Research On The Influence Of Exogenous Forcing Strength On The Predictability Of Initial Values

(1)To explore the predictability of the initial value of the Lorenz system constructed under different external forcings by adjusting the parameter value r that characterizes the external forcing in the Lorenz model,and using the explicit fourthorder Runge-Kutta method.It is concluded that the predictability of the initial value decreases and the error growth increases,so the forecast period is shortened,the forecast effect is worse,and the system is more sensitive to the initial value with the increase of external forcing.The correlation coefficient between the initial value and its superimposed small deviation has three sudden decrease with the increase of external forcing.In the picture of simulated Lorenz system motion trajectory,the strange attractor of the Lorenz system changes from one to two,and the surface around the strange attractor also evolves from one to two,and Chaos phenomenon appears.The variance of the X,Y,and Z values;the number of steps in which the X value and the Y value exceed one standard deviation show an upward trend with the increase of external forcing.The increase in external forcing also reduces the number of integration steps of differentiation and the first reversal used in the Lorenz system,and the parallel time of the two sets of data is shorter and shorter.By counting the number of integration steps in the error range in 5%?10%?20% of X,Y,and Z values,it is found that the error growth of the system increases with the increase of external forcing.It is no longer within a reasonable range,so the predictability of the initial value is reduced and the forecast period is greatly shortened.(2)Using the WRF mode to simulate four sets of tests based on whether external forcing is increased and whether initial disturbances are superimposed and selecting a region in the main body of the plateau to perform regional average of the test data,it was found that the correlation coefficients of each physical quantity in two sets of tests with increasing external forcing(variable was whether to superimpose initial perturbations)were reduced to a different extent than the correlation coefficients in two sets of tests without changing external forcing(variable was whether to superimpose initial perturbations).Defining the deviation method,and calculating the deviation of the two sets of tests with increasing external forcing(variable was whether to superimpose initial perturbations)and two sets of tests without changing external forcing(variable was whether to superimpose initial perturbations),it is found that the absolute value of the difference between these two deviations shows an upward trend over time in all simulation times.Defining the error percentage method,analyzing the change range of each physical quantity values in the two sets of tests with increasing external forcing(variable was whether to superimpose initial perturbations)and two sets of tests without changing external forcing(variable was whether to superimpose initial perturbations)comprehensively,counting the frequency of occurrence of each physical quantity in different ranges of variation within all simulation times,it is found that the frequency of each physical quantity decreased within their respective small change ranges,and the frequency of their physical changes significantly increased within their respective large change ranges after increasing exogenous forcing.This shows that the increasing external forcing causes the initial disturbance to change significantly after a certain period of integration,as a result,the correlation coefficient of each physical quantity decreases;the deviation of each physical quantity shows a clear upward trend;the frequency of large errors in each physical quantity increases,and the overall error increases.As a result,the accuracy of the system's forecast is reduced,and the forecast results become worse,and the predictability of the initial value is reduced.And it leads to the forecast accuracy of the system reduced,the forecast results becoming worse,and the predictability of the initial value of the system reduced.(3)After using the WRF mode to average the data for the first 30 days of the simulation,and then analyze the variation characteristics of each physical quantity in the plateau by using the deviation method.At the beginning of the model simulation,the magnitude of the deviation of each element at 500 h Pa height and the ground layer is almost negligible.After a long time integration,the magnitude of the deviation is gradually enlarged,and some relatively large value areas appear randomly,and the value in the large value area is exceeding the reasonable range of the error.Analyzing the change characteristics of each physical quantity in the plateau by using the percentage of error method,the value of the percentage of error of each element at500 h Pa height and the ground layer increases significantly,and the area with a larger percentage of error is further expanded after increasing external forcing.Each physical quantity gradually changed from being mainly affected by initial disturbances at the beginning of the simulation to being affected by external forcing.The system gradually changed from being adapted to initial value to being adapted to external source forcing,and it reduces the accuracy of the system forecast,and the forecast results gradually deviate from the reasonable range,and the predictability of the initial value is greatly reduced,and the predictable period is greatly shortened.