[1] We present a comparison between a simple but general model of solar windmagnetosphere-ionosphere coupling (the Hill model) and the output of a global magnetospheric MHD code, the Integrated Space Weather Prediction Model (ISM). The Hill model predicts transpolar potential and region 1 currents from environmental conditions specified at both boundaries of the magnetosphere: at the solar wind boundary, electric field strength, ram pressure, and interplanetary magnetic field direction; at the ionospheric boundary, conductance and dipole strength. As its defining feature, the Hill model predicts saturation of the transpolar potential for high electric field intensities in the solar wind, which accords with observations. The model predicts how saturation depends on boundary conditions. We compare the output from ISM runs against these predictions. The agreement is quite good for non-storm conditions (differences less than 10%) and still good for storm conditions (differences up to 20%). The comparison demonstrates that global MHD codes (like ISM) can also exhibit saturation of transpolar potential for high electric field intensities in the solar wind. We use both models to explore how the strength of solar wind-magnetosphere-ionosphere coupling depends on the strength of Earth's magnetic dipole, which varies on short geological timescales. As measured by power into the ionosphere, these models suggest that magnetic storms might be considerably more active for high dipole strengths. [2] Total region 1 current, I 1 , and transpolar potential, È pc , epitomize solar wind-magnetosphere-ionosphere (SW-M-I) coupling. Progress in understanding this subject can almost be measured by how well the field predicts these quantities. (Region 2 currents, which this paper does not treat, are also an important aspect of the story. In section 7 we discuss how they might affect results presented here.) First models of SW-M-I coupling, reviewed by Reiff and Luhmann [1986], assumed one-way coupling from the solar wind to the ionosphere in which magnetic reconnection at the magnetopause taps a fraction of the solar wind potential across the magnetosphere, È sw , to yield an available magnetospheric convection potential È m . È m is then impressed via equipotential magnetic field lines onto the ionosphere, where it becomes the È pc that generates region 1 currents. The envisioned process was therefore linear. Empirical formulas based on this linear assumption work fairly well, except they tend to overpredict È pc for big values of È sw . This tendency has been called saturation of the transpolar potential at high values [Reiff and Luhmann, 1986;Russell et al., 2000].[3] Hill et al. [1976] presented a model of SW-M-I coupling that manifests saturation intrinsically and at about the observed value. (Hill [1984] developed the implications of the model further. We therefore refer to it as the Hill model.) Saturation is a nonlinear process that, in the Hill model, results from a feedback in which the magnetic field generated by region 1 cu...

The objective of a global sensitivity analysis is to rank the importance of the system inputs considering their uncertainty and the influence they have upon the uncertainty of the system output, typically over a large region of input space. This paper introduces a new unified framework of global sensitivity analysis for systems whose input probability distributions are independent and/or correlated. The new treatment is based on covariance decomposition of the unconditional variance of the output. The treatment can be applied to mathematical models, as well as to measured laboratory and field data. When the input probability distribution is correlated, three sensitivity indices give a full description, respectively, of the total, structural (reflecting the system structure) and correlative (reflecting the correlated input probability distribution) contributions for an input or a subset of inputs. The magnitudes of all three indices need to be considered in order to quantitatively determine the relative importance of the inputs acting either independently or collectively. For independent inputs, these indices reduce to a single index consistent with previous variance-based methods. The estimation of the sensitivity indices is based on a meta-modeling approach, specifically on the random sampling-high dimensional model representation (RS-HDMR). This approach is especially useful for the treatment of laboratory and field data where the input sampling is often uncontrolled.

High dimensional model representation is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The HDMR component functions are optimally constructed from zeroth order to higher orders step-by-step. This paper extends the definitions of HDMR component functions to systems whose input variables may not be independent. The orthogonality of the higher order terms with respect to the lower order ones guarantees the best improvement in accuracy for the higher order approximations. Therefore, the HDMR component functions are constructed to be mutually orthogonal. The RS-HDMR component functions are efficiently constructed from randomly sampled input-output data. The previous introduction of polynomial approximations for the component functions violates the strictly desirable orthogonality properties. In this paper, new orthonormal polynomial approximation formulas for the RS-HDMR component functions are presented that preserve the orthogonality property. An integrated exposure and dose model as well as ionospheric electron density determined from measured ionosonde data are used as test cases, which show that the new method has better accuracy than the prior one.

An organized density (and pressure) structure was recently discovered in the neutral thermosphere at high‐latitudes. The structure consists of two to four high‐ and low‐density regions having diameters of 1000 to 2000 km. The density in each region is enhanced or depleted from the hemispheric average by up to 30%. The structure is thus a significant feature of the near‐Earth space environment at high‐latitudes. We refer to each distinct region of enhanced or depleted density as a density “cell.” The cells extend upward from about 120 km into the upper thermosphere, and once formed they remain approximately fixed with respect to the geomagnetic pole. A parametric study of the density cell morphology for different magnetic activity levels is described for equinox solar minimum using the National Center for Atmospheric Research thermosphere ionosphere general circulation model (NCAR‐TIGCM). Density data were sought to verify the existence of the structures first predicted by the NCAR model. The TIGCM simulations were used to predict the large density perturbations observed by the S85‐1 satellite in a circular sun‐synchronous orbit near 200 km altitudes. The most obvious manifestation of the cells was the presence of density peaks located near 70°Λ on the dayside and nightside, and a density minimum near the magnetic pole. Since high‐latitude densities are generally expected to increase during magnetic activity, the low densities over the pole are perhaps the most interesting feature of the cell structure discussed here. The satellite data confirm the existence of the cellular structure over a range of magnetic activity levels. The discovery of the cells is important because the structure provides a unifying framework for the analysis and interpretation of high‐latitude data from both past and future experiments. The cells result from various forms of coupling between the ionosphere and thermosphere. The cell formation is quantitatively consistent with concepts from dynamic meteorology.

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