partition between dissolved concentration and particulate concentration of phosphorus. Figure 4 is the linear relationship between total phosphorus loading and discharge. This regression was also used to calculate the annual loading for the comparison with methods developed in research.

This study further estimated the annual total phosphorus loading using the daily streamflow data and the methods developed herein. Estimated annual loading into the reservoir for 1996 is about 12.5ton/yr. This number compares well with the average total phosphorus concentration in the reservoir calculated by the Vollenweider’s zero-dimensional, simplified model (Vollenweider, 1975).

Feitsui Reservoir is the second largest reservoir in Taiwan. It is the main water supply source for metropolitan Taipei. This study carried out field measurements at Tu-Nan Bridge which controls the main inflow to Feitsui Reservoir.

Figure 5 is an example result of measured vertical velocity distribution at Tu-Nan Bridge. Calculated result from Chiu’s model compares well to the measured data. Figure 6 is the observed vertical total phosphorus distribution vs. model results. Nonlinear adsorption equations were also used in this study. Specifically, linear isotherm, Langmuir isotherm, and Freundlich isotherm were adopted. For the particular set of data in Figure 6, using Freundlich isotherm obtains the best result when compared to the observed data. Details of the study are described in Kuo, et al. (2000).

Methods to estimate the flux of chemicals into a reservoir were developed in this study. These methods combining with Chiu’s models of estimating discharge and sediments over a cross-section form the base for efficient measurements of discharge, sediments, and water quality in reservoir inflows during high flow periods.

Field measurement were carried out for inflows of Te-Chi Reservoir and Feitsui Reservoir in Taiwan. Estimation of dissolved and particulate phosphorus concentrations using the methods developed in this study compares favorably to the measured data. Annual loading of total phosphorus can also be calculated using observed daily or hourly flow data. The annual loading data is essential in reservoir water quality modeling and study.

Field measurement during storm period is a difficult task. Much more field data are needed to calibrate and verify models developed in this study.

This paper is based on work supported by Water Resource Bureau of Taiwan. We thank Prof. Shian-Chee Wu of the Graduate Institute of Environmental Engineering at National Taiwan University and Mr. Cheng-Daw Hsieh of Water Resources Bureau for their assistance in this research work.

Chiu, C. L., “Velocity Distribution in Open-Channel Flow”, J. of Hydraulic Engineering, ASCE, 115(5), 1989, pp. 576-594.

Chiu, C. L. and Y. C. Chen, “Efficient Method of Measuring Discharge and Reservoir-Sediment Inflow’, in Risk Analysis in Dam Safety Assessment, edited by J. T. Kuo and B. C. Yen,Water Resources Publications, LLC, Highlands Ranch, Colorado, U.S.A., 1999, pp. 97-116.

Chiu, C. L. and W. Jin, and Y. C. Chen, “Mathematical Models of Distribution of Sediment Concentration”, J. of Hydraulic Engineering, ASCE, 126(1) , 2000, pp.16-23.

Kuo, J. T., et al., Efficient Measurement of Water Quality for Reservoir Inflows, Project report submitted to Water Resources Bureau of Taiwan, Hydrotech Research Institute, National Taiwan University, June, 2000. (in Chinese).

Thomann, R.. V. and J. A. Mueller, Principles of Surface Water Quality Modeling and Control, Harper & Row, Publishers, New York, 1987.

Vollenweider, “Input-Output Models with Special Reference to the Phosphorus Loading Concept in Limnology”, Schweiz. Z. Hydrol., 37, 1975, pp.53-83.