ISO 5878 Reference Atmospheres for Aerospace Use

What is ISO 5878?

While ISO 2533 defines a single idealized vertical atmosphere, ISO 5878 complements it by providing reference atmospheres — sets of atmospheric conditions that represent different latitude zones, seasons, and altitudes based on actual meteorological observations.

The standard covers three atmospheric characteristics:

• Atmospheric temperature, pressure, and density — Vertical profiles for five latitude zones (15°, 30°N, 45°N, 60°N, 80°N) in seasonal models (January and July), from sea level to 25 km.
• Wind characteristics — Zonal and meridional wind components, scalar mean speeds, and percentile values for four latitude bands (0°–20°N, 20°–40°N, 40°–60°N, 60°–80°N) in January and July, modeled using the circular normal (Rice) distribution.
• Humidity — Water vapor pressure and mixing ratio profiles for the same latitude zones and seasonal models.

Latitude Zones

ISO 5878 provides atmospheric models for five latitudinal bands, representing conditions from the tropics to the Arctic. The 15° zone uses an annual model (tropical conditions vary little seasonally), while the other four zones provide separate January and July seasonal profiles.

Wind Characteristics

Wind is a vector quantity. ISO 5878 models wind speed distributions using the circular normal distribution (also known as the Rice distribution). Observed Zonal and meridional wind components are measured from radiosonde and radar observations. Calculated The Rice PDF, scalar mean speed, and percentile values are derived from the observed parameters.

The probability density function is given by:

where $\nu$ is wind speed, $V_r$ is the magnitude of the vector mean wind, ${\sigma }_r$ is the standard deviation of the vector mean wind, and $I_0$ is the zero-order modified Bessel function of the first kind.

For latitude zones above 20°N, where the meridional component $V_y$ does not exceed 6% of the zonal component $V_x$, it is assumed that $V_y=0$, so $V_r=\left|V_x\right|$.

The expected scalar mean wind speed $V_{\mathrm{sc}}$ and the wind speeds equalled or exceeded on 1%, 10%, 20%, 80%, 90%, and 99% of occasions are calculated from this distribution.

Wind Distribution Calculator

Enter observed wind parameters to compute derived wind characteristics using the Rice distribution per ISO 5878. For the full-featured calculator with PDF/CDF visualization, presets, and percentile charts, see the Wind Calculator.

Humidity Models

ISO 5878 provides humidity profiles for each latitude zone and seasonal model. Observed Mixing ratio values are measured from radiosonde data at meteorological stations. Calculated Vapour pressure, saturation vapour pressure, dew-point temperature, and relative humidity are derived from the observed mixing ratios using thermodynamic formulae.

The humidity mixing ratio $r$ is the primary humidity characteristic — it is the ratio of water vapour mass to dry air mass in the same volume, expressed in g/kg:

The mixing ratio is used as the primary characteristic because it is the most conservative — it remains constant during vertical or horizontal air movements unless condensation or evaporation occurs.

From the mixing ratio, the standard derives:

• Vapour pressure — The partial pressure of water vapour:

• Saturation vapour pressure — The vapour pressure at which moist air exists in equilibrium with its liquid phase. For −20°C < t < 30°C, the following approximation applies:

where a = 7.5 K, b = 237.3 K for t ≥ 0°C; and a = 9.5 K, b = 265.5 K over an ice surface for t < 0°C.

• Dew-point temperature — The temperature to which air must be cooled at constant pressure to reach saturation:

• Relative humidity — The ratio of actual vapour pressure to saturation vapour pressure at the same temperature and pressure:

Humidity profiles are provided as median values by latitude zone and meridian, plus percentile distributions from station data, covering altitudes from sea level to approximately 10 km.

Cold and Warm Stratospheric Regimes

In Arctic and sub-Arctic regions, sudden warmings and coolings of the winter stratosphere and mesosphere produce large changes in the vertical structure of the atmosphere. Observed The 35 km temperature range of roughly 75 K in winter compared with only 20 K in summer comes from empirical radiosonde and rocketsonde data.

The winter temperature distributions in this region are bimodal — temperatures are normally much lower or much higher than the seasonal mean. Consequently, mean monthly or seasonal atmospheric models for the winter months are of limited value for specifying temperature in Arctic and sub-Arctic regions.

ISO 5878 provides separate cold and warm stratospheric regime profiles for 60°N and 80°N in December–January, constructed from observations at Fort Greely (Alaska), Fort Churchill (Canada), West Geirinish (Scotland), and Heiss Island (Russia):

Note: These definitions differ from the Sudden Stratospheric Warming (SSW) definitions used in the meteorological literature.

Atmospheric Variations

Seasonal and latitudinal variations

Maximum and minimum mean monthly temperatures do not occur at all latitudes and levels in the same month. Below 25 km, temperatures follow the expected June/July maximum and December/January minimum pattern. In the upper stratosphere, however, semi-annual and biennial cycles complicate the annual temperature cycle.

A notable feature is the first isopycnic level near 8 km — a level of minimum seasonal density variability where density remains relatively constant throughout the year regardless of geographic location. The levels of maximum seasonal and latitudinal variability in density and pressure are between 65 km and 75 km, with the greatest variability at high latitudes.

In the mesosphere (above 60–65 km), maximum mean monthly temperatures occur in December/January — reversed from lower altitudes.

Longitudinal variations

In summer, longitudinal variations are relatively small at all latitudes up to 80 km. Isotherms parallel latitude circles and the circulation pattern is symmetrical about the poles.

During winter, however, longitudinal variations at 60–80°N become as important as latitudinal and seasonal changes:

• Mean monthly altitudes of pressure surfaces in the lower mesosphere vary by >2,500 m
• Temperatures vary by 15–20 K at 20–35 km
• Densities change by 15–20% at 40–60 km

These differences reflect the longitudinal asymmetry in the winter circulation, driven by the Aleutian anticyclone and the displacement of the polar low toward the Eurasian continent.

Surface Conditions by Latitude

The following table gives the acceleration of free fall at sea level $g_0$, nominal Earth radius $r_{\phi }$, and sea-level temperature and pressure for each latitudinal and seasonal model.

Related Standards

ISO 5878 is part of a family of atmospheric reference standards. For the full bibliography, see the References page.