According to the overall structure diagram are shown in figure 1 below the system analysis, to the prediction equation of acquired data in the analysis of the orderly use of analysis, and to use information technology to develop a variety of prediction methods, only in this way can more accurately forecast the dynamic change of groundwater, and the relationship between the period of dynamic change and climate^{[1]}.

The statistical relationship between forecast objects and forecast factors presents diversity, common types include hyperbolic function, trigonometric function, power function and linearity. This paper mainly discusses four types: first, it refers to the type of linear function, and the corresponding formula is shown as follows:

The second is for the exponential function type, the corresponding function is as follows:

Again, the power function type, the corresponding function is as follows:

Finally refers to the type of exponential function, the corresponding function is as follows:

The corresponding coefficients of the four function relations are calculated respectively for the forecast factor XI and the forecast quantity Yi. The maximum absolute value of the correlation coefficient is the optimal function type of the forecast factor. The prediction equation constructed by this function type belongs to nonlinear prediction equation.

Since the logarithmic function and power function put forward x>0, range normalization should be implemented for the numerical value of the forecast factor first, and the corresponding formula is shown as follows:

In cases where the condition

The calculation formula of correlation coefficient is as follows:

In the case of calculating linear function types, we can get:

In the case of calculating the logarithmic function type, it can be obtained:

In the case of calculating the power function type, we can get:

In the case of calculating the type of exponential function, it can be obtained:

The maximum value calculated according to the target function, and clear after the alpha numeric parameters, to compute about | R3, | | R4 |, contrast analysis | R1, | | and | | R2 and R3, | | R4 | the size of the four values, and combining the maximum value choice of function types to build optimization equation.

The parameter α evaluation problem is the nonlinear function optimization problem. At present, there is no unified method for solving nonlinear differential equations, and different types of nonlinear equations need to choose different application algorithms. Due to the complexity of function derivation in the early stage, this paper chooses quadratic difference method for trial calculation^{[3]}.

In the above formula, xk and xj represent the number of observations in the KTH and JTH years, and the condition that J Thus, it can be obtained:

Thus, when n>10 meets this condition, the standard normal statistical variable Z can be calculated and analyzed using the following formula:

_{1 − a / 2} ≤ _{1 − a / 2} is met, the original hypothesis can be accepted. On the contrary, _{1 − a / 2} proves that the sequence has an obvious downward trend, _{1 − a / 2} indicates that the sequence has an obvious upward trend, and α represents the significance level.

In this paper, according to the groundwater level presumption method, GIS technology is used as an analysis tool, kriging method is used to draw the water level change map in the study area, and the spatial difference method is used to explore the hydrometeorological evolution law in the region. Common methods are as follows:

First, inverse distance weighted difference method. This method will predict the values of other regions based on the values of the identified sample points within the prediction region. Generally speaking, the weight of the known sample closer to the prediction point will exceed the weight of the known sample far from the prediction point during the prediction period, and the corresponding formula is shown as follows^{[4]}:

In the above formula,

In the above formula, P represents the parameter, and the optimal value can be determined by taking the minimum value of mean square and prediction error. Di0 represents the distance between the predicted point, S0 and the known sample point Si.

Second, spline difference method. This method Kriger, the application principle of this method is as follows:

Suppose the research area contains N observation points X1, X2... XN, the corresponding variable value is Z (xi), and the estimation of the real value of the waiting prediction point x0

In the above formula, represents the weight value of the ith side point to the waiting detection point, which meets the condition

The above formula proves that the selection and calculation of weights directly affect the estimated value of waiting measurement points. Therefore, the weight calculation ensures that the estimator complies with the following criteria:

At the same time, the Lagrange multiplier method should be used to ensure that the estimator

In the above formula,

In the above formula,
_{1}(

According to the dynamic characteristics of regional water conservancy and meteorology, the discrete data are used to simulate and analyze. The time interval of discrete data affects the closeness of the sequence. All time series models are composed according to trend, period and random noise. It is assumed that H (t) represents the observation sequence of actual groundwater level, and the overall number of selected samples is N, then it can be obtained^{[5]}:

In the above formula, H (t) represents the dynamic observation series of groundwater level, T (t) represents the trend term, P (t) represents the periodic term, and R (t) represents the random term. Specific analysis is as follows:

First, the trend term. In the empirical study, it is found that the trend term is usually regarded as a real-valued function of time T. Since the overall development trend of water level change is definite, polynomial approximation as follows can be used:

At the same time, the undetermined coefficients c0, C1… were determined by multiple regression method., ck and order K. In order to verify the fitting results, correlation coefficient R of trend curve fitting should be studied, and the specific formula is shown as follows:

In the above formula, n represents the total number of actual measured sequence H (t), and represents the average value of sequence H (t). The closer the calculation result of the above formula is to 1, the closer the linear relation between T' (T) and TK is proved. In the case of definite reliability and degree of freedom, when the value R exceeds the critical value, the regression equation has application value. Second, the period term. This sequence is represented by the superposition of K waves, and the corresponding estimation formula is shown as follows:

In the above formula, k represents the number of harmonics, usually the integer part of N /2; J is regarded as wave number, and it is generally considered that k partial waves each contain n/1, n/2... N/k cycles, in other words, the frequency of the JTH component wave is J /n; A0, AJ and BJ represent The Fourier coefficients, and the actual calculation formula is as follows:

Third, the random term. Autoregressive model was used for solving and analysis, and the corresponding model formula is shown as follows:

In the above formula, p represents the model order, φ I represents the model autoregression coefficient, and is consistent with I = 1, 2… P. For an autoregressive model of a certain order, the autoregressive coefficient φ I can be obtained by similar multiple regression calculation. This paper uses the AIC criterion to clarify the model order, as shown below:

Fourth, accuracy test. By linear superposition of the three components of the above study, the overall prediction model of regional water level change and climate dynamic change can be obtained, as shown below:

The actual prediction accuracy can be analyzed by posterior error method. Assuming that the dynamic sampling sample of actual measurement is: _{1}, _{2}, …, _{n}_{n}_{+ 1}, …, _{n + k}_{1}, The prediction equation obtained by using the first n sampling values is H' (t), _{n}_{+1} ~ _{n + k}_{1} the prediction value at the hypothetical time is

Assuming that the standard deviation of the first n data in the dynamic sample is S1 and the standard deviation of the posterior data residual is S2, the posterior error ratio and small error frequency can be calculated as follows:

The evaluation criteria of forecast accuracy are shown in the following table:

Prediction accuracy evaluation standard table

Forecast level | good | good | qualified | unqualified |
---|---|---|---|---|

p | >0.95 | >0.80 | >0.70 | ≤0.70 |

c | <0.35 | <0.50 | <0.65 | ≥0.65 |

Assuming that both p and C values are within the specified range, the model can analyze and predict regional water level changes and climate dynamics; otherwise, the model needs to be checked and adjusted. After the model is qualified, it is necessary to simulate the sequence randomly, mainly using the long and short series method to judge the practicality of the model.^{[6]}

In order to construct the time series model, it is necessary to make up some missing data by means of regression analysis to obtain the corresponding observation series, and then analyze the trend term, periodic term and random term, and get the time series model of different stations in the linear superposition, so as to provide mathematical basis for the study of dynamic change.

Combined with the above research methods, the prediction and analysis of groundwater level and climate change in a certain region can be obtained as shown in the following table. Table 2 refers to the calculation results of trend term, Table 3 refers to the calculation results of Fourier coefficient of periodic term, and Table 4 refers to the coefficient analysis results of autoregressive model:

Calculation results of trend items

_{0} |
_{1} |
_{2} |
The correlation coefficient |
---|---|---|---|

414.85 | −0.2416 | 0.0014 | 0.9289 |

Calculation results of Fourier coefficients of periodic term

k | _{k} |
_{k} |
---|---|---|

10 | −0.0616 | 0.5846 |

Coefficient analysis results of autoregressive model

Φ_{0} |
Φ_{1} |
Φ_{2} |
---|---|---|

−0.428 | 0.007 | 0.645 |

The analysis process of the autoregressive model of water level is shown in Figure 2 below:

According to the overall prediction model constructed by the above research, the variation of groundwater level is calculated, and the fitting analysis is carried out according to the actual measured values. According to the above analysis, it is found that the fitting effect between calculated predicted values and measured values is relatively high. The specific comparison results are shown in Table 5 below^{[7.8]}:

Comparison results between measured and predicted values in the study area

In | The measured values | Predictive value | Absolute error | The relative error |
---|---|---|---|---|

In January | 407.08 | 408.0688 | −0.99 | 0.24% |

On February | 406.95 | 408.40079 | −1.45 | 0.36% |

march | 409.92 | 408.35768 | 1.56 | 0.38% |

April | 409.85 | 410.09384 | −0.24 | 0.06% |

On may | 409.82 | 409.95276 | −0.13 | 0.03% |

June | 409.93 | 409.82807 | 0.10 | 0.02% |

In July | 409.97 | 409.83206 | 0.14 | 0.03% |

In August | 410.00 | 409.87908 | 0.12 | 0.03% |

On September | 409.95 | 410.02388 | −0.07 | 0.02% |

On October | 409.85 | 410.21619 | −0.37 | 0.09% |

In November, | 409.80 | 410.4408 | −0.64 | 0.16% |

On December | 409.73 | 410.70923 | −0.98 | 0.24% |

According to the analysis in the above table, there is a large gap between the values predicted at the beginning of the year and those predicted at the end of the year, and the trend in the time series prediction shows a downward trend due to the rise of water level. However, the relative error between the two is controlled within the specified range, and the actual test results are good. At the same time, the final results show that the relationship between climate dynamics and regional water level changes is very close. Climate factors themselves change very rapidly and are cyclical in a sense, causing rapid changes in water level dynamics. In the study period of one year, all kinds of climate will follow the seasonal changes in a regular cycle, which will be evident in the dynamic composition of the shallow groundwater. It can be seen that the seasonal and multi-year changes of groundwater dynamics are affected by meteorological factors.

In conclusion, the systematic study of regional water level change and climate dynamic change by using forecast equation can strengthen resource construction and management in China and scientifically deal with the relationship between climate dynamic change and regional water level on the basis of solving the problem of water resource shortage. Therefore, in the context of the new era, facing the increasing demand for water resources, researchers should strengthen their research efforts and use information technology to build a forecast and analysis system, so that they can not only master more accurate and perfect data information, but also have a deep understanding of the relationship between climate dynamics and regional water level changes^{[9]}.

#### Calculation results of Fourier coefficients of periodic term

k | _{k} |
_{k} |
---|---|---|

10 | −0.0616 | 0.5846 |

#### Coefficient analysis results of autoregressive model

Φ_{0} |
Φ_{1} |
Φ_{2} |
---|---|---|

−0.428 | 0.007 | 0.645 |

#### Calculation results of trend items

_{0} |
_{1} |
_{2} |
The correlation coefficient |
---|---|---|---|

414.85 | −0.2416 | 0.0014 | 0.9289 |

#### Prediction accuracy evaluation standard table

Forecast level | good | good | qualified | unqualified |
---|---|---|---|---|

p | >0.95 | >0.80 | >0.70 | ≤0.70 |

c | <0.35 | <0.50 | <0.65 | ≥0.65 |

#### Comparison results between measured and predicted values in the study area

In | The measured values | Predictive value | Absolute error | The relative error |
---|---|---|---|---|

In January | 407.08 | 408.0688 | −0.99 | 0.24% |

On February | 406.95 | 408.40079 | −1.45 | 0.36% |

march | 409.92 | 408.35768 | 1.56 | 0.38% |

April | 409.85 | 410.09384 | −0.24 | 0.06% |

On may | 409.82 | 409.95276 | −0.13 | 0.03% |

June | 409.93 | 409.82807 | 0.10 | 0.02% |

In July | 409.97 | 409.83206 | 0.14 | 0.03% |

In August | 410.00 | 409.87908 | 0.12 | 0.03% |

On September | 409.95 | 410.02388 | −0.07 | 0.02% |

On October | 409.85 | 410.21619 | −0.37 | 0.09% |

In November, | 409.80 | 410.4408 | −0.64 | 0.16% |

On December | 409.73 | 410.70923 | −0.98 | 0.24% |

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learning system under the background of artificial intelligence Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Research on threat assessment problems of island air defence system based on the leader-follower model Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Decisions of competing supply chain with altruistic retailer 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