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.
