Library

const _EXPONENTIAL_ATMOSPHERE_H

Scale height for the exponential atmospheric model [km].

const _EXPONENTIAL_ATMOSPHERE_H₀

Base altitude for the exponential atmospheric model [km].

const _EXPONENTIAL_ATMOSPHERE_ρ₀

Nominal density for the exponential atmospheric model [kg / m³].

Harris-Priester min-max density (kg/m³) vs. altitude (m) table. These data are valid for a mean solar activity.

const _JR1971_CONSTANTS

Constants for the Jacchia-Roberts 1971 atmospheric model.

const _JR1971_ROOT_GUESS

First guess to compute the roots of a polynomial to find the density below 125 km.

struct JB2008Output{T<:Number}

Output of the atmospheric model Jacchia-Bowman 2008.

Fields

• total_density::T: Total atmospheric density [1 / m³].
• temperature::T: Temperature at the selected position [K].
• exospheric_temperature::T: Exospheric temperature [K].
• N2_number_density::T: Number density of N₂ [1 / m³].
• O2_number_density::T: Number density of O₂ [1 / m³].
• O_number_density::T: Number density of O [1 / m³].
• Ar_number_density::T: Number density of Ar [1 / m³].
• He_number_density::T: Number density of He [1 / m³].
• H_number_density::T: Number density of H [1 / m³].

struct JR1971Output{T<:Number}

Output of the atmospheric model Jacchia-Roberts 1971.

Fields

• total_density::T: Total atmospheric density [1 / m³].
• temperature::T: Temperature at the selected position [K].
• exospheric_temperature::T: Exospheric temperature [K].
• N2_number_density::T: Number density of N₂ [1 / m³].
• O2_number_density::T: Number density of O₂ [1 / m³].
• O_number_density::T: Number density of O [1 / m³].
• Ar_number_density::T: Number density of Ar [1 / m³].
• He_number_density::T: Number density of He [1 / m³].
• H_number_density::T: Number density of H [1 / m³].

struct Nrlmsise00Flags

Flags to configure NRLMSISE-00.

Fields

• F10_Mean::Bool: F10.7 effect on mean.
• time_independent::Bool: Independent of time.
• sym_annual::Bool: Symmetrical annual.
• sym_semiannual::Bool: Symmetrical semiannual.
• asym_annual::Bool: Asymmetrical annual.
• asyn_semiannual::Bool: Asymmetrical semiannual.
• diurnal::Bool: Diurnal.
• semidiurnal::Bool: Semidiurnal.
• daily_ap::Bool: Daily AP.
• all_ut_long_effects::Bool: All UT/long effects.
• longitudinal::Bool: Longitudinal.
• ut_mixed_ut_long::Bool: UT and mixed UT/long.
• mixed_ap_ut_long::Bool: Mixed AP/UT/long.
• terdiurnal::Bool: Terdiurnal.
• departures_from_eq::Bool: Departures from diffusive equilibrium.
• all_tinf_var::Bool: All TINF variations.
• all_tlb_var::Bool: All TLB variations.
• all_tn1_var::Bool: All TN1 variations.
• all_s_var::Bool: All S variations.
• all_tn2_var::Bool: All TN2 variations.
• all_nlb_var::Bool: All NLB variations.
• all_tn3_var::Bool: All TN3 variations.
• turbo_scale_height::Bool: Turbo scale height variations.

struct Nrlmsise00Output{T<:Number}

Output structure for NRLMSISE00 model.

Fields

• total_density::T: Total mass density [kg / m³].
• temperature: Temperature at the selected altitude [K].
• exospheric_temperature: Exospheric temperature [K].
• N_number_density: Nitrogen number density [1 / m³].
• N2_number_density: N₂ number density [1 / m³].
• O_number_density: Oxygen number density [1 / m³].
• aO_number_density: Anomalous Oxygen number density [1 / m³].
• O2_number_density: O₂ number density [1 / m³].
• H_number_density: Hydrogen number density [1 / m³].
• He_number_density: Helium number density [1 / m³].
• Ar_number_density: Argon number density [1 / m³].

Remarks

Anomalous oxygen is defined as hot atomic oxygen or ionized oxygen that can become appreciable at high altitudes (> 500 km) for some ranges of inputs, thereby affection drag on satellites and debris. We group these species under the term Anomalous Oxygen, since their individual variations are not presently separable with the drag data used to define this model component.

struct Nrlmsise00Structure{T<:Number, T_AP<:Union{Number, AbstractVector}}

Structure with the configuration parameters for NRLMSISE-00 model. T is the floating-number type and T_AP is the type of the AP information, which can be a Number or AbstractVector.

_ccor(h::T, r::T, h₁::T, zh::T) where T<:Number -> T

Compute the chemistry / dissociation correction for MSIS models.

Arguments

• h::Number: Altitude.
• r::Number: Target ratio.
• h₁::Number: Transition scale length.
• zh::Number: Altitude of 1/2 r.

_ccor2(alt::T, r::T, h₁::T, zh::T, h₂::T) where T<:Number -> T

Compute the O and O₂ chemistry / dissociation correction for MSIS models.

Arguments

• h::Number: Altitude.
• r::Number: Target ration.
• h₁::Number: Transition scale length.
• zh::Number: Altitude of 1/2 r.
• h₂::Number: Transition scale length 2.

_densm(h::T, d0::T, xm::T, tz::T, r_lat::T, g_lat::T, tn2::NTuple{N2, T}, tgn2::NTuple{2, T}, tn3::NTuple{N3, T}, tgn3::NTuple{2, T}) where {N2<:Interger, N3<:Integer, T<:Number} -> float(T), float(T)

Compute the temperature and density profiles for the lower atmosphere.

Arguments

• h::T: Altitude [km].
• d₀::T: Reference density, returned if h > _ZN2[1].
• xm::T: Species molecular weight [ ].
• g_lat::T: Reference gravity at desired latitude [cm / s²].
• r_lat::T: Reference radius at desired latitude [km].
• tn2::NTuple{N2, T}: Temperature at the nodes for ZN2 scale [K].
• tgn2::NTuple{N2, T}: Temperature gradients at the end nodes for ZN2 scale.
• tn3::NTuple{N3, T}: Temperature at the nodes for ZN3 scale [K].
• tgn3::NTuple{N3, T}: Temperature gradients at the end nodes for ZN3 scale.

Returns

• T: Density [1 / cm³] is xm is not 0, or the temperature [K] otherwise.

_densu(h::T, dlb::T, tinf::T, tlb::T, xm::T, α::T, zlb::T, s2::T, g_lat::T, r_lat::T, tn1::NTuple{5, T}, tgn1::NTuple{2, T}) where T<:Number -> T, NTuple{5, T}, NTuple{2, T}

Compute the density [1 / cm³] or temperature [K] profiles according to the new lower thermo polynomial.

Arguments

• h::T: Altitude [km].
• dlb::T: Density at lower boundary [1 / cm³].
• tinf::T: Exospheric temperature [K].
• tlb::T: Temperature at lower boundary [K].
• xm::T: Species molecular weight [ ].
• α::T: Thermal diffusion coefficient.
• zlb::T: Altitude at lower boundary [km].
• s2::T: Slope.
• g_lat::T: Reference gravity at the latitude [cm / s²].
• r_lat::T: Reference radius at the latitude [km].
• tn1::NTuple{5, T}: Temperature at nodes for ZN1 scale [K].
• tgn1::NTuple{2, T}: Temperature gradients at end nodes for ZN1 scale.

Returns

• T: Density [1 / cm³] is xm is not 0, or the temperature [K] otherwise.
• NTuple{5, T}: Updated tn1.
• NTuple{2, T}: Updated tgn1.

_dnet(dd::T, dm::T, zhm::T, xmm::T, xm::T) where T<:Number -> T

Compute the turbopause correction for MSIS models, returning the combined density.

Arguments

• dd::T: Diffusive density.
• dm::T: Full mixed density.
• zhm::T: Transition scale length.
• xmm::T: Full mixed molecular weight.
• xm::T: Species molecular weight.

_get_doy(jd::Number) -> Number

Return the day of the year for the Julian day jd.

_glob7s(nrlmsise00d::Nrlmsise00Structure{T}, p::AbstractVector{T}) where T<:Number -> T

Compute the function G(L) with lower atmosphere parameters p and the NRLMSISE-00 structure nrlmsise00d.

_globe7(nrlmsise00d::Nrlmsise00Structure{T}, p::AbstractVector{T}) where T<:Number -> Nrlmsise00Structure{T}, T

Compute the function G(L) with upper thermosphere parameters p and the NRLMSISE-00 structure nrlmsise00.

Returns

• Nrlmsise00Structure{T}: Modified structure nrlmsise00d.
• T: Result of G(L).

_gravity_and_effective_radius(ϕ_gd::T) where T<:Number -> T, T

Compute the gravity [cm / s²] and effective radius [km] at the geodetic latitude ϕ_gd [°].

_gtd7(nrlmsise00d::Nrlmsise00Structure{T}) where T<:Number -> Nrlmsise00Structure{T}, Nrlmsise00Output{T}

Compute the temperatures and densities using the information inside the structure nrlmsise00d without including the anomalous oxygen in the total density.

Returns

• Nrlmsise00Structure{T}: Modified structure nrlmsise00d.
• Nrlmsise00Output{T}: Structure with the output information.

_gtd7d(nrlmsise00d::Nrlmsise00Structure{T}) where T<:Number -> Nrlmsise00Structure{T}, Nrlmsise00Output{T}

Compute the temperatures and densities using the information inside the structure nrlmsise00d including the anomalous oxygen in the total density.

Returns

• Nrlmsise00Structure{T}: Modified structure nrlmsise00d.
• Nrlmsise00Output{T}: Structure with the output information.

_gts7(nrlmsise00d::Nrlmsise00Structure{T}) where T<:Number -> Nrlmsise00Structure{T}, Nrlmsise00Output{T}

Compute the temperatures and densities using the information inside the structure nrlmsise00d and including the anomalous oxygen in the total density for altitudes higher than 72.5 km (thermospheric portion of NRLMSISE-00).

Returns

• Nrlmsise00Structure{T}: Modified structure nrlmsise00d.
• Nrlmsise00Output{T}: Structure with the output information.

_g0(a::Number, p::AbstractVector)

Compute g₀ function (see Eq. A24d) using the coefficients abs_p25 = abs(p[25]) and p26 = p[26].

_scale_height(h::T, xm::T, temp::T, g_lat::T, r_lat::T) where T<:Number -> T

Compute the scale height.

Arguments

• h::T: Altitude [km].
• xm::T: Species molecular weight [ ].
• temp::T: Temperature [K].
• g_lat::T: Reference gravity at desired latitude [cm / s²].
• r_lat::T: Reference radius at desired latitude [km].

_sg₀(ex::Number, ap::AbstractVector, abs_p25::Number, p26::Number)

Compute the sg₀ function (see Eq. A24a) using the ap vector and the coefficients abs_p25 and p26.

_spline(x::NTuple{N, T}, y::NTuple{N, T}, ∂²y::NTuple{N, T}, xᵢ::T) where {N, T<:Number} -> float(T)

Compute the interpolation of the cubic spline y(x) with second derivatives ∂²y at xᵢ.

Arguments

• x::NTuple{N, T}: X components of the tabulated function in ascending order.
• y::NTuple{N, T}: Y components of the tabulated function evaluated at x.
• ∂²y::NTuple{N, T}: Second derivatives of y(x) ∂²y/∂x² evaluated at x.
• xᵢ::T: Point to compute the interpolation.

_spline_∂²(x::NTuple{N, T}, y::NTuple{N, T}, ∂²y₁::T, ∂²yₙ::T) where {N, T<:Number} -> NTuple{N, T}

Compute the 2nd derivatives of the cubic spline interpolation y(x) given the 2nd derivatives at x[1] (∂²y₁) and at x[N] (∂²yₙ). This functions return a tuple with the evaluated 2nd derivatives at each point in x.

Arguments

• x::NTuple{N, T}: X components of the tabulated function in ascending order.
• y::NTuple{N, T}: Y components of the tabulated function evaluated at x.
• ∂²y₁::T: Second derivative of y(x) ∂²y/∂x² evaluated at x[1].
• ∂²yₙ::T: Second derivative of y(x) ∂²y/∂x² evaluated at x[N].

_spline_∫(x::NTuple{N, T}, y::NTuple{N, T}, ∂²y::NTuple{N, T}, xf::Number) where {N, T<:Number} -> float(T)

Compute the integral of the cubic spline function y(x) from x[1] to xf, where the function second derivatives evaluated at x are ∂²y.

Arguments

• x::NTuple{N, T}: X components of the tabulated function in ascending order.
• y::NTuple{N, T}: Y components of the tabulated function evaluated at x.
• ∂²y::NTuple{N, T}: Second derivatives of y(x) ∂²y/∂x² evaluated at x.
• xf::Number: Abscissa endpoint for integration.

_ζ(r_lat::Number, zz::Number, zl::Number) -> Number

Compute the zeta function.

exponential(h::Number) -> Float64

Compute the atmospheric density [kg / m³] at the altitude h [m] above the ellipsoid using the exponential atmospheric model:

                ┌            ┐
                │    h - h₀  │
ρ(h) = ρ₀ . exp │ - ──────── │ ,
                │      H     │
                └            ┘

in which ρ₀, h₀, and H are parameters obtained from tables that depend only on h.

harrispriester(instant::DateTime, ϕ_gd::Number, λ::Number, h::Number; kwargs...) -> Float64
harrispriester(jd::Number, ϕ_gd::Number, λ::Number, h::Number; kwargs...) -> Float64

Compute the atmospheric density [kg / m³] using the Harris-Priester model.

Arguments

• jd: The Julian day to compute the model.
• ϕ_gd: Geodetic latitude [rad].
• λ: Geodetic longitude [rad].
• h: Geodetic altitude [m].
• n: Cosine exponent in the diurnal bulge modeling (2 <= n <= 6).
  • If n is 2, it models a smooth transition.
  • If n is 6, it models a sharp transition.
  • Default: 4
• alt_ρ::AbstractMatrix: A matrix containing the minimum and maximum density profiles.
  • [:, 1]: Altitude [m].
  • [:, 2]: Minimum density [kg / m³].
  • [:, 3]: Maximum density [kg / m³].
  • Default: _HARRIS_PRIESTER_ALT_RHO (mean solar activity).

Returns

• The atmospheric density [kg / m³].

harrispriester_modified(instant::DateTime, ϕ_gd::Number, λ::Number, h::Number, F10ₐ::Number; n::Number = 4) -> Float64
harrispriester_modified(jd::Number, ϕ_gd::Number, λ::Number, h::Number, F10ₐ::Number; n::Number = 4) -> Float64
harrispriester_modified(instant::DateTime, ϕ_gd::Number, λ::Number, h::Number; n::Number = 4) -> Float64
harrispriester_modified(jd::Number, ϕ_gd::Number, λ::Number, h::Number; n::Number = 4) -> Float64

Compute the atmospheric density [kg / m³] using the modified Harris-Priester model.

This model is a Julia translation of the Fortran code harris_priester_mod_dist.f90 developed by Noble Hatten and Ryan P. Russell [1]. It ensures continuous first derivatives, eliminates singularities, and uses a cubic dependency on the 81-day centered average of the F10.7 solar flux index (F10ₐ) to model density variations.

If F10ₐ is not provided, it will be automatically fetched using the SpaceIndices package. In this case, the initialization of the space indices package with SpaceIndices.init() is required.

References

• [1] Hatten, N., & Russell, R. P. (2017). A smooth and robust Harris-Priester atmospheric density model for low Earth orbit applications. Advances in Space Research, 59(2), 571-586.

Arguments

• instant: The DateTime to compute the model.
• jd: The Julian day to compute the model.
• ϕ_gd: Geodetic latitude [rad].
• λ: Geodetic longitude [rad].
• h: Geodetic altitude [m].
• F10ₐ: (Optional) 81-day centered average of the F10.7 solar flux index [sfu].
• n: (Optional) Cosine exponent in the diurnal bulge modeling. Default: 4. IMPORTANT: The original FORTRAN implementation computes n from orbital inclination: n = 2.001 + 4 * sin²(inclination)
  • For equatorial orbits (inclination = 0°): use n = 2.001
  • For polar orbits (inclination = 90°): use n = 6.001
  • For intermediate orbits: calculate appropriately
  If orbital inclination is unknown, the default n = 4 provides a reasonable approximation. This functionality was purposefully removed here to avoid needing an additional dependency.

Returns

• The atmospheric density [kg / m³].

jb2008(instant::DateTime, ϕ_gd::Number, λ::Number, h::Number[, F10::Number, F10ₐ::Number, S10::Number, S10ₐ::Number, M10::Number, M10ₐ::Number, Y10::Number, Y10ₐ::Number, DstΔTc::Number]) -> JB2008Output{Float64}
jb2008(jd::Number, ϕ_gd::Number, λ::Number, h::Number[, F10::Number, F10ₐ::Number, S10::Number, S10ₐ::Number, M10::Number, M10ₐ::Number, Y10::Number, Y10ₐ::Number, DstΔTc::Number]) -> JB2008Output{Float64}

Compute the atmospheric density using the Jacchia-Bowman 2008 (JB2008) model.

This model is a product of the Space Environment Technologies, please, refer to the following website for more information:

http://sol.spacenvironment.net/JB2008/

If we omit all space indices, the system tries to obtain them automatically for the selected day jd or instant. However, the indices must be already initialized using the function SpaceIndices.init().

Arguments

• jd::Number: Julian day to compute the model.
• instant::DateTime: Instant to compute the model represent using DateTime.
• ϕ_gd: Geodetic latitude [rad].
• λ: Longitude [rad].
• h: Altitude [m].
• F10: 10.7-cm solar flux [sfu] obtained 1 day before jd.
• F10ₐ: 10.7-cm averaged solar flux using a 81-day window centered on input time obtained 1 day before jd.
• S10: EUV index (26-34 nm) scaled to F10.7 obtained 1 day before jd.
• S10ₐ: EUV 81-day averaged centered index obtained 1 day before jd.
• M10: MG2 index scaled to F10.7 obtained 2 days before jd.
• M10ₐ: MG2 81-day averaged centered index obtained 2 day before jd.
• Y10: Solar X-ray & Ly-α index scaled to F10.7 obtained 5 days before jd.
• Y10ₐ: Solar X-ray & Ly-α 81-day averaged centered index obtained 5 days before jd.
• DstΔTc: Temperature variation related to the Dst.

Returns

• JB2008Output{Float64}: Structure containing the results obtained from the model.

jr1971(instant::DateTime, ϕ_gd::Number, λ::Number, h::Number[, F10::Number, F10ₐ::Number, Kp::Number]) -> JR1971Output{Float64}
jr1971(jd::Number, ϕ_gd::Number, λ::Number, h::Number[, F10::Number, F10ₐ::Number, Kp::Number]) -> JR1971Output{Float64}

Compute the atmospheric density using the Jacchia-Roberts 1971 model.

If we omit all space indices, the system tries to obtain them automatically for the selected day jd or instant. However, the indices must be already initialized using the function SpaceIndices.init().

Arguments

• jd::Number: Julian day to compute the model.
• instant::DateTime: Instant to compute the model represent using DateTime.
• ϕ_gd::Number: Geodetic latitude [rad].
• λ::Number: Longitude [rad].
• h::Number: Altitude [m].
• F10::Number: 10.7-cm solar flux [sfu].
• F10ₐ::Number: 10.7-cm averaged solar flux, 81-day centered on input time [sfu].
• Kp::Number: Kp geomagnetic index with a delay of 3 hours.

Returns

• JR1971Output{Float64}: Structure containing the results obtained from the model.

nrlmsise00(instant::DateTime, h::Number, ϕ_gd::Number, λ::Number[, F10ₐ::Number, F10::Number, ap::Union{Number, AbstractVector}]; kwargs...) -> Nrlmsise00Output{Float64}
nrlmsise00(jd::Number, h::Number, ϕ_gd::Number, λ::Number[, F10ₐ::Number, F10::Number, ap::Union{Number, AbstractVector}]; kwargs...) -> Nrlmsise00Output{Float64}

Compute the atmospheric density using the NRLMSISE-00 model.

If we omit all space indices, the system tries to obtain them automatically for the selected day jd or instant. However, the indices must be already initialized using the function SpaceIndices.init().

Arguments

• instant::DateTime: Instant to compute the model represent using DateTime.
• jd::Number: Julian day to compute the model.
• h::Number: Altitude [m].
• ϕ_gd::Number: Geodetic latitude [rad].
• λ::Number: Longitude [rad].
• F10ₐ::Number: 10.7-cm averaged solar flux, 90-day centered on input time [sfu].
• F10::Number: 10.7-cm solar flux [sfu].
• ap::Union{Number, AbstractVector}: Magnetic index, see the section AP for more information.

Keywords

• flags::Nrlmsise00Flags: A list of flags to configure the model. For more information, see [Nrlmsise00Flags]@(ref). (Default = Nrlmsise00Flags())
• include_anomalous_oxygen::Bool: If true, the anomalous oxygen density will be included in the total density computation. (Default = true)
• P::Union{Nothing, Matrix}: If the user passes a matrix with dimensions equal to or greater than 8 × 4, it will be used when computing the Legendre associated functions, reducing allocations and improving the performance. If it is nothing, the matrix is allocated inside the function. (Default nothing)

Returns

• Nrlmsise00Output{Float64}: Structure containing the results obtained from the model.

AP

The input variable ap contains the magnetic index. It can be a Number or an AbstractVector.

If ap is a number, it must contain the daily magnetic index.

If ap is an AbstractVector, it must be a vector with 7 dimensions as described below:

Extended Help

1. The densities of O, H, and N are set to 0 below 72.5 km.
2. The exospheric temperature is set to global average for altitudes below 120 km. The 120 km gradient is left at global average value for altitudes below 72.5 km.
3. Anomalous oxygen is defined as hot atomic oxygen or ionized oxygen that can become appreciable at high altitudes (> 500 km) for some ranges of inputs, thereby affection drag on satellites and debris. We group these species under the term Anomalous Oxygen, since their individual variations are not presently separable with the drag data used to define this model component.

Notes on Input Variables

F10 and F10ₐ values used to generate the model correspond to the 10.7 cm radio flux at the actual distance of the Earth from the Sun rather than the radio flux at 1 AU. The following site provides both classes of values:

ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SOLAR_RADIO/FLUX/

F10, F10ₐ, and ap effects are neither large nor well established below 80 km and these parameters should be set to 150, 150, and 4 respectively.

If include_anomalous_oxygen is false, the total_density field in the output is the sum of the mass densities of the species He, O, N₂, O₂, Ar, H, and N, but does not include anomalous oxygen.

If include_anomalous_oxygen is false, the total_density field in the output is the effective total mass density for drag and is the sum of the mass densities of all species in this model including the anomalous oxygen.