Transcript Prospects for Data Assimilation in Magnetosphere Models Joachim Raeder Space Science Center, University of New Hampshire, Durham, NH GEM Summer Workshop, Portsmouth, VA, June 19,

Prospects for Data Assimilation in
Magnetosphere Models
Joachim Raeder
Space Science Center, University of New Hampshire,
Durham, NH
GEM Summer Workshop, Portsmouth, VA, June 19, 2014
Outline
•
•
•
•
•
•
•
•
Why data assimilation?
Data coverage and the daily forecast.
A step back: subjective and objective analysis.
Model initialization and the assimilation cycle.
Can we use this in the magnetosphere?
DA in regional models.
Parameter estimation and bias correction
Ensemble prediction.
Why do we want data assimilation?
• Weather forecasts have shown dramatic improvements over the
past 60(!) years.
• These improvements are largely due to the use of data
assimilation, and better data coverage.
• Yes, we would like to have that for the magnetosphere too.
From: Kalnay,
2003
Why do we need data assimilation?
Current magnetosphere models stink!
From Pulkkinen et al., 2013
Data coverage for terrestrial weather
• Weather forecasts
use many data
sources
• They need to be
“ingested” into
“synoptic maps”.
• How poor are we
with
magnetosphere
data?
From: Kalnay, 2003
Subjective and objective analysis
Subjective analysis:
Objective analysis:
A forecaster draws a
weather map from the
available observations.
Computer algorithms
deal with data that are
irregular in space and
time and produce
synoptic maps.
NWS, ~1870
How does DA work? The Data assimilation cycle
• Forecast models (solving the physics of wet gases) need to be
initialized.
• Use observations and previous forecast to generate initial conditions
for next forecast.
• Run next forecast.
• Repeat cycle.
• The “data assimilation” is part of the model initialization. Note that
initialization is not just based on data but also on previous model run.
• The goal is an output that minimizes the combined error of model and
data.
DA can also be continuous: 4DVAR, KF:
What data assimilation really does - I
• The data part initializes the model and “keeps the model
on track.” Data are not on the correct grid, either in
space or time!
• The model fills the data gaps. Note that the dynamic
equations are essentially transport equations: The model
propagates information from data rich regions to data
poor regions.
• The DA cycle also filters the data: there are well
separated time scales of atmospheric motion: geostrophic
motion (days) versus inertia-gravity (Rossby) waves, and
sound waves (hours). The faster time scale is considered
noise, and DA helps to filter it out.
What data assimilation really does - II
• DA by itself is not forecasting! There are no data from
the future!
• DA combines data with a dynamic model to obtain synoptic
maps that are more reliable than either data or model
alone.
• Data have errors. With 103 - 107 data points per day
there is no efficient error control possible. Data errors
can be of much worse consequence than model errors.
The best model will produce bad results with bad input
data (garbage in --> garbage out).
• Data errors come in all kinds: outliers, noise, bias, …
• The overall objective of DA is to minimize the errors
between the data and the model.
• In general, there is no a priori knowledge of either the
data errors or the model errors.
Methods - I
• Direct Insertion: Replace select model values with data.
Usually gives very bad results. Assumes data are perfect.
• Optimal Interpolation: Weighed averages between data
and model. Requires a priori knowledge of model/data
errors.
• Variational Methods: Minimize RMS error between model
and data in space (3DVAR) or space-time (4DVAR).
Requires the adjoint operator of the model advance
operator. Expensive in terms of development manpower
and computational power required. But fairly easy to add
new data sources. Used in numerical weather prediction.
Methods - II
• Kalman Filter (KF): Integrate model equations together
with error-covariance. Adds NxN differential equations.
Impractical for 3D systems.
• Reduced/Truncated Kalman Filter: Apply KF to reduced
set of equations. Makes KF feasible, but requires
compromises, and there is no procedure that would work
for every system. Requires a lot of development work.
• Ensemble Kalman Filter (EnKF): Separates co-variance
estimation from model using a Monte-Carlo approach.
Only requires minor modifications to the forecast model.
The tradeoff is that 10s to 100s ensemble member runs
are required, which is computational expensive but
(almost) trivial to parallelize. EnKF is increasingly used
for numerical weather forecast.
Can we do this in the magnetosphere?
• The boilerplate answer: Well, we do not have
that much data. Not a good answer, because
we will likely get more data, sooner or later
(see NASA’s great observatory + DMSP +
GOES + …).
Other considerations
• The atmosphere has a lot of inertia and thus there is
an “initialization problem” (mathematically an IVP).
• The magnetosphere is much more a “driven
dissipative” system.
• For the magnetosphere we face a “boundary
problem” (IBVP). The input to the system is
imperfectly known from SW monitors (monitors are
never on the sun-Earth line at L1!).
• We need to deal with a lot of turbulence, in the
driver (SW/IMF), and possibly with intrinsic
stochasticity.
• The magnetosphere is dominated by fast wave
modes, the atmosphere is dominated by convective
transport. Thus, information travels differently.
The magnetosphere response function
• The magnetosphere has a
short memory for
geomagnetic activity.
• Bimodal response:
– 20 min peak: directly
driven.
– 1.5h peak: substorms.
– Generally no response
after 2h, but there are
exceptions (long quiet
periods, tail plasma
loading, ~6h (Borovsky
et al.).
• By comparison, the impulse
response time of the
atmosphere is days: today’s
Seattle rain will arrive here
next Tuesday!
Bargatze et al., 1985
Can we do this in the magnetosphere?
• A full-blown KF or 3DVAR/4DVAR global MHD based
magnetosphere model is beyond the capability of any
group, given the state of the field and the funding
levels.
• Atmosphere model development has taken decades
and $$B (not $$M!) in funding for numerical DA
forecast models. And, given the nature of the
magnetosphere, the approach taken may not even be
the best for the magnetosphere.
• We don’t quite have the necessary magnetosphere in
situ data yet.
 We need a smarter approach.
The good news
• Some regions of the magnetosphere are transport
dominated and have longer time scales:
– Ring current (hours)
– Radiation belts (days to weeks)
– Plasmasphere (days)
– Plasma sheet (hours, but beware of turbulence)
• And those regions are quite well sampled.
• And they are sensitive to model initialization.
• And the models are relatively simple (1d, 2d).
• And they matter.
• Such models are already in develoment.
This slide courtesy of: S. Naehr, F. Toffoletto, A. Chan, Rice U.
Example: Radiation Belts:
Results from direct insertion of perfect
data from elliptical orbiter:
• Observing points, mapped to (μ,L) space,
denoted by “+” marks
• Corrections gradually diffuse across L, yield
good results if system near steady state
Results from EKF with perfect data from
elliptical orbit:
•Well-distributed data from an elliptical orbit
provides nearly perfect results
•Caveats: the data, diffusion, and magnetic field
are all perfect in this simulation
More good news
•
•
•
•
A simple but possibly useful approach for global magnetosphere
simulations might be “ensemble prediction” (EP).
EP is increasingly used for long-term weather prediction.
EP is based on many model runs with perturbed initial and/or boundary
conditions.
EP provides a “mean forecast” and also probabilities.
From Kalnay, 2003
EnKF:Data Assimilation Research Testbed
(DART)
• Developed by NCAR
• Would be expensive to
develop from scratch.
• Requires only small
modifications to the forecast
model.
• Can work with any data set as
long as there is a projection
operator from model space to
data space.
• DART is a well developed and
well tested EnKF framework
that has been used with more
than a dozen atmospheric and
oceanic models.
A new objective: Parameter optimization
• Global magnetosphere models contain numerous
numerical parameters that are poorly known.
• Examples: parameterized anomalous resistivity, Knight
relation fudge factors to determine e- precipitation,
plasma properties at inner boundary, ….
• The normal “procedure” to optimize such parameters is
a “change parameter  run simulation  compare to
data  use your thumb” cycle.
• This approach is very inefficient and basically fails
once there are more than a few parameters.
• Model sensitivity to parameters remains unknown,
biases are difficult to find, and the procedure yields
no information on correlations between parameters.
Parameter optimization using EnKF
Augment the state vector u (plasma, field) with vector μ
of model parameters for a new state vector x:
The typical model forward step :
With EnKF will then also update the model parameter
vector μ(m)t  μ(m)t+1. Such parameter optimization can
be done with historical data  no need for real-time
feeds, can cover solar cycle.
Benefits
• (Much) improved model parameter specification and
model accuracy.
• Estimation of model biases. Such biases would indicate
deficiencies of the physical description. Example:
cross polar cap potential.
• Estimation of parameter sensitivity. Some parameters
may be unimportant; others may be critical and in need
for better physical understanding.
• Estimation of parameter correlations.
• Estimation of error propagation. How do errors (like
SW/IMF misspecification) propagate through the
magnetosphere?
• Estimation of optimal ensembles for ensemble
predictions.
DART with OpenGGCM
• OpenGGC is a global magnetosphere-ionospherethermosphere model with long heritage and community
model status at the CCMC.
• OpenGGCM is efficient enough that ensembles of 10100 runs can be done in real time with reasonable
hardware requirements (even on PS3!).
• An increasing number of data sources is available:
– Ionosphere: radars, AMPERE, ground
magnetometers, ….
– Magnetosphere: NASA GO, GOES, LANL, DMSP, ….
– Model inputs from L1 or helio prediction (ENLIL).
• An implementation of OpenGGCM – DART EnKF would
be quick and affordable.
• Heliosphere prediction could be included into the DA
cycle.
Summary
• Atmospheric DA methods are well developed and successful, but
it took decades and $$B to get to this stage.
• The global magnetosphere DA problem is not analogous to
atmospheric DA because the magnetosphere is more of a driven
dissipative system compared to the mostly inertial atmosphere.
Boundary conditions are more important than initial conditions.
• There is promise for DA in regional magnetosphere models: RC,
RB, plasmasphere.
• Ensemble prediction and EnKF may be the most promising
approach for the global magnetosphere, in particular for
parameter optimization.
• Suitable EnKF frameworks (DART) are already available.