# Presentation: 532892

## Let’s Get Started: A Radiation Model That’s Within Reach

**Paul O’Brien**

## What We Should Not Do

**Wring our hands and do nothing**
**Build a model that cannot easily be decomposed into readily calculable quantities (“Black Box” or “Database” models)**
**Hard to validate and cannot easily exploit our ad hoc knowledge of the system: topology, global coherence**
**Cannot be easily implemented in a data assimilation framework**
**Build a model that is heavily dependent on magnetic conditions (through fluxes or through field model): **
**This merely shifts the burden of preflight risk assessment from specifying particle radiation to specifying solar/magnetic activity (F10.7 or Kp) and/or magnetic field model inputs. **
**Mixes rising phase and declining phase of solar cycle or main phase and recovery phase magnetic storms**
**Use solar cycle epoch instead**
**easy to predict (launch date + lifetime)**
**Convert activity dependence to epoch by running historical solar cycle(s) and collecting into epoch statistics**
**Waste a lot of time cross-calibrating small datasets that do not provide unique coverage**

## Overview

**An accurate, highly capable radiation specification for the outer zone electrons is well within reach**
**An LWS-funded collaboration between Los Alamos, ONERA, and NOAA has resulted in a large database of cross-calibrated electron measurements in the outer zone ready to be implemented into a specification model**
**The framework is the joint probability distribution of outer zone electron fluxes on a grid in L, equatorial pitch angle, and energy for every 6 months of the solar cycle (in 2 year windows)**
**New capabilities would include:**
**Error bars on mission dose**
**Internal charging spec as P’th percentile flux or T-year worst case**
**A ‘background’ model for Data Assimilation**
**A model to ‘fill in’ between sparse real-time measurements**

## Some thoughts on the Big Picture

**We do not have to wait until we are able to provide an omnibus model**
**The assumptions and approximations we must make are almost guaranteed to be better than those already built into existing specifications**
**Publishing a model will have to require that enough information is given that successor models can be built without repeating all the initial data preparation and analysis**
**We can follow the example of the magnetic field models (e.g. IGRF/DGRF, Olson-Pfitzer, Tsyganenko 89, 96, 01) by publishing major new developments as standards in the open literature**

## Following the Example of Empirical Magnetic Field Models

**Each magnetic field model has its shortcomings, but the user community has managed to do quite well nonetheless**
**The magnetic field models are modularized to include sub-models of the internal field, the external field, the magnetopause, etc.**
**To a large degree fluxes and dose are additive, just like magnetic fields, so modules are a reasonable approach**
**Defense specific (potentially classified) elements should be separate modules to maximize the (international) intellectual talent and data that can be brought to bear on the rest of the specification**
**We will have to do some coordination to make sure that the users are aware of the latest models. IGRF/DGRF does this routinely, coordinated by IAGA, by issuing a new internal field model every 5 years. SEEWG could be a first coordinating group**

## Better Assumptions and Approximations

**Better Assumptions and Approximations**

**CRRES and AE/AP models have to extrapolate the entire solar cycle from a few years of data**
**SAMPEX, Polar, POES, GOES, HEO, GEO, GPS, and Akebono provide much better solar cycle coverage for many of the relevant fluxes**

## The Old Framework

**“****Full” distributions of particle flux at a given L value and pitch angle or B value have been supplied in the past, but only in figures and publications, not as part of the computer code implementation (e.g. AE-8 and CRRESELE)**
**Computer code has provided only mean fluxes**
**We cannot calculate error bars on fluxes**
**No covariances were supplied, preventing proper dose error bars or data assimilation**
**Internal charging specification, which depends on the worst case, cannot be computed from the mean fluxes**
**Instead we rely on orbit-specific internal charging specs, which cannot easily be extrapolated to new orbits**

## A New Framework: Joint Probability

**Desired applications demand that we now provide “marginal” distributions (percentiles) and covariances (correlations) among the fluxes**
**First, we start with the marginal (univariate) distributions that describe the probability distribution of each fiducial flux (i.e. flux at a given energy, L, and equatorial pitch angle)**
**Next, we calculate the rank-order covariance among the fiducial fluxes**
**Then, we put it all together into a single equation that describes the (approximate) joint probability distribution of all the fiducial fluxes in the model (this version for weak correlation, |r| < 1/3):**

## A New Framework: Advantages

**The new framework requires only marginal distributions and covariances to produce the joint probability distribution of all the fluxes**
**Estimation of marginal distributions from sparse data is possible if distribution shape (functional form) is inferred from better-populated regions of model space**
**Covariances map well along field lines, across energies and L, and in solar cycle phase**
**By retaining sample sizes of marginal distributions and covariances, subsequent observations can be folded in easily**
**Enables new applications:**
**Error bars and percentiles on dose**
**Charging spec as T-year worst case or P’th percentile**
**Global now-cast from sparse real-time measurements**
**Data Assimilation**

## Examples of Marginal Distributions for HEO at high and low altitude

**The shape (functional form) of electron marginal distributions changes little along the field line**
**This enables reliable interpolation between different magnetic latitudes**

## Examples of Covariances for HEO at high and low altitude

**The covariance across energies is very similar at high and low altitude and changes little with the solar cycle**
**This enables reliable interpolation between different magnetic latitudes and through poorly sampled parts of the solar cycle**

## Recently Calibrated Electron Data

**This is **_**vastly**_** more data than went into AE-8 or CRRESELE**
**Calibration required a major effort by LANL, ONERA, and NOAA which started in 2000, funded by LWS, as part of an effort to start data assimilation in the Salammbo model**
**Electron data were cross-calibrated to agree with CRRES MEA/HEEF**
**Vehicles with pitch-angle data can be used to establish background pitch-angle distributions for vehicles that only measure omnidirectional fluxes**
**Long-term data sets at LEO and GEO can be used to infer solar cycle variations at other locations**

## Quiet time magnetic conjunctions are identified
Effective GPS channel energies are adjusted to fit CRRES
Calibration to within a factor of 2 is achieved
Gain changes must also be accounted for

**Effective GPS channel energies are adjusted to fit CRRES**
**Calibration to within a factor of 2 is achieved**
**Gain changes must also be accounted for**

**GPS Calibration Example**

## Mapping sparse measurements to “fill in” a larger region: Example at GEO

**A single real-time measurement is mapped to other local times along a curve of constant percentile (assumes rank order correlations are exactly 1)**
**Simplified joint probability model for omnidirectional electrons at various energies > 50 keV, drift averaged, **
**Occasional flux dropouts near midnight can throw off the mapping**

- 12

- 20

- 04

- 08

- 16

- 24

- 00

- 10%

- 25%

- 50%

- 75%

- 90%

- Real-Time Measurement at ~09 LT

- Percentiles from marginal distribution at each LT

- Electron Flux

- Local Time

- “Mapped” fluxes estimate in entire GEO orbit

## Capturing Timescales: A First Approximation

**The longer you average fluxes, the lower the worst case gets.**
**Why is this?**
**Because trapped fluxes, like many geophysical systems and financial systems, exhibit strong autocorrelation (red noise, random walk, etc)**
**If our model describes the statistical distribution of fluxes averaged over a typical time window of T, then the distribution of fluences over a window of N*T can be estimated by the sum of a set of correlated variables with rank-order covariance**
**where r is the autocorrelation at lag T.**
**This is not too hard to do. It amounts to some integrals.**
**For N >> 1/(1-r****2****), the central limit theorem applies and we can use a Gaussian approximation allowing for the autocorrelation**

## True Worst Cases Exist but are Hard to Estimate

- Estimated limit prior to 2004 was exceeded in July. A new limit has been estimated at a factor of 3 higher—and outside 95% error bars

**Extreme value theory, developed largely for insurance, enables us to detect the existence, and sometimes even estimate the value, of actual upper limits on particle fluxes.**
**We have evidence that flux limits exist for outer zone relativistic electrons over a large range of L and energy**
**However, quantitative estimates are difficult because the particular distributions observed approach the limit very slowly**
**Without some backing from EVT, there is no real justification for declaring a “worst case” specification—it’s always a “T-year worst case”**

## Main Stops on the Road Map for an Arbitrary Particle Population

**Average model with B-L-MLT-Periodicities**
**AE-8, AP-8 codes already there in some form, other populations in progress**
**Add percentiles to model **
**Published AE-8, AP-8 models (i.e. on paper, not coded)**
**Gives some sense of variability, assumes exact “global coherence”**
**Add covariance to model (realistic “global coherence”)**
**Allows proper error bars for composite quantities like Dose**
**Add autocorrelation to model**
**Allows proper specification of short-term phenomena, like internal charging**
**Add scenario capability for episodic events**
**Monte Carlo and Ensemble forecasts of storms, SEPs, shocks**
**Engineers probably not really ready to use this type of model, yet**
**Full blown climate models based on first principles**
**Physicists not really capable of this type of model, yet**
**Data assimilation for space weather not so far off**

## Final Thoughts

**The joint probability distribution framework described here allows us to make the most of sparse or voluminous data and it can incorporate new data or even results from numerical models**
**The same framework can be used to extend an existing ring current ion model based on Polar observations**
**LEO observations from DMSP, SAMPEX and POES could also be integrated into a LEO-specific model**
**Magnetic field models provide an informative example of how to proceed**

## SpWx in 10 years: Overview

- AnomalyResolution

**SpWx in 10 years: Overview**

**A robust space weather program consists of operations and science elements that work together to mutual benefit**
**Modeled after the Numerical Weather Prediction and Climate Reanalysis programs**
**Operational models start out more empirical and become more physical as development progresses**
**Operational utility demands expert systems (including human forecasters) to translate physical model outputs into straightforward threat assessments**

- Forecastsand Nowcasts

- Reanalysis

- ModelValidation

- HistoricalData

- Real-TimeData

**Operations**

**Science**

- WatchesandWarnings

**Research Cycle**

## SpWx in 10 years: Toward Real-Time Operations

**Beyond the open data policy – ****	****a Real-Time Data Policy**
**Future NASA and other US Govt. missions should produce low latency, near-real-time data like ACE rtSW and GOES SEM, at least for the operationally useful key parameters**
**More contact between Operations and Science, e.g. SpWx Week, SEEWG**
**Physical models should be modified to be able to assimilate real-time data**
**Historical climatologies/specifications with covariance should be built**
**Covariance enables realistic data assimilation**
**First priority is quantities with operational or design implications**
**Second priority is quantities needed for assimilation in physical models**
**Expert systems and other automated reasoning tools should be built to help non-experts interpret nowcasts and forecasts**

## SpWx In 10 years: Reanalysis

**Scientists around the world use the reanalysis data for:**
**Climate studies**
**Seasonal climate prediction**
**Climate variability studies**
**Initial/boundary conditions for regional/sub-grid-scale models**
**Diagnostic studies**
**Verification of climate models**
**Testbed for operational models**
**All this for about $10M/year (not verified)**
**Reanalysis development is coupled to other atmospheric science efforts (measurement, calibration, theory, modeling, data analysis)**

**The US atmospheric science community produces a standardized ‘reanalysis’ (via NCEP and NCAR)**
**The reanalysis is built by going back as far as the data allows and running a consistent standard data assimilative physics-based global analysis model**
**The reanalysis provides numerous climate and weather data for the entire globe on a standard grid. The reanalysis is run after the fact, when all data are available.**