At present, the main methods to study the relationship between water level and discharge are:
(1) comprehensive drop index method: the flow of Qilishan station in Chenglingji is treated as a single value, and the formula is as follows.
q = Qm/δHβ= f(H)
( 1)
δH =α 1δH 1+α2δH2+α3δH3
(2)
Where Qm is the measured discharge, H is the water level of Qilishan Station, δ H 1, δ H2 and δ H3 are the drops from Lujiao to Qilishan, Qilishan to Jianli and Qilishan to Luoshan, respectively, α 1, α2 and α3 are the corresponding distances (km), and β is the undetermined index. The typical year is selected as the single water level-discharge relationship in each main period.
(2) Power function fitting method: According to some hydrological data before and after the bend, the relationship between water level and discharge of Qilishan Station and Jianli Station under a certain jacking flow is established, and the power function fitting method is adopted, and the formula is as follows
Z=αQβ
(3)
Where z is the water level, q is the flow rate, α and β are undetermined coefficients, and α and β values are different for different flows. ?
Researchers believe that the above methods generally have good correlation, except for a few points, the correlation coefficient can reach above 0.9.
In this paper, the relationship between water level and discharge in the corresponding reach and even downstream Luoshan Station and Wuhan Guan Station is deeply analyzed, and the results of the relationship model are put forward, which will overcome the shortcomings of the above two methods. And (1) only has one station water level data. (2) Change the hierarchical flow relationship into a unified flow relationship.
2 Determination of analytical methods and basic relationships
2. 1 Characteristics of water level changing with discharge
Draw the daily hydrological relationship from Jianli Station 1980 to 1987, as shown in figure 1. As can be seen from the figure, the maximum fluctuation range of water level can reach 4 ~ 5m under the same discharge in Jianli. This decentralized relationship is the result of the outflow from the lower reaches of Dongting Lake. Under the same flow condition, the station water level is high when the downstream water level is high, and vice versa. Even if the flow rate is below 15000m3/s and the flow rate increases from 4000m3/s to 13000m3/s, the water level correspondingly rises from 2 1.2m to 27.8m, with a change range of 6.6m The main factor of this change is the elevation of the downstream water level. When the downstream water level changes little, the upstream water level change caused by the flow change is much smaller. Take the downstream snail water level of 20 ~ 2 1m as an example, the discharge changes from 3960m3/s to 12900m3/s, and the Jianli water level rises from 23.4m to 25.8m, with a change of only 2.4m.. ..
If the water level of the downstream Luoshan station is divided into several groups according to the size, we can know that Jianli Q and H of each group have the characteristics shown in Figure 2.
Figure 1 1980 to 1987 daily water level and discharge relationship of Jianli station
Jianli Station 1980 ~ 1987 Relationship between Water Level and Discharge
Fig. 2 Relationship diagram of water level and discharge at Jianli Station (h Luoshan = 20 ~ 2 1m)
Relationship between water level and discharge at Jianli Station (Luoshan =20~2 1m)
According to the analysis, Jianli water level consists of the following two parts: one is the intersection of the extension line of the midpoint in Figure 2 and Q=0, which is denoted as H0; The second is the change of water level caused by the change of flow, which is recorded as Δ HQ, i.e.
h =δHQ+H0
(4)
2.2 Determination of δ HQ and H0
The relationship between the daily flow of Jianli Station in the statistical year and the water surface gradient from Jianli to Luoshan is drawn in Figure 3. The point group is very dispersed, and the downstream water level grouping method is also adopted, such as grouping points under H = 20 ~ 2 1m, as shown by the "+"point in Figure 4. Points below H = 27 ~ 28m are also plotted in Figure 4, which are indicated by "*" points.
Fig. 3 Relationship between Jianli-Luoshan Jianli discharge and water surface gradient
Relationship between discharge of Jianli station and water surface gradient of Jianli-Luoshan reach
Relationship between monitoring discharge and water surface slope at different snail water levels.
Relationship between discharge and water surface gradient at Jianli Station under different water levels in Luoshan Station
? As can be seen from the points in the figure, the scattered points in figure 3 are formed by the confluence of different groups of data of downstream water level, and the Q ~ J relationship of each group is very regular. Under the same group conditions, the specific drop increases monotonically with the increase of flow rate. Further analysis shows that the increase of j and q can be expressed by linear relationship. If J0 is used to represent the gradient value at the intersection of Q=0 and JQ is used to represent the gradient change caused by flow, it can be obtained.
J=JQ+J0
(5)
Comparison formula (4) shows that Jianli water levels Δ hq and H0 can be expressed as JQL and j0l+h respectively (L is the distance between two stations and H is the water level of the next station). Have it at once
H up =JQL+J0L+H down.
(6)
2.3 empirical fitting
As can be seen from the above, in the same set of data? J and q? Linear relationship, which can be expressed as
Jq = φ (under h) q
(7)
After analyzing the hydrological data of several stations, it is found that the expressions (under H) and J0 are respectively
(H) = 10aH b+c
(8)
J0=d+eH
(9)
Substituting equations (8) and (9) into equations (5) and (6) is the basic expression of the relationship between water level and discharge established in this paper.
H = (b+c in 10ah) QL+(d+eh) L+H
( 10)
or
B+ c)q+(d+eh) at j =( 10ah.
( 1 1)
Where a, b, c, d and e are the coefficients to be found, and a, b, c and d, e? Each coefficient has a clear mathematical meaning and its simple calculation method, which will be introduced in detail later. Other symbols have the same meanings as before.
3 Example calculation
3. Determination of1coefficient
Hydrological data are grouped according to the water level of Luoshan Station downstream of Jianli 1980 ~ 1987, and calculated by twice least square method. Fitting each group of data points, and finding J0 and φ (under H) respectively, the results are plotted in Figures 5 and 6.
Fig. 5 Relationship between Luoshan Water Level and Jianli J0
Relationship between Luoshan Water Level and J0 of Jianli Station
Fig. 6 Relationship between water level of Luoshan River and Jianli φ (H)
Relationship between Luoshan Water Level and φ (below H) at Jianli Station
a，b，c，d，e？ Five undetermined coefficients (gradient j is11000, flow? Q is 103, and the distance l is kilometers). The coefficient values are listed in table 1. Similarly, the daily hydrological data of Qilishan Station (Luoshan Station), Luoshan Station (Longkou Station) and Wuhanguan Station (Huangshi Station) 1980 ~ 1987 are analyzed to determine the coefficients of each station, which are listed in table 1.
Table 1 coefficient value (1980 ~ 1987)
Value of coefficient (1980~ 1987)
Radio station name
Jianli (Luoshan)
Qilishan (Luoshan)
Luoshan (Longkou)
Wuhan Pass (Huangshi)
First class
4.22
3.7634
4.6267
-0.85460
Aortic second sound
-5.333
-5.2259
-6. 1998
- 1.9 122
a3
0.000308
0.000043304
0.0002 1897
-0.000026073
a4
-0.0006 1278
-0.0007 1889
-0.00062 1 14
0.00055556
a5
0.03 1678
0.049650
0.028696
0.0006667
3.2 Checking calculation results
In Figure 7(a, B, C, D), the comparison results of integral calculation in statistical years are plotted. It can be seen that the calculated results are completely consistent with the measured points.
Based on the above analysis, we can draw the following conclusions: (1) No matter whether the discharge site of hydrological station is scattered or single, the water level of this station is mainly affected by the water level change of downstream stations; (2) Using the above-mentioned relationship (10), when any two of the three parameters of this station's flow, water level and next station's water level are known, they can all be counted.
Fig. 7 Comparison between measured water level and calculated value
Comparison between observation stage and calculation stage
Fig. 8 Comparison between measured flow and calculated value at Jianli Station
Comparison between measured flow and calculated flow at Jianli station
Calculate the third parameter value. Taking Jianli Station as an example, the Jianli discharge is calculated from the water level of Jianli Station and the downstream water level, compared with the measured discharge, and drawn in Figure 8, with the point falling on the 45 line; (3) It is difficult to define the concept of uniform flow in natural rivers, but the basic formula of uniform flow is J = Q2N2/A2R4/3; The causal relationship between the parameters in the formula is still unclear. In fact, q, n and j are all independent quantities. If the side wall conditions are different, the change of water depth or water level will cause the change of n value, reflecting the resistance characteristics along the way. It can be considered that the change of discharge only causes the change of water depth (water level), and should not affect the value of n. The formula of water level and discharge recommended in this paper contains a specific gradient term unrelated to discharge, namely J0(=d+eh). When the natural river flows evenly, the values of q and n cannot be determined, which still needs to be studied in the future. However, the specific calculation of this item is indeed a progress in solving this problem, and the research in this area needs to be further deepened.