Observing Network Design Applied to Antarctic Weather Monitoring and Forecastinghakim/papers/hryniw_etal... · 2016. 5. 27. · Observing Network Design Applied to Antarctic Weather

Observing Network Design Applied to Antarctic Weather Monitoring and

Forecasting

Natalia Hryniw⇤, Gregory J. Hakim

Department of Atmospheric Sciences, University of Washington, Seattle, Washington1

Guillaume S. Mauger2

Climate Impacts Group, University of Washington, Seattle, Washington3

Karin A. Bumbaco4

Joint Institute for the Study of Atmosphere and Ocean, University of Washington, Seattle, WA5

Jordan G. Powers6

National Center for Atmospheric Research, Boulder, CO7

⇤Corresponding author address: Natalia Hryniw, Department of Atmospheric Sciences, Box

351640, University of Washington, Seattle, Washington 98195-1640

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E-mail: [email protected]

Generated using v4.3.2 of the AMS LATEX template 1

ABSTRACT

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The Antarctic surface weather observing network is crucial for support-

ing scientific and logistical operations over the continent. The harshness of

weather conditions make it difficult to support a dense network, and so it is

critical to place new weather stations in locations that are optimally and ob-

jectively chosen for a given purpose. Here a network design algorithm is

employed that uses ensemble sensitivity to identify optimal locations for new

Automated Weather Station (AWS) locations. Here we define the optimal

location as the one that reduces the total variance of the measurement field

by the largest amount. This algorithm is used with data from the Antarctic

Mesoscale Prediction System (AMPS) to identify the best locations for two

metrics: (1) measuring the 2-m temperature field and, (2) reducing forecast

errors at lead times of 12, 24, and 36 hours, both as a “blank slate” network,

and an augmented network that is conditional on currently existing stations

that report at least 90% of the time during the data period. These stations are

also ranked in terms of their importance in capturing the 2-m air temperature

field and reducing forecast errors. The most important locations for moni-

toring 2-m air temperature are found to be near Vostok in East Antarctica,

in Marie Byrd Land, and in Queen Maud Land. Among existing stations,

the locations with highest impact are Vostok, Siple Dome, and South Pole.

Results for forecast error networks are fairly similar for all lead times, with

prime locations in Oates Land, Marie Byrd Land, Cape Adare, and central

East Antarctica near Vostok. The three most important currently existing sta-

tions for reducing forecast errors are Vostok, McMurdo, and Halley.

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1. Introduction

Antarctica has some of the harshest and most extreme weather on Earth, and so travel to the

continent and logistical operations for explorations and support of scientific campaigns can be

challenging. An important part of maintaining safety and supporting operations is having a robust

observing network to identify potentially hazardous weather and provide information for forecasts.

Because of the harsh conditions, maintenance of stations is costly and difficult, so there is a strong

motivation to have measurements that provide good coverage and do well with regard to perfor-

mance measures.

Optimal network design is a methodology for finding the best location for weather monitoring and

forecasting. It is a type of experimental design methodology that provides a framework for finding

the best measurements for a given experiment. The optimal measurement is usually found through

finding the observation that produces largest change in a measure, such as total variance or a par-

ticular eigenvalue of a covariance matrix (for a general overview from a statistics perspective, see

Chaloner and Verdinelli (1995) andFedorov (1972)). Many different approaches to optimal net-

work design have been extensively explored within the geophysical literature, including adjoint,

singular vector, variational, and ensemble approaches for both fixed and targeted observations.

Adjoint and singular value techniques, such as Dimet and Talagrand (1986), Baker and Daley

(2000), Buizza and Montani (1999), Buizza et al. (2007), find optimal locations by examining the

sensitivity of a particular location to forecast singular vectors or to produce a sensitivity field to

locations using an adjoint model. A large variety of ensemble Kalman filter (EnKF) approaches

have also been used for both fixed and targeted optimal network design. The general approach in

Kalman filter methods is to used archived forecasts to calculate model covariances and estimate

the impact of new observations (either fixed or targeted) on these model covariances without using

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an adjoint model. One method, the Retrospective Design Algorithm (RDA) described in Khare

and Anderson (2006), tests the impact of sets of fixed networks by maximizing an objective func-

tion of covariance matrices that have been updated to reflect the potential new networks. Bishop

et al. (2001) and Majumdar et al. (2002b) developed an ensemble transform Kalman filter (ETKF)

approach to find optimal observations. The ETKF approach has been used to design both adap-

tive and fixed observational networks in both simple model and fieldwork implementations. The

ETKF approach also uses archived forecasts to find optimal observations for any desired forecast

lead time, but does so by transforming the forecast error covariance matrix within an EnKF frame-

work into an orthonormal vector form to quickly solve for optimal locations. Many subsequent

studies have successfully used the ETKF for optimizing and developing a wide variety of networks

(e.g., Majumdar et al. (2002a), Aberson (2003), Xue et al. (2006)). Similar to the ETKF approach

is the ensemble sensitivity approach developed in Ancell and Hakim (2007), which we used for our

experiments. The ensemble sensitivity approach does not transform covariance matrices, and uses

the sensitivity of state variables to a generic metric function (which can be non-state variables)

to find optimal measurements. The ensemble sensitivity approach has been tested in theoretical

modeling for time-averaged observations (Huntley and Hakim 2010), used to identify an optimal

climate observing network for the Pacific Northwest (Mauger et al. 2013), and to find salinity and

sea surface paleoclimate estimates from corals (Comboul et al. 2005).

The optimal network design approach here uses existing deterministic model analyses and fore-

casts (not archived ensembles) to find locations that best measure some field (such as temperature

or 500hPa heights) by finding the locations that most reduce the total variance in a chosen metric,

for an ensemble sample. The statistics of the field are then updated to reflect this new hypothetical

measurement, and then a second favorable location conditional on the first may be found by op-

timizing over the new statistics. This allows for finding an optimal network sequentially without

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needing to run a model and is a flexible methodology that can take into account other concerns,

such as masking out locations that may not feasibly support a weather station from the optimal

design calculation.

The outline of the remainder of the paper is as follows. In section 2 we describe the data used

for this work and provide a brief assessment of the current Antarctic surface observing network

as performed in previous work. We also describe the theoretical underpinnings of the optimal

network design approach and algorithm used, as well as the statistical approach for implementing

the optimal network design algorithm. In section 3 we discuss the results of three optimal network

calculations. The first is a set of “blank slate” calculations, in which no other stations are assumed

to exist. The second is a set of augmented networks conditional on existing stations. The third

experiment ranks a subset of the existing surface stations. Each set of experiments optimizes for

two objective measures: surface temperature monitoring at 0000 UTC, and for reducing forecast

errors in surface temperature, which allows a comparison between the geographic locations and

variance reduction for both metrics. Finally, section 4 provides a discussion of the results and

suggestions for further work in this area.

2. Data and Methods

a. Data

The model temperature data for this study was taken from the Antarctic Mesoscale Prediction

System (AMPS) (Powers et al. 2012). AMPS is a real-time numerical weather prediction system

run by the National Center for Atmospheric Research (Skamarock and Klemp 2008) in support

of the weather forecasting needs of the United States Antarctic Program (USAP) and its Antarctic

scientific and logistical operations. AMPS runs a polar-modified version of the Weather Research

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and Forecasting Model (WRF), and the system uses the WRFDA (Barker et al. 2004) (Huang et al.

2009) data assimilation package employing a 3-dimensional variational (3DVAR) approach for the

ingest of Antarctic observations. The system has run WRF on multiple grids covering Antarctica

and the Southern Ocean (see, e.g., Powers et al. 2012), and the archived gridded model output

used in this study is from a domain covering the continent at 15-km resolution. The area shown in

the plots of Fig. 1 reflects this domain.

Forecasts from AMPS have been verified and evaluated, including when AMPS used MM5 as a

predecessor to WRF (see, e.g., Powers et al. (2003), Bromwich et al. (2005), Monaghan et al.

(2005), Lazzara et al. (2012), Bromwich et al. (2013)). The statistics of AMPS output have been

shown to be in good agreement with the statistics of observations. A recent example is that of

Bumbaco et al. (2014), who found good agreement between station observations and AMPS out-

put, both for 2-m temperature and surface pressure, as well as good agreement between forecast

fields and observations, lending confidence that AMPS output can be used for optimal network

design. To date, the AMPS Schlosser et al. (2010)). Here, the data used are WRF 2-m temperature

(from the 15-km continental grid) over the period 31 September 31 2008 to 1 October 1 2012.

Data beyond Oct 2012 were not used due to a change in the AMPS resolution. All data reflect the

0000 UTC analyses and forecasts initialized at 0000 UTC with lead times of 12, 24, and 36 hours.

b. Antarctic Surface Observing Network

The current Antarctic surface network consists of Automatic Weather Station (AWS) sites main-

tained by different countries and efforts, as well as various manned surface stations and bases.

The AWS sites provide crucial observational data over the entire continent and provide informa-

tion that is assimilated into AMPS forecasts. In addition to real time observation, AWS stations

provide historical data for many Antarctic weather and climate studies (Lazzara et al. 2012). The

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network has also primarily grown to serve the purposes of the United States Antarctic Program

(USAP) and the research efforts of the National Science Foundation (NSF). While the network is

important for furthering these goals, both existing and potential new stations may also be quite

valuable for the analysis of specific phenomena or the forecasting for a specific area of operations.

c. Network Design Theory

We take an ensemble sensitivity approach in this study to find optimal station locations. The

general idea behind the ensemble sensitivity approach is to use existing data to calculate perturba-

tions about some mean state and then use those perturbations to calculate the impact of a potential

new observation on some value describing the system. The theoretical framework for finding op-

timal observations for a scalar using ensemble sensitivity theory was derived in Ancell and Hakim

(2007). This scalar ensemble sensitivity approach has been used for Pacific Northwest climate

monitoring (Mauger et al. 2013), and salinity and sea surface temperature paleoclimate estimates

from corals (Comboul et al. 2005).

In most situations the observations must be optimized to accomplish more than one goal, which

is not possible with the scalar approach. Here we use a multivariate generalization approach,

which allows for simultaneous optimization with respect to multiple metrics, similar to the ETKF

method described in Bishop et al. (2001) and Majumdar et al. (2002b). However, unlike the ETKF

approach, this approach can be used optimize for any general function of state and/or non-state

variables, not simply covariances of state variables. We choose our general metric function to be

the trace of a covariance matrix for the metrics, and define the best measurement as the one that

maximizes the change in the trace (the total variance) when that measurement is incorporated.

First, a vector metric to optimize for is chosen,

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J =

2

6666666664

J0

J1...

Jn

3

7777777775

(1)

where J0 . . .Jn are a set of scalar values or components of a multivariate quantity. A leading-order

Taylor approximation to the metric, J, dependent on the vector state of the system, x, gives

dJ ⇡

∂J∂x

�Tdx (2)

where superscript T represents the transpose operation. The total variance of J is then approxi-

mated by

d⌃2J = {dJdJT}⇡

∂J∂x

�TA

∂J∂x

�(3)

where

A = {dxdxT}

is the state covariance matrix and the curly braces denote an expectation.

When a new observation is incorporated, the state covariance A changes to A0, and the variance

of the metric also changes. Therefore, from (3), we have that

d⌃2J =

∂J∂x

�T(A

0 �A)

∂J∂x

�. (4)

The optimal location is the one that maximizes d⌃2J. As shown in Ancell and Hakim (2007),

this relationship may be written in terms of a covariance,

d⌃J =�1E⇥DJTAHT

⇤⇥DJTAHT

⇤T (5)

DJTAHT = {dJ(Hdx)T} (6)

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where D is the Jacobian operator and H is the observation operator that maps from state to met-

ric space. The state in the context of this study is the field of temperature values where there could

be a potential new observation. E is the scalar total error variance of a potential new observa-

tion, given by E = HAHT +R, with R being the measurement error covariance matrix. Eq. 6 is

used to calculate the change in the trace of the covariance matrix without explicitly calculating

the covariance matrix itself (which can be computationally expensive). Instead, only the metric

perturbations, observation operator, and state perturbations are needed to calculate the change in

covariance trace.

The general procedure for finding optimal locations uses the following algorithm.

1. Choose a vector metric that quantifies an aspect of the system of interest (such the covariance

matrix for temperature across a region)

2. Calculate the total variance for the metric (trace of the metric covariance matrix)

3. Calculate change in the total variance for all possible locations

4. Choose as the optimal measurement location the point that maximizes the change in total

variance

5. Update the metric and state to reflect the chosen measurement

6. Repeat the procedure for the next measurement, using the updated state and metric to find the

next location conditional on the previous measurement (i.e., repeat steps 4–6)

Our metrics in this work are 0000 UTC 2-m temperature and 12-, 24-, and 36-hr 2-m forecast

temperature errors at every 20th grid point on the 15-km AMPS continental grid.

The change in total variance is given in Eq. 5. To find an optimal station, Eq. 5 is evaluated

for every potential observation location (which is every 5th model gridpoint), and the location of

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Guillaume

Guillaume

Guillaume

I still think a plain english definition of the Jacobian would be helpful here

suggest moving this sentence up to where you first define x

maximum change is chosen as the optimal location. The state and metric perturbations are updated

using the square root form of the ensemble Kalman filter (Whitaker and Hamill 2002),

dxa = dxp � K̃Hdxp (7)

where the superscript a denotes the value after assimilating a new observation, and p the value

prior to assimilation. The modified Kalman gain K̃ is given by

K̃ = aK = aApHTE�1

where

a =

1+r

RHApHT +R

!�1

Once the state and metric are updated to reflect the new observation, the process repeats until the

desired number of stations is reached. This procedure ensures that each station, with the exception

of the first, is conditional on previous optimal stations.

d. Sampling and Bootstrap Error Estimates

Since the exact covariance matrix and probability density function of the surface temperature

field are unknown, we estimate sample covariances from the available AMPS data for the optimal

design calculation. Each iteration of the optimal calculation is done by randomly choosing

250 ensemble members each time from the AMPS temperature output, which are then used to

calculate the state and metric perturbations. 250 ensemble members were chosen for several

reasons. A variety of ensembles sizes were tested, from 30 members to 1000 members, and

250 member ensembles gave results that were qualitatively and quantitatively consistent with

the largest ensembles. Smaller ensembles did not produce results that were geographically

localized, instead resembling a random selection of observations. 250 was also close to the

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Guillaume

Guillaume

out of a total sample size of ???

in this case, “ensemble” refers to a collection of different observation times. This may not be clear to the non-statisticians

computational rank of the temperature covariance matrix (when every grid point across the entire

data period was used to calculate the covariance matrix). Hence, a smaller ensemble size might

underestimate covariances, and using an ensemble larger than 250 would not provide enough

additional information to justify the computational cost of using a very large ensemble.

The number of degrees of freedom of the surface temperature field are also large, and because

sampling error must be addressed, we use this random sampling with a Monte Carlo bootstrap

approach to estimate the uncertainty in the network calculation. This bootstrap approach also

allows us to examine the error in the change in total variance for each station. Each iteration

of the optimal calculation is done by randomly choosing a new ensemble of 250 members

each time from the AMPS temperature output, which samples a large variety of different states

of the temperature field. The network identification results are determined for this ensemble,

as described in the algorithmic approach above, until 20 locations are found for the idealized

network. The process is repeated 10000 times, providing 10000 sets of 20 locations, allowing for

statistics on station location.

3. Results for Constructing Networks

We constructed two types of networks for weather and climate monitoring, one optimized for

0000 UTC 2-m temperature (monitoring), and one optimized for reducing 2-m temperature fore-

cast errors. The analysis network is constructed by using the covariance matrix of 2-m temperature

at 0000 UTC and calculated using every 20th grid point over the continent, and every 5th grid point

is considered as a possible observation (and is also used to calculate the state vector). The forecast

error network is constructed by using 2-m temperature forecast errors at a lead times of 12, 24,

and 36 hours also at every 20th grid point over the entire continent, and the state is the 0000 UTC

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Guillaume

Guillaume

Guillaume

Guillaume

Guillaume

Guillaume

time step? (instead of grid point)

isn’t it not the computational cost but the ability to have meaningful differences among samples in your bootstrap procedure?

Why 20? This should be justified somewhere too.

I still think there needs to be some stated rationale for the 20th / 5th grid point subsamples

I find this notation more distracting than the simpler “00Z” notation

first use of “analysis” — needs to be defined

temperature at every 5th grid point 12, 24, and 36 hours prior.

For both networks, we consider three experiments. The first experiment (“blank slate”) finds the

best observation locations in Antarctica assuming no other stations currently exist. The second

experiment (“CD90”) is an “augmented” network, where the influence of existing stations are

removed before new stations are found. In this second case, the influence of Antarctic surface sta-

tions that report at least 90% of the time (subsequently denoted as CD90), as described in Bumbaco

et al. (2014), are first removed through multiple linear regression, and then the optimal calculation

algorithm is applied on the residual state and metric perturbation values. This method assumes

that the observations are perfect and does not take into account their error, which probably results

in too much variance being removed. This second experiment produces an optimal network that is

conditional on the current network, and shows the optimal locations to add new stations. The third

experiment is one where the CD90 stations are ranked based on how well the stations capture the

variance of the temperature field or reduce forecast errors. The metric remains the same as in the

other networks, but only grid points which are closest to CD90 locations are considered for the

observations.

a. Monitoring Networks

1) BLANK SLATE NETWORK

The first network chosen by the optimal design algorithm is one where no currently existing

stations are taken into account – the network is designed “from scratch”. The results for the

monitoring networks are given in Figs. 3 and 4. In the blank slate calculation in Fig. 3, the most

frequently chosen first station is in the Megadunes region in East Antarctica. This location is

chosen about 22% of the time, and explains nearly half of the total variance of the temperature

field. The closest CD90 station is Vostok, but the point chosen most often is within a large

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Guillaume

Guillaume

Guillaume

as before: is this regardless of rank or do you mean that it’s chosen as the top location?

an overestimate of the variance explained

which 2 networks?

Your description of the 3rd experiment doesn’t seem consistent with what you have in your results section

gap in the existing network in East Antarctica. This region corresponds to some of the longest

correlation length scales in Antarctica (Bumbaco et al. 2014). Locations with long correlation

length scales allow information from measurements to affect a large area, which yields a relatively

larger change in the total variance compared to locations with shorter correlation length scales. A

physical explanation for why relatively long correlation length scales exist in East Antarctica is

that the strong winds, katabatic flows, and strong stability in this region dominate the variability

in the two-meter temperature field, which can have a large geographic space (e.g., Dadic et al.

(2013)). Another possible reason for the interior being chosen is that given that only land/ice

shelf locations were used for the metric and potential new observations. Coastal variability is not

a large portion of the total temperature variance over land/ice, and so locations in the interior of

the polar vortex dominate the variability over Antarctica. The second station, chosen about 22%

of the time, is very close to Siple Dome in West Antarctica, indicating its potential importance

in monitoring continental surface temperature. The third station (chosen about 4% of the time)

is located on the polar plateau poleward of in Queen Maud Land in another gap in the surface

network.

2) AUGMENTED NETWORK

The results for the augmented network are presented in Fig. 4. The results are significantly

different from the blank slate network, reflecting the contribution from existing AWS stations.

The change in variance of the stations chosen is an order of magnitude smaller than the change

in variance in the blank slate network, since much of the variance has been regressed out. The

first station (about 35%) is on the coast of East Antarctica in Coats Land and near the Ronne Ice

Shelf. The second location (about 58%) is close to the second location chosen in the blank slate

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Guillaume

Guillaume

odd coincidence that both are chosen 22% of the time

This is an important point — would be worth exploring in another paper, and also worth repeating in your conclusions.

calculation, but further from Siple Dome. Perhaps counterintuitively, the second station is chosen

more frequently than the first, but some of this is due to spatial uncertainty. A second location is

chosen fairly frequently for the first station, close to the most frequent point. The second station

only has one frequent location, with less spatial uncertainty. This does indicate that some of

the variance after regressing the CD90 stations maybe be at the level of noise, since the linear

regression overestimates the impact of existing stations by not taking into account observational

error.

The third location (about 15%) is in Queen Maud Land in East Antarctica. Since much of the

total variance has already been removed, it is difficult to connect these results to large-scale

meteorological influences, and these results are likely due to local topological/meteorological

effects that cannot be explained by the CD90 network. The multiple linear regression used to

account for existing stations has likely overestimated the impact of the CD90 stations, and so

further work would be needed to determine a more realistic impact of these stations.

3) CD90 RANKINGS

Although the results of the blank slate calculation are suggestive of which CD90 stations are

important for surface monitoring, an additional calculation to gauge the relative importance of the

CD90 stations compares the variance reduction for the points nearest the CD90 stations to that for

the blank-slate calculation. The results are summarized in Table 1. The first station, Vostok, is

chosen about 99% of the time and is the CD90 location closest to the blank slate top station in

the Megadunes vicinity as shown in Fig. 3. Vostok reduces a similar amount of variance as the

first station of the blank slate calculation - the median variance explained by the first station in

the CD90 calculation is 43%, which is within a one standard deviation envelope of the median

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variance explained by the first station in the blank slate calculation (45%). The second and third

stations, Siple Dome and South Pole, are the two closest CD90 stations to the most frequently

chosen locations for the second and third stations in the blank slate calculation. These results

show that Vostok, Siple Dome, and South Pole are the most important stations for monitoring

surface temperature, albeit suboptimally (meaning they explain less of the total variance than the

optimal locations). These stations are important for logistical and research purposes as well, and

putting in stations in the optimal locations may provide excellent redundancy in the network for

situations where these CD90 stations cannot report or have data interruptions.

b. Forecast Error Reduction Networks

1) BLANK SLATE NETWORK

We constructed another “from scratch” network, but this time finding optimal locations to reduce

forecast errors for temperature at various lead times. The results for reducing 2-m forecast errors

over Antarctica for forecast lead times of 12, 24, and 36 hours are shown in Figs. 5, 6, and 7,

respectively. For all the lead times, there is more spatial uncertainty in terms of the most optimal

location, and there is a smaller percentage change in the total variance compared to the analysis

network. The first station for reducing 12-hr 2-m temperature forecast errors is located near Terra

Nova Bay, the second is in Marie Byrd Land in West Antarctica, and the third station is close to

the first, but closer to Cape Adare. The Terra Nova Bay/Marie Byrd Land/Ross Shelf locations

are places of some of the most significant mesoscale activity concurring with katabatic flows in

Antarctica, especially compared to the Antarctic Peninsula (Carrasco et al. 2003). The first three

locations are likely statistically sensitive to large-scale conditions that can give rise to significant

mesoscale activity, which dominates the surface temperature variability on short time scales. If

the right conditions for such activity are captured by surface observations, then forecasts can be

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somewhat

It would be great to include this comparison for all 3 top stations in Table 1, by adding an additional column that lists the corresponding variance reduction for the nearby blank slate location

associated

improved and thus forecast errors reduced for lead times of 12 hours.

The results for the 24- and 36-hr lead time networks are similar to those for 12-hr lead times, with

the first most frequent location in East Antarctica near Vostok, the second in Marie Byrd Land

(close to the 12-hr second location), and the third near Halley in East Antarctica (Coats Land). For

the 36-hr network, a location near Cape Adare is chosen relatively frequently as well (although it

is not the most frequently chosen location). These results are consistent with the analysis network

and the 12-hr network, which we suspect is due to the fact that East Antarctica is a location with

long correlation length scales for surface temperature, and so more optimally observing surface

temperature in this region (and assimilating it into a forecast model) will likely reduce 24- to 36-hr

forecast errors. The locations of significant mesoscale and katabatic activity are also highlighted

as regions to measure to help reduce forecast errors.

2) AUGMENTED NETWORKS

Once again an augmented network conditional on the existing CD90 stations is constructed for

forecast lead times of 12, 24, and 36 hours. The results are presented in Figs. 8, 9, and 10 respec-

tively. For all three lead times, similar locations are chosen as in the unaugmented forecast error

networks. This calculation is different from the monitoring network results, where both the “blank

slate” and augmented networks give fairly similar results. The first location is in Marie Byrd Land,

the second in East Antarctica in Coats Land, and the third near Cape Adare. A significant portion

of the surface temperature forecast error variance is removed through the linear regression used

to remove the influence of the CD90 stations, so the locations chosen only explain a very small

amount of variance ( 1%-2%). As in the monitoring experiments, the results are consistent with

each other and are still somewhat geographically localized. This suggests that the current CD90

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Guillaume

Does it make sense that the 12-, 24-, and 36-hour networks highlight similar locations w.r.t. the mesoscale/katabatic activity? I would think there would be a lagrangian effect that would be important — i.e., longer lead times point further upstream..

Too vague. What exactly do you mean? This doesn’t logically support the subsequent sentence.

network may not be capturing some variance in the temperature field that could reduce forecast

errors for 12, 24, and 36 hours.

3) CD90 RANKINGS

The CD90 stations were also ranked in terms of their importance in reducing 12-, 24-, and 36-hr

forecast errors. The results are given in Tables 2 - 4. The station chosen most frequently for the

first location for 12- and 24-hr forecast lead times was Vostok (which was also the most chosen

location for the analysis network), and McMurdo was chosen for the top location for 36-hr forecast

errors. The second and third stations are in different locations from the second and third stations

chosen in the forecast error analysis network. Siple Dome and South Pole were the second and

third stations chosen for the analysis network. For reducing forecast errors, McMurdo and Halley

are chosen as the best locations (with the exception of 36 hours, where Vostok is second and

Halley is third). These results are consistent with the blank slate forecast error networks – the

region near Vostok is highlighted significantly for all three lead times. McMurdo is not far from

the second location chosen in Queen Maud Land, although it is not the closest (Siple Dome is), but

it probably covaries more with the location in Queen Maud Land than Siple Dome does. Halley

is on the East Antarctic coast, and is the closest CD90 station to the location chosen for the third

observation in the blank slate calculations. However, as in the network chosen for monitoring at

0000 UTC, these stations are suboptimal compared to the optimally chosen stations for forecast

errors. If one is interested in reducing forecast errors for surface temperature, assimilating Vostok,

McMurdo, and Halley more often may be worth investigating. If stations were installed in the

locations chosen in the blank slate calculations, the already-existing stations could provide useful

redundancy for the optimally sited stations.

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have you noted previously that these are not consistently assimilated, and why? An unacquainted reader might

assume that these are always assimilated, by default.

c. Statistical Significance and Error in Results

All of the optimal networks constructed here are for 20 stations. This number was chosen to

examine the variance reduction predicted by the optimal design calculation beyond just a few

stations, but not so many as to be computationally too intensive. In real world situations the

number of new stations place will likely be affected by practical concerns, such as budget or time

to service only a certain number of stations during a field season in Antarctica. However, it is

important to know how many stations can be chosen by this optimal design approach before the

variance reduction of a new station is no longer statistically significant and so is not providing any

new information above a randomly chosen station.

To test whether the variance reduction of each station was distinct, we performed a Kolmogorov-

Smirnov (KS) test between the variance reduction distribution of a station obtained from Monte

Carlo sampling and the next one chosen (for instance, between the distribution of the 3rd and 4th

station). For all of the experiments discussed above, all 20 stations pass the KS test at a 99%

confidence level, but all of the stations beyond the 2nd or 3rd only remove a small percentage of

the total variance ( 1-2%). It is not clear whether these small percentage changes are choosing

meaningful locations. A large fraction of this variance is removed by the first station. For

example, the first station for the 0000 UTC temperature monitoring network removes about 45%

of the total variance (as seen in Fig. 3). This is possibly an overestimate of the impact the first

station has on the total variance, and so subsequent stations may be optimizing over residual

variances that could be on par with noise. A similar concern is also at play for the augmented

networks. The linear regression used to remove the influence of the CD90 stations removes

about 85-95% of the total variance, leaving little variance with which to find optimal location

conditional on the CD90 stations. The variance reduction of the augmenting stations are very

19

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Somehow, this section needs to be incorporated into the methods section instead of here. I see the issue: you discuss the results below, but that problem can be solved by separating out the pieces that should go under Summary/Discussion. Otherwise readers have no basis for understanding your choice of 20 stations in earlier parts of the manuscript.

too

suggest replacing with something simpler, like “such as accessibility, maintenance requirements, and available budget”.

Suggest deleting this paragraph entirely, and adapting the first sentence to be an introduction to the second paragraph below.

e.g.: “For simplicity, all of the optimal network calculations are truncated after 20 stations have been identified.”

One possibility is that the variance explained by the first station is overestimated, leaving artificially small residuals for

subsequent stations, which may not be distinct from random noise. This could also be the issue for the augmented networks.

statistically robust

latter sites

the

small, and so the variance reduction on new stations may not be significant. This is suggested in

geographic distribution of locations chosen in some of the networks. The first location chosen is

geographically localized (a few points being chosen frequently, and most other points chosen are

clustered around the most frequent points). The second and third stations are more geographically

distributed, with a few locations chosen most frequently but with a lot of geographic variability

over all 10000 iterations. A purely random selection would choose all points over Antarctica

with the same frequency, and so a large geographic distribution of points chosen approaches the

random result.

One technique that can be employed to adjust variance reduction calculation is covariance

localization. Spurious correlations may occur due to sampling error or other effects between

geographically distant locations that in reality are uncorrelated. For instance, the top of the

West Antarctic peninsula may have a spurious correlation with a point in the interior of East

Antarctica on daily timescales in our analysis. However these two points are distant, separated

by significant topography, have very different weather on short timescales (coastal versus high

plateau), and the correlation length scales in the peninsula are much shorter than the distance

to East Antarctica (Bumbaco et al 2014). Some part of this correlation is likely a statistical

anomaly and not physically real. Covariance localization seeks to either remove or minimize these

spurious correlations. This is usually done by weighting covariances using a function of distance

– covariances between points that are far apart are weighted less, and covariances between points

closer together are weighted more.

As a sample calculation, we applied covariance location as described in Gaspari and Cohn (1999)

to the variance calculation by multiplying the Kalman gain in equation 7 for the blank slate

monitoring network case. A localization radius of 2000km, roughly the average correlation length

scale over Antarctica, was used for the calculation.

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the

In particular because in a model, which will tends to under-represents local-scale influences on weather variability

or an artifact of the AMPS model

The results are shown in Fig. 11. The top three stations are in similar locations are the top the

stations for the unlocalized calculation, but the variance reduction of the stations are an order of

magnitude smaller than the variance reduction in the unlocalized calculation. As such it is likely

many more stations could be found before the results are not statistically different from that of

randomly chosen stations. The qualitative similarities between both localized and unlocalized

results that an unlocalized approach can be used to find a few stations, but for a large amount of

stations a localization approach may be necessary. However, how localization should be applied

(what is the appropriate radius, should it be adaptive, how to apply localization in time for forecast

errors etc.) is very dependent on the particular covariance structures of a system of interest. In

order to make decisions concerning where to place new stations, localization should be explored

and understood in the specific context of a desired network in future work.

Another valuable experiment for further work, especially for determining where to place new

stations in Antarctica, would be an Observing System Experiment (OSE). An OSE is an

experiment that is used to evaluate the impact of observations on a model analysis or forecast

in a context that mimics a real-world forecast system. Once an OSE is performed, it can be

used to adjust the optimal design calculation (by adjusting how much variance is removed, how

much localization is applied), and so can provide a more realistic variance reduction spectrum,

especially for finding optimal locations to reduce forecast errors. An OSE runs an actual forecast

model, and so more accurately captures the nonlinear relationship between a current time and a

future forecast hour. In our approach, the relationship between an observation and forecast errors

12, 24, and 36 hours in the future is treated as linear. Although this relationship may be accurate

to first order on short timescales and short geographic distances, it will not hold well for longer

lead times where more nonlinear dynamics and large changes in synoptic conditions come into

play, and so our ensemble sensitivity approach overestimates the impact of an observation on re-

21

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suggests?

calibrate?

ducing forecast errors by overestimating how much that observation correlates with forecast errors.

4. Summary and Discussion

Good observations are crucial for supporting science and operations over the Antarctic conti-

nent. Due to the unique and harsh conditions in Antarctica, it is expensive to install and maintain

a dense observing network. This means that it is critical to weigh the potential costs and benefits

when deciding where to place new stations and whether or not to retain current stations. Optimal

design provides a means of maximizing the information and coverage of the observing network,

and provide an objective framework to help make such decisions.

Two types of networks have been considered – one aimed at accurately monitoring 2-m tempera-

ture over the continent, and one aimed at reducing forecast errors at lead times of 12, 24, and 36

hours. The data used to perform these calculations come from AMPS over a period of 4 years. A

multivariate ensemble sensitivity approach with Monte Carlo bootstrapping is used to find optimal

locations, with optimal locations being those which maximally reduce the total variance of the

metric (which in this case was surface temperature). Three calculations were performed for three

types of networks. First, a blank slate calculation is done to find optimal locations if no stations

currently existed in Antarctica. The second calculation involved regressing out the influence of

the CD90 stations, and then optimizing over the residuals, providing an optimal network that is

conditional on already existing networks. The third calculation is a ranking of the CD90 stations,

where only the grid points closest to those stations were considered as potential observations to

allow for gauging their relative importance with respect to the metrics.

For the blank slate calculation where no other stations exist for monitoring daily surface tem-

perature, the top three locations are central East Antarctica near Vostok, in Marie Byrd Land on

22

the Siple Coast, and again East Antarctica but near South Pole. The most variance is explained

by the first station, and all the results give clear, geographically localized areas that are most

sensitive to the surface temperature field over 10000 Monte Carlo iterations. The augmented

network provides slightly different results, with the top locations being near Halley, a different

location along the Siple Coast, and a location in East Antarctica in Queen Maud Land. A lot of the

variance in the metric is removed, and so these conditional stations explain very little of the total

variance, suggesting that the current CD90 network already provides adequate coverage, although

some gaps do exist, especially in East Antarctica (see Bumbaco et al. (2014)). The CD90 ranked

network chooses stations that are geographically close to the optimal blank slate locations, with

the top 3 stations being Vostok, Siple Dome, and South Pole. East Antarctica is an area of long

correlation length scales on daily timescales, and so a station in East Antarctica will explain much

of the total temperature variance since it will covary with much of the region.

The networks for forecast errors are fairly consistent with each other for all lead times. The

blank slate network chooses Oates Land, Marie Byrd Land, and Cape Adare for the first three

stations for a lead time of 12 hours. These locations are places of largest mesocyclone activity in

Antarctica, and hence may be a large source of forecast errors if large-scale conditions suitable for

mesocyclone development are not captured adequately by the observing network. For lead times

of 24 and 36 hours, East Antarctica near Vostok, Marie Byrd Land, and a place on the coast in

Queen Maud land near the Weddell Sea are chosen as the top three stations. The calculation with

the CD90 stations regressed out highlights the same areas, suggesting there may be additional

information that could be measured to reduce forecast errors that the current network is not

capturing. Finally, the CD90 rankings choose the same 3 stations for all lead times as the best -

Vostok, McMurdo, and Halley. These locations are geographically close and statistically similar

to the locations identified in the blank slate calculation, but do not explain as much total variance

23

as the optimally chosen locations. As with the analysis case, if new stations are installed, these

three stations would provide important redundancy in the network for the optimal stations.

The uses of the Antarctic surface network are manyfold, and so a more complete evaluation is

necessary to . However, the framework presented here provides a flexible methodology to do

so without the need to run forecasts. Because we used the total variance as metric, the results

are consistent with a statistical analysis of correlation length scales. However, this methodology

is not constrained to simply using total variance – other metrics, such as leading eigenvalue or

determinant of the covariance matrix (which measure information content), may also be used

within the same general algorithm. This methodology can also take into account already existing

stations and find new locations conditional on those stations, providing an objective means to do

so.

More work needs to performed, however, to address the statistical significance of stations chosen

and what adjustments need to be made to the algorithm for specific applications of this optimal

design approach. Our work likely overestimates the impact a station has on a metric, and so the

variance removed by the first few stations is too large. The residual variance used to find more

stations is noisy and does not provide statistically significant results. These issues need to be

investigated before the optimal design algorithm is used to make decisions on where to place new

stations in Antarctica or elsewhere. Further work should focus on adjusting the variance reduction

in the optimal design calculation. This may be done through applying covariance localization and

performing OSEs.

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is needed

variance explained by a particular station

5. Acknowledgements

This work was funded by NSF grant number 1043090. The authors would like to thank Kevin

Manning for providing the AMPS data. The authors would also like to thank Matthew Lazzara for

all of this helpful discussions concerning the Antarctic surface observing network, and Eric Steig

for his discussions concerning Antarctic weather and climate.

25

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LIST OF TABLESTable 1. Ranked results of top three CD90 stations chosen to optimize for continent-

wide two-meter temperature. The frequency chosen for the stations 2 and 3indicate how often that location is chosen, but not conditional that the previousstation be optimal (i.e., every time the top location for station two is chosen thetop first station chosen may not have been the most frequently chosen stationover all trials). The variance reduction gives the median conditional variancereduction over all trials. . . . . . . . . . . . . . . . . . 30

Table 2. Ranked results of top three CD90 stations chosen to optimize for continent-wide two-meter temperature forecast errors for a lead time of 12 hours. Thefrequency chosen for the stations 2 and 3 indicate how often that location ischosen, but not conditional that the previous station be optimal (i.e., every timethe top location for station two is chosen the top first station chosen may nothave been the most frequently chosen station over all trials). The variancereduction gives the median conditional variance reduction over all trials. . . . . 31



30

TABLE 1. Ranked results of top three CD90 stations chosen to optimize for continent-wide two-meter tem-

perature. The frequency chosen for the stations 2 and 3 indicate how often that location is chosen, but not

conditional that the previous station be optimal (i.e., every time the top location for station two is chosen the top

first station chosen may not have been the most frequently chosen station over all trials). The variance reduction

gives the median conditional variance reduction over all trials.

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35

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Station Number Name Frequency Chosen Median Variance Reduction in Metric

Station 1 Vostok 98.54% 43.08%

Station 2 Siple Dome 74.81% 5.71%

Station 3 South Pole 62.61% 5.29%

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Suggest adding a column with the variance reduction corresponding to the nearby optimal location in each case

The “Frequency Chosen” numbers are unclear: Does this refer to the frequency that this site is chosen in any of the top X stations (e.g., any that fall above the threshold for statistical significance)?

I assume you are instead listing the % of the time it’s selected for the specific ranking that’s most common — e.g., Vostok is selected 1st 98.54% of the time. But this might be misleading, since one location may be selected frequently but not consistently placed in one specific ranking.

TABLE 2. Ranked results of top three CD90 stations chosen to optimize for continent-wide two-meter temper-

ature forecast errors for a lead time of 12 hours. The frequency chosen for the stations 2 and 3 indicate how often

that location is chosen, but not conditional that the previous station be optimal (i.e., every time the top location

for station two is chosen the top first station chosen may not have been the most frequently chosen station over

all trials). The variance reduction gives the median conditional variance reduction over all trials.

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Station 2 McMurdo 70.60% 4.84%

Station 3 Halley 63.68% 2.62%

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LIST OF FIGURESFig. 1. Plot of the AMPS grids, including the 15km grid. Taken from Powers et al. (2012). . . . . 35

Fig. 2. Antarctica with referenced regions and locations. . . . . . . . . . . . . . 36

Fig. 3. First three optimal stations for monitoring 0000 UTC 2-m temperature over the entire con-tinent. Cells that are colored indicate that location was chosen at least once, and colorindicates the frequency with which that location is chosen over 10000 iterations. The greencircles represent the CD90 stations. The green boxes indicate the median percentage of thetotal variance that is explained by top three stations. The boxes in the spectrum plot indicatethe lower to upper quartile range for the optimal change in total variance over all iterations,and whiskers extend to 99.3% (two standard deviations) of the distribution. . . . . . . 37

Fig. 4. Same as Fig. 3, but with the influence of the CD90 stations regressed out before optimalstations are chosen. . . . . . . . . . . . . . . . . . . . . . 38

Fig. 5. Same as Fig. 3, but using 2-m temperature 12-hr forecast errors over the entire continent asthe metric. . . . . . . . . . . . . . . . . . . . . . . . 39



Fig. 8. Same as Fig. 5, but using 2-m temperature 12-hr forecast errors over the entire continent asthe metric, with the influence of the CD90 stations regressed out. . . . . . . . . . 42



Fig. 11. Same as Fig. 3, but with covariance localization applied. The variance reduction of thefirst 3 stations are about an order of magnitude smaller than the variance reduction of theunlocalized network. . . . . . . . . . . . . . . . . . . . . 45

35

FIG. 1. Plot of the AMPS grids, including the 15km grid. Taken from Powers et al. (2012).

36

I assume you’ll generate a higher resolution version of this image? I like the format, but this is too grainy

FIG. 2. Antarctica with referenced regions and locations.

37

This should either be integrated into Figure 1 or shown alongside it as Fig 1a and 1b — same domain/etc.; one shows elevation (and maybe ice shelves), the other shows the referenced regions/locations

FIG. 3. First three optimal stations for monitoring 0000 UTC 2-m temperature over the entire continent. Cells

that are colored indicate that location was chosen at least once, and color indicates the frequency with which that

location is chosen over 10000 iterations. The green circles represent the CD90 stations. The green boxes indicate

the median percentage of the total variance that is explained by top three stations. The boxes in the spectrum

plot indicate the lower to upper quartile range for the optimal change in total variance over all iterations, and

whiskers extend to 99.3% (two standard deviations) of the distribution.

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56

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58

59

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Clarify that this is the blank slate calculation, for comparison with Fig 4

FIG. 4. Same as Fig. 3, but with the influence of the CD90 stations regressed out before optimal stations are

chosen.

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61

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FIG. 5. Same as Fig. 3, but using 2-m temperature 12-hr forecast errors over the entire continent as the metric.

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41


42

FIG. 8. Same as Fig. 5, but using 2-m temperature 12-hr forecast errors over the entire continent as the metric,

with the influence of the CD90 stations regressed out.

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FIG. 9. Same as Fig. 5, but using 2-m temperature 24-hr forecast errors over the entire continent as the metric,

with the influence of the CD90 stations regressed out.

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FIG. 10. Same as Fig. 5, but using 2-m temperature 36-hr forecast errors over the entire continent as the

metric, with the influence of the CD90 stations regressed out.

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FIG. 11. Same as Fig. 3, but with covariance localization applied. The variance reduction of the first 3 stations

are about an order of magnitude smaller than the variance reduction of the unlocalized network.

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