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Code and Data description: Code was implemented in Wolfram Mathematica. Functions are written in Wolfram Language Package files (.wl) and they are executed in Notebook files (.nb). Folder **code**: **L05III.wl** 1. **Filter**: function for expressing the variables (Eqs. (13)-(14)). 2. **L05III**: L05-3 system (Eq. (12)). 3. **PPL05III**: function for calculating initial conditions of L05-3 system (fourth-order Runge-Kutta method). **L05III0.wl** 1. **L05III0**: L05-3 system (Eq. (12)) with initial errors. 2. **PPL05III0**: function for calculating initial conditions of L05-3 system with initial errors (fourth-order Runge-Kutta method). **AnsambleL05III.wl** 1. **Ansamble1III**: Calculation of "reality" of L05-3 system (fourth-order Runge-Kutta method). 2. **Ansamble2III**: Calculation of "prediction" of L05-3 system (fourth-order Runge-Kutta method). 3. **PrumerGeoIII**: Calculation of average initial error growth (Eq. (16)). 4. **RustCasIII**: Calculation of Fig. 2b and 3b. 5. **RustDerLyap3III**: Calculation of Fig. 2a, 3a, 4a, 4b and 4c. 6. **RustDerLyap4III**: Calculation of Fig 4d. 7. **AproxRustCasIII**: Numerical solution of Eq. (19) (fourth-order Runge-Kutta method). 8. **AproxRustCasLnIII**: Numerical solution of Eq. (20) (fourth-order Runge-Kutta method). **ECMWF.wl** 1. **RustCasECMWFPPP**: Calculation of Fig. 5b and 5d. 2. **RustLjapECMWFPP**: Calculation of Fig. 5a and 5c. 3. **RustGraf**: Calculation of Fig. 6 - Fig. 8. Folder **Data/ECMWF**: 1. **ECMWFPPjg.wl**: data set (Fig. 5). 2. **aPowerLaw.wl**: data set (Fig. 6a). 3. **bPowerLaw**: data set (Fig. 6b). 4. **LjapKvModelNew.wl**: data set (Fig. 7a - blue curve). 5. **LjapPrum.wl**: data set (Fig. 7a - black curve). 6. **betaKvModel**:data set (Fig. 7b). 7. **ElimKvModelNew.wl**: data set (Fig. 8 - blue curve). 8. **ElimPowerLaw.wl**: data set (Fig. 8 - red curve). 9. **ElimPrum**: data set (Fig. 8 - black curve). Folder **Data/L05**: 1. **PPIII390.wl**: initial condition - L05-3 system (Eq. (12)). 2. **Egeo39002.wl**: average initial error growth (Eq. (16)). Folder **Figs**: Procedures for displaying Fig. 1 - 9.