Factor analysis method-based research method for variation degree of discharged water temperature of high dam reservoir in cold region

Abstract

The invention provides a cold region high dam reservoir discharged water temperature variation degree research method based on a factor analysis method. The method comprises the steps that a water temperature index system is constructed; selecting a research area, obtaining original data, and preprocessing the original data; performing zero-mean standardization on the original data to obtain effective data; and evaluating the variation degree of the discharged water temperature of the reservoir by using a factor analysis method. According to the method, the variation degree of the discharged water temperature of the high dam reservoir in the cold region is evaluated through a factor analysis method, related variables are summarized into several independent common factors, each variable is loaded on one factor as much as possible, the obtained common factors reflect information of original variables more accurately compared with principal components, the data analysis efficiency is improved, and the accuracy of data analysis is improved. And each index weight represents the comprehensive contribution proportion of the factor analysis evaluation score.

Description

Technical Field

[0001] The present invention relates to the field of water environment science and technology, and in particular to a method for studying the variation degree of discharged water temperature from a high dam reservoir in a cold region based on a factor analysis method. Background Art

[0002] my country's water resources are unevenly distributed in time and space. The amount of water varies greatly between different regions and in different periods of time in the same region. In addition, the rapid economic and social development has caused a prominent contradiction between water supply and demand, and the water resource situation is very serious. In order to achieve the redistribution of water resources between time and region and improve the utilization efficiency of water resources, water conservancy facilities such as reservoirs are built on natural rivers. The construction of reservoir dams has become a common way to achieve comprehensive functions such as resisting floods, supplying water for irrigation, improving navigation, allocating water resources and increasing energy. It also witnesses the wisdom of human water management and water use; at the same time, dams have caused various environmental and social problems at different scales, and are the most extensive and significant events that humans have had on the ecological environment of rivers.

[0003] At present, my country's water conservancy and hydropower development is booming, and hydropower development is also in the stage of developing towards the high-altitude cold regions in the west. Under the constraints of special geographical environment, climate and other conditions, the construction mode and temporal and spatial distribution law of reservoirs in cold regions are significantly different from those in other regions. However, the current research on river water temperature mainly uses long-series water temperature data and water temperature models to analyze the law of river water temperature changes under the influence of climate change and reservoir construction. Therefore, it is necessary to systematically summarize the impact of different geographical locations, water conservancy scales, and operation modes on the downstream river water temperature when building reservoirs in these areas. Clarifying the construction scale and dispatching mode of high-dam reservoirs in cold regions will be of great significance to water security, water resources management and ecological and environmental protection in the basin. However, under the influence of the harsh climate environment in high-altitude cold regions, the lack of relevant data has seriously hindered the construction of reservoirs in cold regions.

[0004] Therefore, it is necessary to design a research method based on factor analysis to study the variation degree of water temperature of high-dam reservoirs in cold regions, in order to solve the problem that the existing technology does not fully consider the uniqueness of reservoir construction methods and temporal and spatial distribution laws under the special geographical environment and climatic conditions in cold regions, and cannot systematically summarize the specific impact of factors such as different geographical locations, water conservancy scales, and operation methods on the water temperature of downstream rivers. It is difficult to clarify the important significance of the construction scale and scheduling method of high-dam reservoirs in cold regions to water security, water resources management and ecological environmental protection in the basin, and there are obvious deficiencies in coping with the complexity of water temperature research in cold region reservoirs. Summary of the invention

[0005] In view of this, the present invention proposes a research method for the variation degree of discharged water temperature of high-dam reservoirs in cold regions based on factor analysis, aiming to solve the problem that in the existing technology of high-dam reservoir research in cold regions, due to the influence of the harsh climatic environment in high-cold regions, relevant data are scarce, it is difficult to comprehensively obtain the water temperature data required for reservoir construction and operation, which seriously hinders the construction of reservoirs in cold regions, does not take into account the particularity of cold regions, cannot summarize the influence of various factors on water temperature and the importance of reservoir-related factors, and is difficult to cope with the problem of research complexity.

[0006] In one aspect, the present invention proposes a method for studying the variation degree of water temperature discharged from high dam reservoirs in cold regions based on factor analysis, comprising:

[0007] Construct a water temperature index system;

[0008] Select the research area, obtain the raw data, and pre-process the raw data;

[0009] The original data were normalized to zero mean to obtain valid data;

[0010] Factor analysis method is used to evaluate the variability of the downstream water temperature of the reservoir.

[0011] Furthermore, the construction of the water temperature index system includes:

[0012] The deviation of water temperature from the baseline level is taken as the factor affecting the reservoir's impact on river water temperature. The statistical indicators of natural changes in river thermal conditions are used as the basis for the water temperature baseline. The river water temperature indicators are divided into annual water temperature statistics, monthly average water temperature, the amount and duration of extreme water temperature, the frequency and duration of exceeding the water temperature threshold, and the time of occurrence of the water temperature threshold.

[0013] Furthermore, the annual water temperature statistics include: annual average water temperature, annual water temperature amplitude, and occurrence time of water temperature peak;

[0014] The monthly average water temperature is the monthly average water temperature from January to December;

[0015] The amount and duration of extreme water temperatures include: the annual average of the 7-day sliding average water temperature, the minimum values ​​of the 7-day, 30-day, and 90-day sliding average water temperature, and the maximum values ​​of the 7-day, 30-day, and 90-day sliding average water temperature;

[0016] The frequency and duration of exceeding the water temperature threshold include: the number of days when the 7-day sliding average water temperature exceeds 10°C and the longest consecutive days when the 7-day sliding average water temperature exceeds 10°C, the number of days when the 7-day sliding average water temperature exceeds 6°C and the longest consecutive days when the 7-day sliding average water temperature exceeds 6°C

[0017] The occurrence times of the triggering water temperature threshold include: the time when the daily water temperature reaches 10℃ and the time when the daily water temperature reaches 6℃.

[0018] Furthermore, the selecting of the research area, obtaining the raw data, and preprocessing the raw data include:

[0019] The high dam reservoir in the cold region is taken as the research area, and the downstream water temperature of the reservoir is taken as the original data;

[0020] The range of water temperature is determined based on the statistical characteristics of historical data, and invalid data in the original data is eliminated.

[0021] Furthermore, the zero-mean normalization of the raw data to obtain valid data includes:

[0022] The mean of each variable is adjusted to 0 and the standard deviation is adjusted to 1. The standardized formula is:

[0023]

[0024] Among them, X is the original data, μ is the mean, and σ is the standard deviation.

[0025] Furthermore, the evaluation of the variability of the downstream water temperature of the reservoir by using the factor analysis method includes:

[0026] The valid data were subjected to KMO test and Bartlett sphericity test, and the KMO value of the valid data was calculated. When the KMO value was greater than 0.6, the river water temperature index corresponding to the cumulative variance rate after rotation was selected, and the corresponding river water temperature index was used as the common factor; when the KMO value was less than or equal to 0.6, the approximate chi-square dfp value was calculated. When the approximate chi-square dfp value was less than 0.05, the river water temperature index corresponding to the cumulative variance rate after rotation was selected, and the corresponding river water temperature index was used as the common factor.

[0027] Furthermore, for each of the common factors, the load coefficients of all the corresponding factors are calculated respectively to obtain the factor load coefficient values ​​of all the common factors. The factor load coefficient values ​​with absolute values ​​greater than 0.6 are used to obtain the rotated factor score matrix using the maximum variance method, and the factor calculation model is obtained based on the factor score matrix.

[0028] Furthermore, based on the factor calculation model, the comprehensive score of the reservoir to be evaluated on all the common factors is calculated, and the weight calculation is performed using the variance explanation value after rotation, so as to obtain the weights of all the common factors; based on the weights of all the common factors, the degree of variation of the water temperature discharged from the reservoir is obtained.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] The present invention constructs an evaluation index system for the discharge water temperature of high dam reservoirs in cold regions, and the evaluation index system can be used to more accurately evaluate the variation of the discharge water temperature of reservoirs in cold regions.

[0031] The present invention uses factor analysis to evaluate the degree of variation of water temperature discharged from high-dam reservoirs in cold regions, summarizes relevant variables into several independent common factors, and makes each variable load on one factor as much as possible. The obtained common factors reflect the information of the original variables more accurately than the principal components, improve the efficiency of data analysis, and the weight of each indicator represents the comprehensive contribution ratio of the factor analysis evaluation score. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the detailed description of the preferred embodiments below. The accompanying drawings are only for the purpose of illustrating the preferred embodiments and are not to be considered as limiting the present invention. Moreover, the same reference symbols are used throughout the accompanying drawings to represent the same components. In the accompanying drawings:

[0033] Figure 1 The present invention is a flow chart of a method for studying the variation degree of discharged water temperature from high dam reservoirs in cold regions based on factor analysis in an embodiment of the present invention. DETAILED DESCRIPTION

[0034] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to be able to fully convey the scope of the present invention to those skilled in the art. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with the implementation regulations.

[0035] Reference Figure 1 As shown, in some embodiments of the present application, a method for studying the variation degree of discharged water temperature of high dam reservoirs in cold regions based on factor analysis method includes:

[0036] Construct a water temperature index system;

[0037] Select the research area, obtain the raw data, and pre-process the raw data;

[0038] The original data were normalized to zero mean to obtain valid data;

[0039] Factor analysis method is used to evaluate the variability of the downstream water temperature of the reservoir.

[0040] Specifically, the deviation of water temperature from the baseline level is taken as the factor affecting the reservoir's impact on river water temperature, and the statistical indicators of natural changes in river thermal conditions are used as the basis for the water temperature baseline. The river water temperature indicators are divided into annual water temperature statistics, monthly average water temperature, the amount and duration of extreme water temperature, the frequency and duration of exceeding the water temperature threshold, and the time of occurrence of the water temperature threshold.

[0041] It is understandable that the research method based on factor analysis takes the deviation of water temperature from the baseline level as the key factor, constructs a water temperature baseline based on statistical indicators of natural changes in river thermal conditions, and scientifically classifies river water temperature indicators, covering multiple aspects such as annual water temperature statistics. Its advantage is that it can comprehensively and systematically consider the impact of reservoirs on river water temperature, effectively integrate multi-dimensional water temperature data through factor analysis, and accurately analyze the degree of variation in water temperature discharged from high-dam reservoirs in cold regions, providing a solid scientific basis and powerful analytical means for in-depth understanding of the relationship between reservoir and river water temperature, ensuring water ecological security in river basins, and rationally planning water resource utilization.

[0042] Specifically, annual water temperature statistics include: annual average water temperature, annual water temperature amplitude, and the time of occurrence of peak water temperature;

[0043] The monthly average water temperature is the monthly average water temperature from January to December;

[0044] The amount and duration of extreme water temperatures include: the annual mean of the 7-day sliding average water temperature, the minimum values ​​of the 7-day, 30-day, and 90-day sliding average water temperature, and the maximum values ​​of the 7-day, 30-day, and 90-day sliding average water temperature;

[0045] The frequency and duration of exceeding the water temperature threshold include: the number of days when the 7-day sliding average water temperature exceeds 10°C and the longest consecutive days when it exceeds 10°C, the number of days when the 7-day sliding average water temperature exceeds 6°C and the longest consecutive days when it exceeds 6°C

[0046] The occurrence times of the triggering water temperature threshold include: the time when the daily water temperature reaches 10℃ and the time when the daily water temperature reaches 6℃.

[0047] Specifically, high-dam reservoirs in cold regions are used as the study area, and the downstream water temperature of the reservoir is used as the original data;

[0048] The range of water temperature is determined based on the statistical characteristics of historical data, and invalid data in the original data is eliminated.

[0049] The mean of each variable is adjusted to 0 and the standard deviation is adjusted to 1. The standardized formula is:

[0050]

[0051] Among them, X is the original data, μ is the mean, and σ is the standard deviation.

[0052] Specifically, the valid data were subjected to KMO test and Bartlett sphericity test, and the KMO value of the valid data was calculated. When the KMO value was greater than 0.6, the river water temperature index corresponding to the cumulative variance rate after rotation was selected, and the corresponding river water temperature index was used as the common factor. When the KMO value was less than or equal to 0.6, the approximate chi-square dfp value was calculated. When the approximate chi-square dfp value was less than 0.05, the river water temperature index corresponding to the cumulative variance rate after rotation was selected, and the corresponding river water temperature index was used as the common factor.

[0053] For each common factor, the load coefficients of all corresponding factors were calculated respectively to obtain the factor load coefficient values ​​of all common factors. The factor load coefficient values ​​with absolute values ​​greater than 0.6 were used to obtain the rotated factor score matrix using the maximum variance method, and the factor calculation model was obtained based on the factor score matrix.

[0054] Based on the factor calculation model, the comprehensive score of the reservoir to be evaluated on all common factors is calculated, and the weight calculation is performed using the variance explanation value after rotation to obtain the weights of all common factors; based on the weights of all common factors, the degree of variation of the downstream water temperature of the reservoir is obtained.

[0055] It is understandable that by performing KMO test and Bartlett sphericity test on valid data, appropriate river water temperature indicators can be scientifically screened out as common factors to ensure the validity and reliability of subsequent analysis. At the same time, the factor loading coefficient is calculated and the value with an absolute value greater than 0.6 is screened out, and then the factor score matrix is ​​obtained by maximum variance method rotation, which can enhance the interpretability of the data. The factor calculation model based on the factor score matrix can not only calculate the comprehensive score of the reservoir to be evaluated on the common factor, but also calculate the common factor weight using the variance explanation rate value after rotation, and then obtain the degree of variation of the water temperature discharged from the reservoir, which is helpful to comprehensively, objectively and systematically evaluate the variation of the water temperature discharged from high dam reservoirs in cold regions from multiple dimensions, clearly reveal the relationship between various factors, and provide an accurate and comprehensive quantitative analysis method for in-depth understanding of the law of reservoir water temperature change, optimization of reservoir scheduling and management, and maintenance of water ecological balance in cold regions.

[0056] Embodiment 1

[0057] Analyzing the impact of reservoirs on river water temperature requires defining the change of water temperature from the baseline level. The water temperature baseline is usually based on statistical indicators that describe the natural changes in the thermal conditions of the river. In existing research literature, the classification of river water temperature indicators takes into account the amount, frequency, duration and extreme event triggering time of water temperature. Based on the above indicator types, this paper divides the indicators into five categories for selection. The first category is annual statistics, such as annual mean, annual mean deviation coefficient CV, highest daily water temperature in the year, lowest daily water temperature in the year, daily water temperature variation in the year and daily water temperature accumulation in the year; the second category is the average water temperature of each month; the third category is the amount and duration of extreme water temperature events, including weekly mean, weekly extreme value, monthly extreme value and seasonal extreme value; the fourth category is the frequency and duration of exceeding the water temperature threshold. The frequency of occurrence is related to the reproduction or death of organisms. The water temperature threshold specifically refers to the threshold of chronic and acute changes in biological characteristics; the fifth category is the time of occurrence of the water temperature threshold, which can be regarded as a signal of a specific life cycle or life activity of aquatic organisms. Since the water temperature data in the study area lacks daily water temperature conditions, and there are few research results on biological water temperature thresholds. Therefore, the daily water temperature characteristic indicators are not considered for the time being, and the water temperature threshold is set as the water temperature limit threshold for fish spawning and reproduction. The key protected fish in the study area are schizothorax, which usually reach sexual maturity at 3 to 6 years old, require a water temperature of more than 10°C during the breeding season, reproduce from March to August, and spawn in large numbers from April to May. The main breeding season of key fish protection objects such as thick-lipped naked heavy lip fish is from May to June, and the water temperature requirement for spawning is 6°C to 11°C; the water temperature of the spawning ground of spotted naked carp is about 10°C; the spawning water temperature of the polar flat pharyngeal tooth fish is 6°C to 10°C; the bone-lipped Yellow River fish spawns in May; the Yellow River plateau loach spawns around August; the pseudo-catfish plateau loach spawns from July to August. Therefore, the two selected water temperature thresholds are 6°C (the minimum water temperature value for spawning) and 10°C (the minimum water temperature value during the breeding period). The specific water temperature indicators are shown in Table 1.

[0058] Table 1 Classification of river water temperature indicators

[0059]

[0060]

[0061] Taking Longyangxia, Liujiaxia and Jiudianxia, ​​typical high-dam reservoirs in cold regions, as the research objects, the specific research data are: the daily discharge water temperature of Longyangxia Reservoir from 2006 to 2020, Liujiaxia Reservoir from 1976 to 1987, and Jiudianxia Reservoir from 2009 to 2020 as the basic data, and 28 water temperature indicators as samples, the variation degree of river water temperature under the influence of different reservoirs is studied.

[0062] 1. Data preprocessing

[0063] Before performing factor analysis, the original data must be preprocessed. First, filter out invalid data to ensure that there are no factors such as data deviation in subsequent analysis.

[0064] Among the selected water temperature indicators, there are two data with significantly different value ranges for temperature and number of days. To eliminate the influence of dimensions and make the influence of each feature on the result more balanced during data analysis, data standardization is required: perform zero-mean standardization (Z-score standardization) on the original data, adjust the mean of each variable to 0, and the standard deviation to 1. This can eliminate the influence of dimensions and make the contributions of each variable more balanced. The standardization formula is:

[0065]

[0066] where X is the original data, μ is the mean, and σ is the standard deviation.

[0067] 2. Factor Analysis

[0068] Factor analysis can not only achieve the internal correlation between main factors, but also synthesize multiple variables into fewer variables, effectively represent the relationships between subsidiary factors under different main factors, and thus explore the influence degree of different factors on the research object. Suppose the total number of evaluation factors is p, then the specific expression of the evaluation index set is as follows:

[0069] X = {x1, x2,..., x p}

[0070] where x p represents the evaluation index element.

[0071] The factor analysis model of the p-dimensional variable x = [x1, x2,..., xp]T is:

[0072] x = Af + e

[0073] where f = [f1, f2, fm]T is the extracted common factor vector, representing m (m < p) mutually independent common influencing factors that objectively exist in the original variables; A = (aik) is the factor loading matrix, and aik is the loading of variable xi on common factor k, reflecting their correlation coefficient. The larger the absolute value, the stronger the correlation. The key to establishing a factor analysis model for the multi-dimensional variable x is to solve the factor loading matrix A and the common factor vector f. The steps are as follows:

[0074] Calculate the covariance matrix s of the sample, and its elements are:

[0075]

[0076] Perform eigenvalue decomposition on the sample covariance matrix s and obtain p eigenvalues ​​λ1≥λ2≥...≥λp≥0. The corresponding eigenvalue vectors are γ1,γ2,γp. The eigenvectors of the first m largest eigenvalues ​​can be taken to estimate the factor loading matrix. At the same time, to ensure that the variance of each component of the common factor vector is 1, it needs to be divided by the corresponding standard deviation λj. The corresponding eigenvector γj in the factor loading matrix needs to be multiplied by λj. Therefore, the factor loading matrix can be obtained:

[0077]

[0078] The parameter m is determined by the cumulative variance contribution rate of the common factors, that is,

[0079]

[0080] It is generally believed that when the cumulative variance contribution rate of the first m common factors exceeds 80%, it can be considered that the linear combination of the first m common factors can basically restore the original variable information.

[0081] The common factor vector f, that is, the specific scores of the original variables on the common factors, can be estimated by regression method:

[0082]

[0083] Through the above steps, after obtaining the factor loading matrix and common factor vector, the special factor vector of the original variable can be obtained as follows:

[0084]

[0085] Step 1: Factor suitability test

[0086] The KMO and Bartlett test results are used to determine whether the variables are suitable for factor analysis. The KMO test is used to determine the correlation and partial correlation between variables. The closer the result is to 1, the greater the correlation between the variables, and the greater the role of factor analysis. If the KMO statistic is less than 0.5, it indicates that the data is not suitable for factor analysis. The Bartlett sphericity test can also determine whether there is a correlation between variables. If Sig. < 0.05, it means that there is a correlation between the variables and factor analysis can be performed.

[0087] This step is performed in the SPSS software. Select the water temperature index data of the three reservoirs after construction, select Analysis - Dimensionality Reduction - Factor, and select 28 variables into the variable box.

[0088] Table 2 KMO and Bartlett's test

[0089]

[0090] The KMO test statistic indicates whether the partial correlation between variables is strong enough. As can be seen from the table above, the KMO score is 0.727>0.5, indicating that the overlap of information between variables is acceptable. The Sig. result is 0.000<0.05, indicating that there is a strong correlation between variables, the approximate chi-square is 1937.755, and the df value is 210, so it is considered that the selected data is suitable for factor analysis.

[0091] Step 2: Construct variable factors

[0092] The common factor variance and total variance explanation can be obtained in the SPSS analysis results, and the common factor eigenvalue, variance contribution rate and cumulative contribution rate can be further calculated.

[0093] Common factor variance

[0094] Common factor variance refers to the representativeness of the common factors that can be extracted from the original information contained in each variable. It not only reflects the amount of information contained in each variable, but also reflects the possible connections and differences between the variables, and can be used to measure the similarities or differences between different samples.

[0095] The first column is the variable name, and the second column "Initial" represents the commonality of the variables in the initial solution, that is, the commonality when all variables are considered as common factors, so the value is 1. The third column "Extracted" represents the final commonality of the variables after factor analysis, which refers to the degree of explanation of all common factors on the initial variables. The larger the value, the better the representativeness.

[0096] Table 3 Common factor variance

[0097]

[0098]

[0099] Common factor variance contribution rate and cumulative contribution rate

[0100] The present invention extracts common factors based on the principle of principal component analysis. According to the characteristic value>1, the standard for extracting common factors is that the cumulative contribution rate is above 60%, and the variance contribution rate and cumulative contribution rate of a common factor can be obtained. As can be seen from the table, a total of 5 common factors were selected this time.

[0101] Table 4 Total variance explained

[0102]

[0103] Building the factor loading matrix

[0104] The present invention uses the maximum variance rotation method (varimax) to perform rotation and reassign the relationship between the factors and the original variables, thereby making it easier to explain.

[0105] Table 5 Rotated component matrix

[0106]

[0107] A total of 5 factors were selected for this analysis. Based on the extracted 5 common factors, the contribution rates of the rotated common factors were reduced compared with those before rotation, and the information they carried was redistributed, but the cumulative variance contribution rate remained unchanged. The factor loading coefficient (the factor loading coefficient value indicates the degree of correlation between the analysis item and the factor) is calculated as shown in the table:

[0108] From the rotational loading results, we can see that the absolute values ​​of the factor loading coefficients of the 28 indicators are all greater than 0.4, which means that there is a corresponding relationship between the research items and the factors, and there is a strong correlation.

[0109] For the first factor, the water temperature indicators with larger loads include max_30 / ℃, mean_7 / ℃, max_7 / ℃, Annual_A / ℃, max_90 / ℃, AnnualM / ℃, aug / ℃, jul / ℃, oct / ℃, jun / ℃, MinTCnt / d, sep / ℃, MinTDur / d, may / ℃, mar / ℃, and f1 is named the cooling factor; for the second factor, the water temperature indicators with larger loads include jan / ℃, min_7 / ℃, min_30 / ℃, feb / ℃, min_90 / ℃, dec / ℃, f2 is named as the warming factor; for the third factor, the water temperature indicators with large loads include J_Mean / Julianday, MeanTCnt / d, MeanTDur / d, Annual_t / Julianday, and f3 is named as the water temperature delay factor; for the fourth factor, the water temperature indicators with large loads include apr / ℃, J_Min / Julianday, and f4 is named as the water temperature fluctuation factor; for the fifth factor, the water temperature indicator with large loads is nov / ℃, and f5 is named as the November water temperature variation factor. Compared with before rotation, the meaning of each factor after rotation is clearer, more reasonable, and more conducive to the interpretation and application of variable data.

[0110] Factor scores

[0111] According to the factor loading matrix, the score value of each common factor is obtained. The factor score coefficient matrix is ​​the coefficient of the factor score function calculated by regression.

[0112] Table 6 Component score coefficient matrix

[0113]

[0114]

[0115] According to the component score coefficient matrix, we can get a common factor for the original water temperature ratio index, and its linear calculation model to obtain the score function of each factor:

[0116] F1=0.195x1+0.199x2-0.115x3-0.048x4-0.079x5+0.166x6+0.028x7+0. 166x8+0.173x9+0.189x10+0.192x11+0.167x12+0.175x13+0.014x14-0. 063x15+0.202x16+0.200x17-0.065x18+0.202x19-0.065x20+0.196x21- 0.095x22+0.076x23+0.076x24-0.169x25-0.167x26-0.049x27-0.040x28

[0117] F2=-0.019x1-0.031x2+0.032x3+0.090x4+0.084x5-0.037x6+0.016x7-0 .037x8-0.042x9-0.030x10-0.031x11-0.053x12-0.047x13+0.039x14+0. 073x15-0.010x16-0.028x17+0.088x18-0.026x19+0.088x20-0.033x21+ 0.080x22-0.027x23-0.027x24+0.007x25-0.010x26+0.023x27+0.058x28

[0118] F3=0.005x1+0.003x2-0.014x3-0.004x4-0.005x5+0.007x6+0.001x7+0. 007x8+0.007x9+0.007x10+0.006x11+0.005x12+0.002x13-0.004x14-0. 005x15+0.005x16+0.004x17-0.005x18+0.004x19-0.005x20+0.005x21- 0.005x22+0.019x23+0.019x24-0.003x25-0.005x26-0.019x27-0.006x28

[0119] F4=0.006x1+0.006x2-0.007x3-0.003x4+0.014x5+0.015x6+0.077x7+0. 015x8+0.006x9+0.008x10+0.008x11+0.013x12+0.008x13-0.017x14-0.0 19x15+x0.019x16+0.007x17-0.003x18+0.008x19+0.004x20+0.007x21+ 0.016x22+0.011x23+0.011x24+0.023x25+0.016x26+0.006x27-0.055x28

[0120] F5=0.008x1+0.003x2+0.006x3+0.009+x4+0.009x5-0.021x6-0.008x7-0 .021x8-0.017x9-0.009x10-0.006x11+0.000x12+0.015x13+0.075x14+0. 039x15+0.005x16+0.002x17+0.004x18+0.002x19+0.006x20+0.000x21+ 0.009x22-0.005x23-0.005x24+0.044x25+0.033x26+0.017x27+0.008x28

[0121] Comprehensive evaluation

[0122] Since the five common factors reflect the variation of water temperature discharged from cold region reservoirs from different aspects, but it is difficult to make a comprehensive evaluation using a single common factor, the corresponding variance contribution rate of each common factor is considered as the weight to calculate the score.

[0123] The variance explanation rate after rotation was used for weight calculation. The variance explanation rates of the five common factors after rotation were 24.48%, 6.12%, 14.78%, 25.66%, and 22.04%, respectively. The cumulative variance explanation rate after rotation was 93.08%.

[0124] According to the contribution rate of each common factor in the total variance explanation, the score function rate of downstream water temperature variation evaluation is obtained:

[0125] F=(24.48*F1+6.12*F2+14.78*F3+25.66*F4+22.04*F5) / 93.08

[0126] The expression was used to calculate the annual water temperature variation scores of the reservoir. It was found that when the F value is large, the variation is small; on the contrary, the smaller the F value, the greater the variation. The variation degree is divided into 5 levels according to the score (low impact: 0-20, medium-low impact: 20-40, medium impact: 40-60, medium-high impact: 60-80, high impact: 80-100)

[0127] The comprehensive scores of the reservoirs in each year were calculated and converted into percentages for ease of analysis. The results are shown in the table.

[0128] Table 7 Comprehensive scores of reservoirs in each year

[0129]

[0130]

[0131] The results show that the water temperature change degree of Longyangxia Reservoir is the highest, with the lowest being 48.12% and the highest being 88.32%, all of which are above the moderate impact; except for 1980 when it reached a medium-low impact, the water temperature change degree of Liujiaxia in other years was low, indicating that its water temperature change degree was smaller than that before the reservoir was built; Jiudianxia has a small reservoir capacity, so the impact is low and medium-low, with the maximum impact being 26.37% in 2010.

[0132] F1 is the cooling factor, which reflects the cooling level of the downstream water temperature in spring and summer after the reservoir is put into operation. It is mainly related to the cooling level of water temperature in spring and summer, the maximum values ​​of the 7-, 30-, and 90-day sliding water temperatures, and the longest number of consecutive days when the water temperature exceeds 6°C. The Longyangxia Reservoir has the largest cooling range, followed by Jiudianxia and Liujiaxia.

[0133] F2 is the warming factor, which reflects the level of warming of the downstream water temperature in autumn and winter after the operation of the reservoir. It is mainly related to the degree of water temperature increase in autumn and winter and the minimum values ​​of 7-day and 90-day sliding water temperatures. The warming of Longyangxia Reservoir in autumn and winter is the most significant, but the water temperature changes little in winter after operation, indicating that the water temperature in Longyangxia Reservoir is stable in autumn and winter. The warming of Liujiaxia Reservoir and Jiudianxia Reservoir is small, indicating that the water temperature changes slowly to the natural river water temperature in autumn and winter.

[0134] F3 is the water temperature delay factor, which reflects the delay caused by the reservoir on the temporal characteristics of the river water temperature, which in turn affects the water temperature identification signal of aquatic organisms in the river and has a certain impact on the growth and reproduction of aquatic organisms. It mainly includes the annual water temperature amplitude, the delay of the water temperature peak, and the time when the 7-day sliding water temperature exceeds 10 degrees. The arrival time of the water temperature peak of the Longyangxia Reservoir is significantly different from the natural water temperature peak. The arrival time of the water temperature peak of the Liujiaxia and Jiudianxia reservoirs is not much different from the water temperature in the natural state, but there is a delay. This shows that after the reservoir is put into operation, the water temperature state of the river is not suitable for the growth and reproduction of fish.

[0135] F4 is the water temperature fluctuation factor, which reflects the temporal fluctuation characteristics of the water temperature threshold of the river under the influence of the reservoir, which will affect the reproduction and growth of fish and other aquatic organisms. It mainly includes the water temperature variation in April and the time when the daily water temperature reaches 6°C. In April, the water temperature of the reservoir reached a uniform mixing state. The water temperature of the river under the influence of different reservoirs was relatively stable, reflecting that the downstream water temperature fluctuated little when the reservoir transitioned from mixing to stratification in winter. In terms of the time when the daily water temperature reached 6°C, Longyangxia was also the most affected, while Liujiaxia and Jiudianxia reservoirs were less affected.

[0136] F5 is the water temperature variation factor in November, reflecting the variation characteristics of the reservoir in November. The maximum temperature rise of the three reservoirs occurred in November, and the water temperature of the river increased significantly. Among them, the water temperature of Longyangxia Reservoir reached more than 2 times that before water storage, and the water temperature of Liujiaxia and Jiudianxia also increased significantly.

[0137] It should be noted that:

[0138] In the description provided herein, a large number of specific details are described. However, it is understood that the embodiments of the present application can be practiced without these specific details. In some instances, well-known structures and technologies are not shown in detail so as not to obscure the understanding of this description.

[0139] Furthermore, those skilled in the art will appreciate that although some embodiments described herein include certain features included in other embodiments but not other features, the combination of features from different embodiments is meant to be within the scope of the present application and to form different embodiments.

[0140] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for studying the variation of discharge water temperature of high dam reservoirs in cold regions based on factor analysis, characterized in that: include: Construct a water temperature index system; Select the research area, obtain the raw data, and pre-process the raw data; The original data were normalized to zero mean to obtain valid data; Factor analysis method is used to evaluate the variability of the downstream water temperature of the reservoir.

2. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 1 is characterized in that: The water temperature index system is constructed as follows: The deviation of water temperature from the baseline level is taken as the factor affecting the reservoir's impact on river water temperature. The statistical indicators of natural changes in river thermal conditions are used as the basis for the water temperature baseline. The river water temperature indicators are divided into annual water temperature statistics, monthly average water temperature, the amount and duration of extreme water temperature, the frequency and duration of exceeding the water temperature threshold, and the time of occurrence of the water temperature threshold.

3. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 2 is characterized in that: The annual water temperature statistics include: annual average water temperature, annual water temperature amplitude, and the time of occurrence of water temperature peak; The monthly average water temperature is the monthly average water temperature from January to December; The amount and duration of extreme water temperatures include: the annual average of the 7-day sliding average water temperature, the minimum values ​​of the 7-day, 30-day, and 90-day sliding average water temperature, and the maximum values ​​of the 7-day, 30-day, and 90-day sliding average water temperature; The frequency and duration of exceeding the water temperature threshold include: the number of days when the 7-day sliding average water temperature exceeds 10°C and the longest consecutive days when the 7-day sliding average water temperature exceeds 10°C, the number of days when the 7-day sliding average water temperature exceeds 6°C and the longest consecutive days when the 7-day sliding average water temperature exceeds 6°C The occurrence times of the triggering water temperature threshold include: the time when the daily water temperature reaches 10℃ and the time when the daily water temperature reaches 6℃.

4. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 1 is characterized in that: The selected research area, obtaining the raw data, and preprocessing the raw data include: The high dam reservoir in the cold region is taken as the research area, and the downstream water temperature of the reservoir is taken as the original data; The range of water temperature is determined based on the statistical characteristics of historical data, and invalid data in the original data is eliminated.

5. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 1 is characterized in that: The zero-mean normalization of the raw data to obtain valid data includes: The mean of each variable is adjusted to 0 and the standard deviation is adjusted to 1. The standardized formula is: Among them, X is the original data, μ is the mean, and σ is the standard deviation.

6. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 1 is characterized in that: The evaluation of the variability of the downstream water temperature of the reservoir by using the factor analysis method includes: The valid data were subjected to KMO test and Bartlett sphericity test, and the KMO value of the valid data was calculated. When the KMO value was greater than 0.6, the river water temperature index corresponding to the cumulative variance rate after rotation was selected, and the corresponding river water temperature index was used as the common factor; when the KMO value was less than or equal to 0.6, the approximate chi-square dfp value was calculated. When the approximate chi-square dfp value was less than 0.05, the river water temperature index corresponding to the cumulative variance rate after rotation was selected, and the corresponding river water temperature index was used as the common factor.

7. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 6 is characterized in that: For each common factor, the load coefficients of all the corresponding factors are calculated respectively to obtain the factor load coefficient values ​​of all the common factors. The factor load coefficient values ​​with absolute values ​​greater than 0.6 are used to obtain the rotated factor score matrix using the maximum variance method, and the factor calculation model is obtained based on the factor score matrix.

8. The method for studying the variation degree of discharge water temperature of high dam reservoirs in cold regions based on factor analysis according to claim 7 is characterized in that: Based on the factor calculation model, the comprehensive score of the reservoir to be evaluated on all the common factors is calculated, and the weight is calculated using the variance explanation rate value after rotation, so as to obtain the weights of all the common factors; The degree of variability of the water temperature discharged from the reservoir is obtained based on the weights of all the common factors.

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