Flood Simulation based on ArcGIS in the Ungauged Area from Fugu to Wubao of the middle Yellow River

The Qingliangsigou and Jialuhe in the middle Yellow River are selected as the typical tributaries, history flood data in 1980-2013 and Horton infiltration capacity curve are used to calculate the stable infiltration rate and establish the model of runoff yield and concentration, the parameters are calibrated and applied in the ungauged area from Fugu to Wubao. The study area is divided into 20 units based on ArcGIS, Muskingum method parameters in each unit are calibrated, and typical floods of ungauged area from Fugu to Wubao are simulated. The results show that the simulation effects are good: the average error of peak time is about -0.4h, the error of peak discharge is in the forecasting allowable range, and the deterministic coefficient is 0.66.


Introduction
The Yellow River is the second longest river in China, about 5464 km in length from source to estuary. Originating in the Qinghai-Tibetan plateau of Qinghai province, it wends its way through eight provinces and autonomous regions before flowing down into the Bohai Sea north of the Shandong Peninsula on the east coast of China. The Fugu-Wubao region of the middle Yellow River locates in the North of Shanxi Shaanxi gorge on the Loess Plateau. The catchment area is 29475 km 2 , and the river length is 242 km. The ungauged area is 9187 km 2 , occupies 31.2% of the total area ( Fig.1). Fig.1 Location of Fugu-Wubao region and its ungauged area in the Yellow River basin Regional rainstorm often occurs in ungauged area in Fugu-Wubao, which is short period and high intensity heavy rain. The daily rainfall in storm center is up to the value from 100 to 600mm, and rainfall concentrates in the 6~20 hours. In addition, the basin slope is steep, runoff yield and convergence conditions are good, so large leptokurtic flood often occurs, with large peak discharge and small water amount. Once heavy rain occurred in the ungauged area, flood forecast is difficult, due to the rainstorm area and the source of flood are unknown. Due to lack of adequate flood and rainfall data to calibrate parameters, and flood process is difficult to obtain in the ungauged area, the two tributaries, Qingliangsigou (QLSG)and Jialuhe, which are adjacent to  study area and with good historical data were selected to calibrate parameters (Fig.2). Then the parameters will apply in the ungauged area of Fugu-Wubao.

Unit division
Based on ArcGIS, distributed hydrology forecasting model is established, and the whole basin is divided into a number of units. The principle of unit division: each unit is a closed basin as far as possible, at least a rainfall station within each unit. It is divided into 3 units for each typical tributary, and geographic parameters of each unit are shown in Table 1. It is divided into 20 units for ungauged area of Fugu-Wubao, shown in Fig.5 and Table 2. The ungauged region of 9 primary tributaries is independent unit. The ungauged area is relatively large for Lanyi River, thus it is divided into 2 units. There are 9 points, tributaries junction into the Yellow River between Fugu and Wubao, which divided the other region into 10 units.

Analysis of Horton infiltration capacity curve 3.1 Method
(1) Antecedent precipitation If sunny in the former two days, the antecedent precipitation equation is as follows: Where: 1 ,  t a P , antecedent precipitation after one day of the time t, mm; t a P , , antecedent precipitation at the time t, mm; K, daily regression or reduction coefficient of soil water content. If rainfall in the day while without runoff, the formula is If rainfall in the day and with runoff, the formula is . Antecedent precipitation Pa should not be greater than the maximum water storage WM, therefore when the calculated Pa value is greater than WM, take Pa as the WM value of the day. K is constant coefficient, approximately equals 0.85.
(2) Equation of Horton infiltration capacity curve The equation of Horton infiltration capacity curve is the following: (2) Where: f, infiltration rate, mm/h; fc, stable infiltration rate, mm/h; f0, initial infiltration rate, mm/h; t, time; k, index of soil infiltration rate decreasing。 The equation of Horton cumulative infiltration curve is: (3) Stable infiltration rate The initial infiltration rate f0 is related to the initial soil moisture content W0. The smaller the W0 is, the greater the f0 is. When W0=0, f0=fm, it is the maximum initial infiltration capacity. When W0= Wm, f0= fc, it is the steady infiltration rate. The flood data after storm was selected, then Pa is approximately equal to Wm, and the loss of rainfall is mainly stable infiltration rate. The stable infiltration rate is calculated by the following equation: Where: T is rainfall duration.

Results
Using the observed rainfall, runoff and calculating antecedent precipitation, to analyze the infiltration capacity of QLSG and Jialuhe basin. The relation of f~W0~Ft is obtained ( Fig.7 and Fig.8). The stable infiltration rates of the two tributaries are calculated, which is 1.9mm/h and 3.1mm/h respectively.  The empirical relation between the mean velocity and peak discharge is the following: Where: V1, V3 and V2, V4 are intercept and slope in the double logarithmic coordinates of correlation line; QV, discharge in the turning point of relation line, m 3 /s. The empirical relation between discharge factor and peak discharge is the following: Where: X1, X3 and X2, X4 are intercept and slope in the double logarithmic coordinates of correlation line; QX, discharge in the turning point of relation line, m 3 /s.

Results
(1) Confluence parameters of Muskinggum method The yielding and confluence parameters of Muskinggum method in typical tributaries are obtained by the history observed flow data and the formula (5) ~ (8), shown in Table 3. (2) Calibration of runoff yield and concentration parameters The flood simulation is carried out in 1980~2013 in the two tributaries, to calibrate the runoff yield and concentration parameters, and the results are shown in Table 4. The mean parameters of the two tributaries are regarded as the parameters of the ungauged area in Fugu-wubao.  Table 5.

Tab.3 Confluence parameter of Muskinggum method in typical tributaries
Tab.5 Confluence parameter by Muskinggum method of each unit in Fugu-Wubao ungauged area

Flood simulation
The history typical floods are simulated in the ungauged area of Fugu-Wubao, according to the runoff yield and confluence parameters calibrated in Qingliangsigou and Jialuhe, and confluence parameters of Muskingum method which are calculated by history floods. Flood simulation of "19950729" in ungauged area of Fugu-Wubao is shown in Figure 10.

Accuracy evaluation
The accuracy evaluation of simulation for the above 7 floods in ungauged area of Fugu-Wubao is carried out, and the results are shown in Table 6. The simulation results are relatively good, the average peak time error is about -0.4 hour. Considering the peak priority principle, all the peak errors are in the allowable range of forecasting, and the average certainty coefficient is 0.66.

Conclusions and suggestions 6.1 Conclusions
(1) The Qingliangsigou and Jialuhe, adjacent to the ungauged area of Fugu-Wubao and with good historical data, are selected as typical tributaries. The observed data from 1980 to 2013 are used to analyze the infiltration curve, and the relation of f~W0~Ft is established. The stable infiltration rate of the two tributaries is 1.9 mm/h and 3.1mm/h respectively.
(2) The history typical floods are simulated in the ungauged area of Fugu-Wubao region by the runoff yielding and confluence parameters calibrated in Qingliangsigou and Jialuhe. The simulation results are relatively good, all the peak errors are in the allowable range of forecasting, and the average certainty coefficient is 0.66.

Suggestions
(1) The ungauged area occupies 31.2% of the total area of Fugu-Wubao region, and the regional, short duration and high intensity rainfall often occurs, thus the storm-flood model should be further strengthen, and flood forecasting scheme should be developed as soon as possible.
(2) Considering the principle of distribution uniformity and economic feasibility based on the original rainfall stations, the rainfall stations should be added in the ungauged area of Fugu-Wubao, in order to reach the sparse network density allowed by the international meteorological organization.