The global numerical first principle 3D model of the upper atmosphere (UAM) for the heights 60–100,000 km is presented. The physical continuity, motion, heat balance and electric potential equations for the neutral, ion and electron gases and their numerical solution method are described. The numerical grids, spatial and time integration steps are given together with the boundary and initial conditions and inputs. Testing and obtained geophysical results are given for many observed situations at various levels of solar, geomagnetic and seismic activity.
- global numerical model
- solution method
- integration steps
- upper atmosphere
- space weather
- solar and geomagnetic activity
The upper atmosphere is a part of the gas envelope of the Earth. It is located from the height
The upper atmosphere is divided into several height regions depending on its gas composition and dominating physical process: the thermosphere (from ~80–90 km to ~400–800 km) and the exosphere (above ~400–800 km) in relation to the neutral particles; the ionosphere, the plasmasphere and the magnetosphere in relation to the charged particles.
The ionosphere is located at the height range from ~50 km (the upper part of the middle atmosphere—mesosphere) to ~1000 km. The plasmasphere is located above the ionosphere up to the plasmapause—the geomagnetic force line with
The upper atmosphere state is part of Space Weather. It experiences regular annual, seasonal and diurnal variations as well as disturbances caused by the solar, geomagnetic and lithosphere activities, both globally and locally. Along with the meteorological weather, the Space Weather greatly affects human activity. Such disturbances as geomagnetic storms and substorms, auroras lead to disruptions of the radio communication in the HF range up to its blackout, faulty operation of the navigation satellite systems and electronic onboard equipment of the aircrafts. They generate intense geomagnetic-induced currents in the long conducting lines (transmission facilities, telecommunication, cables, railways and oil and gas pipelines), which create failures of the automatic and relay protection systems and, as a consequence, they cause emergency shutdowns of power supply systems, etc. Therefore, monitoring and forecasting of the upper atmosphere state is an extremely important task.
Monitoring of the near-Earth space is conducted by measurements of different physical plasma parameters (temperatures, concentrations and velocities of neutral and charged components, electric and magnetic fields, etc.) at different heights and areas of the globe, both ground-based and on the board of airplanes, rockets and satellites. Despite the growing level of the technical perfectness, it is impossible to provide stable and global monitoring, and “white areas” still remain over the Earth. These areas are those where measurements cannot be conducted or experience various difficulties (especially over the oceans and near the poles). In such cases, the method of the numerical simulation becomes valuable, and the calculations of the desired parameters fill the “white gaps”. The numerical models use the basic fundamental laws of nature to describe quantitatively the near-Earth environment and/or interpret the measurements.
The Upper Atmosphere Model (UAM), described in this chapter, is a global, 3D, self-consistent, numerical model covering
The UAM was developed previously in Kaliningrad under the supervision of Prof. A.A. Namgaladze as the Global Self-consistent Model of the Thermosphere, Ionosphere and Protonosphere (GSM TIP) [1, 2] and further improved in Murmansk. The modern version called as UAM [3, 4] differs from the GSM TIP by implementation of algorithms for the integration with variable latitude steps and by including empirical models of the ionosphere and thermosphere to use their data for initial and boundary conditions and for the UAM testing.
Most of the modern numerical models (NCAR TIE-GCM , CTIM , CTIPe , GITM , SWMF [9, 10]) either cover the near-Earth space in very limited ranges in heights and latitudes, or perform a combination of several models without physical coupling between the parts. The UAM covers the near-Earth space as a coupled system and is still superior to all existing models by spatial coverage and resolution. This makes the UAM suitable to investigate a variety of physical processes, both globally and locally.
2. Basic equations
The fundamental conservation laws are used in the UAM: the quasi hydrodynamic equations of the continuity (1), momentum (2), heat balance (3) and electric current continuity (4).
Due to the changes in gas composition and the predominance of different physical processes at different heights, the UAM is divided into several computational blocks: the neutral atmosphere and lower ionosphere block; the F2-layer and plasmasphere block and the magnetosphere block. A special block calculates the electric field potential by solving the continuity equation for . Each block covers a particular height range, uses its own particular equations, coordinate system and calculates its own set of parameters and exchanges with other blocks at each time step of numerical integration.
The block of the neutral atmosphere and lower ionosphere uses the spherical geomagnetic coordinate system and calculates the 3D variations of
where is the neutral wind velocity, is the diffusion velocity vector, which has only a vertical component equal to the sum of molecular and turbulent diffusion velocities,
The meridional and zonal components of are obtained from the projection of Eq. (2) on the horizontal axes of the geographical coordinate system:
By summing up for
With the calculated
For concentrations of O2+, N2+ and NO+ ions in the D, E and F1 layers, the photochemical, local heating and heat exchange processes dominate over the transport processes, since the lifetime of the molecular ions is many times smaller than the transport characteristic time due to high collision frequencies of the charged particles with neutrals and each other. Thus, Eq. (1) for the molecular ions in the lower ionosphere block is written as:
The momentum equation for the molecular ions is written as:
In the momentum equation for electrons, we neglect all terms containing
This gives the electric field of the ambipolar diffusion:
where is the rate of Joule’s heating, are the rates of the ions’ heat exchange with electrons and neutrals, respectively, and are the rates of the electrons’ heat exchange with ions and neutrals, respectively, and are the rates of the electrons’ heating by the photoelectrons and electrons precipitating from the magnetosphere, respectively.
In the block of the F2-layer and plasmasphere
In the continuity equation, along with the production rates
gives the Lagrangian time derivatives along the trajectory of the charged particle’s electromagnetic drift perpendicular to the geomagnetic field line with the velocity:
The electrons’ velocity along the field lines is calculated as:
The atomic ions’ motion equation for the
where is the rate of Joule’s heating for the ion gas; , and are the rates of the heat exchange between ions, between ions and electrons and between ions and neutrals, respectively; , and are the rates of the electrons’ heat exchange with the
The magnetospheric block of the UAM calculates the plasma layer
We assume that the pressure of the plasma layer is isotropic and constant along . The pressure of the plasma layer electrons is neglible in comparison with
In the block of the electric field potential
where and are the densities of the magnetosphere and lower ionosphere electric currents, and is the ionosphere electric current density given by Ohm’s law for the plasma:
where is the electric field vector defined as the sum of the electrostatic field with the potential
Thus, the equation for the electric current continuity is given as:
where is the tensor of the ionospheric electric conductivity for the coordinate system with axes along , and :
The integration of Eq. (27a) is conducted along the electric conducting layer, from the lower boundary of the UAM up to 175 km, where we neglect the dependency of the electric field intensity on
3. Equations solutions: initial and boundary conditions
The integration of the model equations is carried out using a finite-difference numerical method. The near-Earth environment is considered as a discrete three-dimensional grid, and each computational block uses its own coordinate system. The derivative operators are replaced by the difference ratios, and the solution is obtained in the nodes of the numerical grid. Steps in the numerical grid are chosen depending on the task and the characteristic scale of the investigated process. Usually, the integration step in longitude is chosen as a constant value between 5° and 15°. The integration steps in latitude are variable and depend on the latitude. Near the geomagnetic equator the step is chosen in the range of 2.5–5.0° and 1° near the poles, because a tighter numerical grid is required for a precise calculation in the aurora zones and across the polar caps. Steps of the numerical integration along the height are also variable. In the blocks where a spherical coordinate system is used, the step is 3 km at the lower boundary of the UAM and increases exponentially with altitude.
The solutions of Eqs. (1)–(4), which are containing derivations of coordinates, require boundary conditions: the distribution of the desired parameters at the boundaries of the numerical blocks. At the lower boundary
For the upper boundary conditions in the block of the neutral atmosphere (at 520 km) the diffusion equilibrium for
In the F2-layer and plasmasphere block the boundary conditions are defined as follows. At the altitude of 520 km, the concentration of the neutral hydrogen is set according to the empirical model of the neutral atmosphere . For atomic ions
The model equations are integrated along the geomagnetic field lines in the areas with closed lines of force (±75° in geomagnetic latitude). In the regions with open geomagnetic field lines (poleward of 75° geomagnetic latitude)
Solutions of those equations, which are containing time derivatives, require initial conditions: parameter distributions at the start of the numerical calculation. For quiet geophysical conditions, stationary solutions are used as initial conditions after the multiple runs of the model. The initial conditions for perturbed periods are the solutions obtained for the previous quiet days. It is also possible to use data from empirical models (NRLMSISE-00 , HWM-93 , IRI-2001  or IRI-2007 ) as initial conditions.
4. Model inputs
The inner state of the simulated space and external forcings acting on it are characterized by the model inputs set up by the user: (1) date and time to set an initial placement of the numerical grid nodes relative to the Sun; (2) spectra of the solar UV and EUV radiation; (3) fluxes of the high energetic electrons precipitating from the magnetosphere; (4) the FACs connecting the ionosphere with the magnetosphere and/or (5) the distribution of
The solar UV and EUV spectra define the coefficients of O2 dissociation and O2+, N2+, NO+ and O+ production rates due to the photoionization of the corresponding neutral components. The UV and EUV spectra dependence on the solar activity is set up according to Ref. . The intensity of the night scatter radiation intensity is 5 kR for the emission with wave length
The precipitating electrons’ fluxes are set up at the upper boundary of the thermosphere, at 520 km, and their intensity
The magnetospheric sources in Eq. (27a) specify the distribution of FACs. The FACs of the Region 1 (R1) flow from the magnetosphere into the ionosphere on the dawn side and out of the ionosphere on the dusk side, at latitudes higher ±75°. The FACs of the Region 2 (R2) flow in the opposite direction, at areas equatorward of the R1 currents. The distribution of current densities depends on the geophysical conditions and is setup in the UAM in several different ways depending on the task, either as distribution of the FACs in the R1, 2 and the cusp region according to the model , or as the distribution of electric potential at the boundary of the polar cap  with the FACs in the cusp region and the R2.
The so-called seismogenic electric currents are the vertical electric currents switched on to simulate the ionosphere effects of various mesoscale phenomena in the lower ionosphere, such as earthquakes, thunderstorms, etc. Used as a model input, the vertical are added locally to Eq. (27a) at the lower boundary of the UAM.
The geomagnetic activity is used in the UAM by setting up the planetary geomagnetic indices
5. The UAM versions
The UAM provides the possibility of integrating various empirical models and data of the upper atmosphere. The comparison of the self-consistent UAM version and the UAM versions with different combinations of the empirical models allows testing both the UAM and the empirical models.
In the UAM-MSIS version,
In the UAM-HWM version the distribution of the horizontal thermospheric wind is calculated using the empirical model HWM-93 . The vertical component of the wind velocity is calculated by the numerical solution of the continuity equation for
The magnetospheric block of the UAM simulates the transport processes in the plasma sheet by solving the system of the equations for the plasma sheet ions (see item 2). In Ref. , the initial values are taken as
There are several ways to set up FACs spatial-temporal distributions in the UAM, such as empirical data from the magnetic field measurements from the Dynamics Explorer 2  and the Magsat satellites , the FACs empirical models by Papitashvili  in [25, 26], by Lukianova  in Ref.  and MFACE  in Ref. . All these versions with various FACs take into account the dependence of FACs on the interplanetary magnetic field (IMF). Such methods of setting the FACs distribution allow using any other empirical data of FACs.
In the UAM version , the positions of the auroral oval boundaries, the values of electron flux intensities and the latitudes and longitudes of the intensity maxima were set from precipitation patterns observed by DMSP. The spectra of the precipitating electrons are assumed to be Maxwellian in this case.
The UAM-P version [32, 33], created in Potsdam, differs from the UAM by the electric field block simulation. This block uses magnetic dipole coordinates instead of spherical geographical ones within
The Canadian Ionosphere and Atmosphere Model (Canadian IAM or C-IAM) is comprised of the extended Canadian Middle Atmosphere (CMAM) and the UAM, currently coupled in a one-way manner . This version was used to investigate the physical mechanisms responsible for forming the four-peak longitudinal structure of the 135.6 nm ionospheric emission observed by the IMAGE satellite over the tropics at 20:00 local time from March 20 to April 20, 2002. The study showed that main mechanism is driven by the diurnal eastward propagating tide with zonal number 3.
During its development and improvement, the UAM was used to perform a number of numerical experiments aimed at testing and comparison of calculation results with measurements and other models. The UAM successfully showed its ability to reproduce the general behavior of ionospheric and thermospheric parameters such as at low and high geomagnetic and solar activity conditions. A good agreement of the numerical simulations’ results was achieved in comparison with observations by incoherent scatter radars located at various latitudes and longitudes (ISRs) , digital ionosonde CADI in the Voeykovo Main Geophysical Observatory , several chains of the ionospheric tomographical receivers [36, 37, 38], satellites, including CHAMP and GPS [3, 4, 26, 30, 39, 40, 41, 42], as well as with empirical models such as various types of IRI, MSIS, HWM [42, 43, 44, 45, 46, 47], etc. and other theoretical models .
In addition to the UAM testing and comparison with the observations for the different levels of solar and geomagnetic activities, the model has been widely used to study
Thus, the UAM was tested and used in many helio- and geophysical situations. Nevertheless, the amount of the UAM simulations remains to be insufficient despite the IT progress. This is related with the specifics of the geophysics as science at all. The near-Earth space environment varies due to the solar, seismic and human activities. This does not allow performing the repeated fixed experiments as in usual physical laboratories to obtain correctly the standard statistical error estimates. Moreover, the observations themselves are very limited. None of them has 3D spatial and time resolutions satisfying to the requirements of the modern technical means of the Space weather practical usage. This was well known long ago  and such models as UAM are aimed solving this important problem.
Further development of the UAM means a huge amount of further numerical experiments to its mathematical and physical quality. These experiments have to take into account all modern achievements of the numerical mathematics and computer science. The numerical grids, steps, various iterations, etc. should be tested to find their optimal combinations for the best stability and accuracy. The user’s manuals should be constructed, including the UAM website. The UAM prognostic features have to be improved by modeling many case studies for various helio- and geophysical situations especially for geomagnetic and seismogenic disturbances. Comparisons with ground-based and satellite observations, empirical and other theoretical models have to be made continuously. The frame approach should be widely used by including separate observational, empirical and theoretical blocks into the UAM, such as the real geomagnetic field, polar wind, plasma sheet, electric fields, lower atmosphere, aerosols, tides, etc. An international cooperation is absolutely necessary for these future scientific UAM perspectives.
We thank many people who have worked with the UAM, developed and improved it, such as A. N. Namgaladze, M. A. Volkov, E. N. Doronina, Yu. V. Romanovskaya, I. V. Korableva, Yu. A. Shapovalova, M. G. Botova, M. I. Rybakov, I. V. Artamonov, E. V. Vasilieva, V. A. Medvedeva, V. A. Shlykov, L. A. Chernyuk and many others.
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Namgaladze AA, Klimenko MV, Klimenko VV, Zakharenkova IE. Physical mechanism and mathematical modeling of earthquake Ionospheric precursors registered in Total electron content. Geomagnetism and Aeronomy. 2009; 49(2):252-262. DOI: 10.1134/S0016793209020169
Zolotov OV, Namgaladze AA, Zakharenkova IE, Martynenko OV, Shagimuratov II.Physical interpretation and mathematical simulation of ionospheric precursors of earthquakes at midlatitudes. Geomagnetism and Aeronomy. 2012; 52(3):390-397. DOI: 10.1134/S0016793212030152
Karpov MI, Namgaladze AA, Zolotov OV. Modeling of Total electron content disturbances caused by electric currents between the earth and the ionosphere. Russian Journal of Physical Chemistry B. 2013; 7(5):595-598. DOI: 10.1134/S1990793113050187
Namgaladze AA, Karpov MI. Conductivity and external electric currents in the global electric circuit. Russian Journal of Physical Chemistry В. 2015; 9(4):754-757. DOI: 10.1134/S1990793115050231
Namgaladze АА. Earthquakes and global electrical circuit. Russian Journal of Physical Chemistry B. 2013; 7(5):589-593. DOI: 10.1134/S1990793113050229
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