The benefit of using sea ice concentration satellite data products with uncertainty estimates in summer sea ice data assimilation

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Introduction
For the past 30 years, the Arctic sea ice extent and volume consistently decreased in all seasons with a maximum decline in summer (IPCC, 2013).Arctic sea ice decline opens new economic opportunities such as shipping and tourism.Accurate summer sea ice forecasts are therefore urgently required to thoroughly manage the opportunities and risks associated with Arctic climate change (Eicken, 2013).Introduction

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Full Realistic initial model states are important for accurate sea ice prediction; hence sea ice data assimilation (DA) plays a pivotal role in sea ice forecasting.Data assimilation requires both reliable observed quantities and realistic uncertainty estimates.These requirements, especially regarding data uncertainties, are now also increasingly recognized by the sea ice remote sensing community.Previous studies have shown that the assimilation of sea ice concentration data can improve sea ice concentration estimates (e.g., Lisaeter et al., 2003;Lindsay and Zhang, 2006;Stark et al., 2008;Tietsche et al., 2013;Buehner et al., 2014) and also summer sea ice thickness fields through cross-correlations between ice concentration and thickness (Yang et al., 2015a).Given that error estimates in previous efforts were assumed to be constant, there is scope for further improvement through the use of more realistic uncertainty estimates.
In 2010, the European Meteorological Satellite Agency (EUMETSAT) Ocean and Sea Ice Satellite Application Facility (OSISAF, www.osi-saf.org)released a climate data record of sea ice concentration based on SMMR and SSM/I data that covers the years 1978-2009 (Eastwood et al., 2011;Product OSI-409).This dataset features an explicit correction of the satellite signal due to atmosphere weather, dynamic adaptation of algorithm tie-points, and spatio-temporally varying maps of uncertainties.In fact, this OSI-409 dataset and its uncertainties were already successfully used for data assimilation purposes (e.g., Massonnet et al., 2013).
In May 2014, the European Space Agency (ESA)-Sea Ice Climate Change Initiative (SICCI) released a sea ice concentration data set with associated uncertainty estimates (Version 1.11) to the public.In many respects, the SICCI sea ice concentration dataset features an update of the algorithms and processing methodologies used for the OSISAF OSI-409 dataset and, importantly, revised uncertainty estimates (Lavergne and Rinne, 2014).Although the SSM/I time-series produced in SICCI, v1.11 is shorter than that of the OSI-409 (covering only 1992OSI-409 (covering only -2008)), it includes sea ice concentration maps from AMSR-E (2002AMSR-E ( -2011)), which were not available in the OSISAF OSI-409 dataset.This new data set provides an Introduction

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Full opportunity to study the effect of the revised local (i.e., spatially varying) uncertainties on the assimilation of sea ice concentration data, and hence sea ice prediction skill.In this study, we follow the approach of Yang et al. (2015a, b) by focusing on the summer of 2010 and using the same local ensemble-based Singular Evolutive Interpolated Kalman (LSEIK) filter (Pham et al., 1998;Pham, 2001).The purpose of the study is to quantify the impact of different uncertainty approximations on sea ice data assimilation through a comparison with independent ice concentration and ice thickness observations.

Forecasting experiment design
We use the MITgcm sea ice-ocean model (Marshall et al., 1997;Losch et al., 2010Losch et al., , 2014) ) Following Yang et al. (2015a, b), this study employs an Arctic regional configuration with a horizontal resolution of about 18 km and open boundaries in the North Atlantic and North Pacific (Losch et al., 2010;Nguyen et al., 2011).To explicitly include flow dependent uncertainty in atmospheric forcing, the approach by Yang et al. (2015a) was used in which UK Met Office (UKMO) ensemble forecasts from the TIGGE archive (THORPEX Interactive Grand Global Ensemble; http://tigge.ecmwf.int/)drive the ensemble of sea ice-ocean models.Each of the selected UKMO ensemble forecasts consists of one unperturbed "control" forecast and an ensemble of 23 forecasts with perturbed initial conditions.For further details the reader is referred to Bowler et al. ( 2008) and Yang et al. (2015a).
The simulated and satellite observed sea ice concentration are combined using a sequential SEIK filter with second order exact sampling (Pham et al., 1998;Pham, 2001) coded within the Parallel Data Assimilation Framework (PDAF, Nerger and Hiller, 2013; http://pdaf.awi.de).The SEIK filter algorithm is selected to assimilate the sea ice concentration because it is computationally efficient when applying with nonlinear models (Nerger et al., 2005).The filter algorithm includes the following Introduction

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Full phases: initialization, forecast, analysis and ensemble transformation.The sequence of forecast, analysis and ensemble transformation is repeated.The required initial ensemble approximates the uncertainty in the initial state of the physical phenomena.Following Yang et al. (2015a), we used a model integration driven by the 24 h UKMO control forecasts over the period of 1 June to 31 August 2010 to estimate the initial state error covariance matrix of sea ice concentration and thickness.The leading Empirical Orthogonal Functions (EOFs) of the considered model variability are used to generate the initial ensemble of the sea ice state (concentration and thickness).An ensemble size of 23 states is chosen to match with the ensemble size of UKMO perturbed forcing.In the forecast phase, all ensemble states are dynamically evolved in time with the fully nonlinear sea ice model driven by the UKMO ensemble atmospheric forcing.The analysis step combines the predicted model state with the observational information and computes a corrected state every 24 h.The error covariance matrix and ensemble of model state are also updated.With the SEIK filter as a reduced-rank square-root approach, the updated ensemble samples the analyzed model uncertainties according to the leading EOFs.
The SEIK analysis is performed locally for each water column of the model surface grid by assimilating the observational information only within a radius of 126 km (∼ 7 grid points).Within the radius, we weighted the observations assuming quasi-Gaussian (Gaspari and Cohn, 1999) dependence of the weights on the distance from the analyzed grid point (see Janjić et al., 2012).As the atmospheric errors are already explicitly accounted for by the ensemble forcing, an ensemble inflation simulating model errors is not needed in this LSEIK configuration (Yang et al., 2015a).
Three daily sea ice concentration data sets are used in this study.The SICCI fields from AMSR-E (Lavergne and Rinne, 2014) and the OSISAF fields from SSM/I (Product OSI-401-a; Eastwood et al., 2011) are used in the data assimilation, these products consist of daily fields provided on a 25 and 10 km polar stereographic grid, respectively.The two processed data sets come from different satellite sensors, and the SICCI uses more advanced algorithms and processing details, for example, SICCI Introduction

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Full uses a revised algorithm merging method and tunes the tie-points dynamically with a smaller time window than OSISAF (Lavergne and Rinne, 2014) 1 for the locations).The error in ULS measurements of ice draft is estimated as 0.1 m (Melling et al., 1995) Drafts are converted to thickness by multiplying by a factor of 1.1 (Nguyen et al., 2011).
Following Yang et al. (2015a, b), in this study, the system's forecasting skills are evaluated with a series of 24 h forecasts over the period of 1 June-30 August 2010 during which the LSEIK filter is applied every day.During this summer melting period the Arctic sea ice extent (area with at least 15 % sea ice concentration) shrank from 11.8 million km 2 on 1 June to 5.3 million km 2 on 30 August 2010 (calculation from the NSIDC data).Although there are some difference between the SICCI and the OSISAF sea ice concentration, both data show a clear picture of sea ice melting in Arctic summer: on 1 June, most of the Arctic Ocean was covered with heavy sea ice, while on 30 August, the sea ice area was shrunk to the central Arctic and the concentration was also much reduced ( 1. LSEIK-1: OSISAF SSM/I sea ice concentration data were assimilated with a constant uncertainty value of 0.25 (one standard deviation).This constant uncertainty value is larger than the measurement error to account for a representation error.
2. LSEIK-2: SICCI sea ice concentration data were assimilated with a constant uncertainty value of 0.25.This experiment has the same configuration as LSEIK-1.
3. LSEIK-3: Same as LSEIK-2 but using the uncertainty fields provided with the SICCI product.A minimum uncertainty of 0.01 is imposed to avoid complications due to divisions by very small numbers.
To reflect the uncertainties in the interpolated sea ice concentration from SICCI over the data-void North Pole, a constant uncertainty of 0.30 is used in this region for all experiments.

Results
Figure 2 compares the root mean square error (RMSE) for ensemble mean ice concentration forecasts with and without data assimilation with respect to independent NSIDC SSMIS ice concentration for the period 1 June-30 August 2010.As errors tend to be large for small ice concentrations, all RMSE are evaluated only at grid points where either the model or the observations have ice concentrations larger than 0.05 (Lisaeter et al., 2003;Yang et al., 2015b).
All the data assimilation experiments reduce deviations of the forecasted ice concentration from the satellite-based data.Compared to the free run without data Introduction

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Full assimilation, mean RMSE of LSEIK-1, LSEIK-2, LSEIK-3 and LSEIK-4 ensemble mean forecasts are reduced from 0.24 to 0.13, 0.12, 0.09 and 0.11.Assimilating the SICCI data set with a constant uncertainty of 0.25, LSEIK-2 agrees better with the independent NSIDC observations during most of the time than LSEIK-1, which assimilates OSISAF with the same constant uncertainty.At all times, LSEIK-3 and LSEIK-4, using the SICCI-provided uncertainty estimates and adjusted minimum uncertainties, agree better with the independent NSIDC observations than LSEIK-2, which employs a constant uncertainty.Furthermore, it is worth pointing out that LSEIK-3, with the SICCI-provided uncertainties, agrees best with the independent NSIDC observations.This shows that the forecasting system produces a more realistic ensemble mean state for sea ice concentration when time and space dependent uncertainties provided with the satellite observations are used.
The time series of daily 24 h forecast of sea ice thickness are compared to in situ ULS-observations BGEP_2009A (Fig. 3a) and BGEP_2009D (Fig. 3b).Note, that the numerical model carries mean thickness (volume over area) as a variable.The observed thickness is multiplied by SICCI local ice concentration to arrive at the observed mean thickness shown in Fig. 3.At BGEP_2009A, the mean thickness on 1 June was about 2.5 m.With ice melting, the thickness was rapidly reduced in July, and reached about 0.2 m on 30 August.Similarly, the mean thickness at BGEP_2009D was about 3.5 m on 1 June and was reduced to less than 0.1 m on 30 August (Fig. 3).Using the same constant uncertainty of 0.25, LSEIK-1 with assimilation of OSISAF data overestimates the mean ice thickness in July, while LSEIK-2 with assimilation of SICCI data agrees better with observations at both BGEP_2009A (Fig. 3a) and BGEP_2009D (Fig. 3b).By using the original SICCI uncertainty, LSEIK-3 gives a good agreement Introduction

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Full with the in situ observations at BGEP_2009D (Fig. 3b), but over-estimates the mean sea ice thickness at BGEP_2009A (Fig. 3a), especially from mid-July to mid-August.By imposing a minimum uncertainty of 0.10 in the original uncertainties, the LSEIK-4 thickness agrees better with the BGEP_2009A data, and is basically equivalent to LSEIK-2.

Discussion
Based on the OSISAF and the recently released SICCI sea ice concentration data that provides uncertainty estimates, a series of sensitivity experiments with different data error statistics has been carried out to test the impact of sea ice concentration uncertainties in data assimilation.Compared to a DA configuration with constant uncertainty of 0.25, the DA of SICCI data with provided uncertainties can give a better short-range ensemble mean forecasts for sea ice concentration in summer.
For ice thickness forecasts the influence of observational uncertainties is ambiguous (beneficial in one case while seemingly detrimental in another).
The sensitivity of the data assimilation to the observation uncertainties can be explained by the employed (atmospheric) model and data error statistics in the LSEIK assimilation system.Although we have not directly included the model errors due to the possible suboptimal sea ice internal parameters, the ensemble forcing approach used here was shown to be very effective at representing model uncertainty associated with atmospheric forcing fields (Yang et al., 2015a).Data error is represented by the original observational data uncertainties of ice concentrations that are provided with the SICCI data set and are supposed to reflect errors in satellite retrievals and data processing.In Fig. 4, we show the provided observation uncertainties on 1 and 16 June, 1 and 16 July, 1 and 16 August 2010.Larger uncertainties up to 0.3 are present at the ice edge.However, for the summer sea ice pack the data uncertainties seem to be very low.For concentration estimates are known to underestimate the sea ice cover, the provided uncertainties at the sea ice pack area are still lower than 0.06 (Fig. 4d).
In fact, Lavergne and Rinne (2014, Sect. 2.2.1.1 "summer melt-ponding") report that AMSR-E and SSM/I, like all other passive microwave sensors, cannot distinguish ocean water (in leads) from melt water (in ponds) because of the very shallow penetration depths of the microwave signal.Therefore, these radiometric sea ice concentrations are closer to one minus the open water fraction (ponds and leads), than to the physical sea ice concentration in our models.This point is further elaborated in Ivanova et al. (2015).
It is worth highlighting two important issues: first, even if the targeted quantity is not the physical ice concentration, the SICCI product should probably feature larger uncertainties in summer.Second, the mismatch between the measured and modelled quantities calls for a matching relation in form of an observation operator to be embedded in the data assimilation procedure.Given the scope of this study, the solution implemented in LSEIK-4, that is to enlarge the observation uncertainties using a minimum value of 0.10, is a pragmatic but effective approach.
The ensemble-represented SDs of sea ice concentration for LSEIK-3 turn out to be relatively small.For example, on 30 August 2010, most of the SDs in the Arctic central area and the sea ice edge area are less than 0.01 and 0.03, respectively (Fig. 5c).This means that all members are very close to the ensemble mean and the data assimilation will have only little effect.LSEIK-4 has a similar spread distribution pattern of higher SDs in the sea ice edge area and lower SDs in the concentrated central ice area but overall higher SDs than LSEIK-3.Together with the fact that LSEIK-3 does not fit the thickness observations as well as LSEIK-4, this suggests that the ensemble forecast spread for sea ice concentration is too low and cannot reflect the uncertainty.As only observations of sea ice concentration are assimilated, sea ice thickness is influenced indirectly during the data assimilation through the point-wise covariance between the ice concentration and thickness.Here, the very small sea ice concentration variance leads to a very small sea ice thickness spread (Fig. 6c).This may explain why the LSEIK-3 system is not very effective at improving the sea ice Introduction

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Full thickness estimates.However, by raising the minimum uncertainty to 0.10, which is meant to account for the mismatch between the observed and modelled quantities as well as the underestimated observation uncertainties, the ensemble spread of sea ice concentration is increased in LSEIK-4.The increased spread in the sea ice concentration allows the system to better represent the uncertainties and leads to a larger ice thickness spread (Fig. 6d).The sea ice thickness forecasts are improved accordingly.

Conclusions
In this study, we assimilate OSISAF and SICCI sea ice concentration data during the summer period.While the OSISAF data is assimilated with a constant data uncertainty, and the summer SICCI sea ice concentration data takes into account the data uncertainties provided by the distributors.Even with a constant data uncertainty for the SICCI data, its assimilation results in better estimates of the sea ice concentration and thickness.This is expected because the retrieval of SICCI concentration data uses an improved algorithms and processing methodologies (Lavergne and Rinne, 2014).
The estimates are further improved when the SICCI-provided uncertainty estimates are taken into account.However, it was found that our data assimilation system cannot give a reasonable ensemble spread of sea ice concentration and thickness if we use the provided uncertainty directly.This is because (1) there is a mismatch between the sea ice concentration as observed by the passive microwave sensors (radiometric concentration) and that simulated by our model (physical concentration), and (2) the provided observation uncertainties are probably underestimated.A simple and pragmatic approach appears to correct this by imposing a minimum threshold value on the provided uncertainties in summer.We finally note that the mismatch between the observed and modelled ice concentration (radiometric vs. physical) does not exist in winter when there is no surface melting, and that fully resolving the mismatch in Introduction

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Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Fig. 1); the open water was found in the interior pack ice near the North Pole as early as 12 July 2010 (NSIDC, http://nsidc.org/arcticseaicenews/2010/07/).Four experiments, which mainly differ in the way uncertainties are represented, form the backbone of this study: Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | All forecasts with DA show improvements over the free-running MITgcm after late July.The ice thickness RMSE at BGEP_2009A has been reduced from 0.86 m in the free model run to 0.58 m in LSEIK-1, 0.46 m in LSEIK-2, 0.64 m in LSEIK-3, and 0.46 m in LSEIK-4.The RMSE at BGEP_2009D has been reduced from 0.93 m in the free model run to 0.85 m in LSEIK-1, 0.59 m in LSEIK-2, 0.55 m in LSEIK-3, and 0.62 m in LSEIK-4.
Discussion Paper | Discussion Paper | Discussion Paper | example, on 16 July 2010 when surface ice melting prevails and the satellite-based ice Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Figure 1 .
Figure 1.The OSISAF (OSI-401-a; a, b) and SICCI (c, d) sea ice concentration on 1 June (a, c) and 30 August 2010 (b, d).The locations of BGEP_2009A and BGEP_2009D are shown as a square with white line and a triangle with white line, respectively.
. In the SICCI data set, the North Pole data gap is filled by interpolation, and daily maps of total standard error (uncertainty) are provided.The ice concentration data used for evaluation are from the National Snow and Ice Data Center (NSIDC; Cavalieri and others, 2012; http: //nsidc.org/data/docs/daac/nsidc0051_gsfc_seaice.gd.html).This product consists of daily fields with 25 km grid spacing.Note that NSIDC concentration for summer 2010 is derived from another passive microwave sensor SSMIS onboard DMSP F-17, so it is independent from the SICCI and OSISAF data used in the assimilation.We compare our simulation results to measurements of sea ice draft from the Beaufort Gyre Experiment Program (BGEP) Upward Looking Sonar (ULS) moorings located in the Beaufort Sea (BGEP_2009A, BGEP_2009D; http://www.whoi.edu/beaufortgyre; see Fig.