The impact of error covariance matrix structure of GRACE’s gravity solution on the mass flux estimates of Greenland ice sheet

Abstract. The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model. GEN_BE allows for a simpler, flexible, robust, and community-oriented framework that gathers methods used by some meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks of different modeling of B and showing some of the new features in data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to implement new control variables. While the generation of the background errors statistics code was first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily applied to other domains of science and chosen to diagnose and model B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

Download Full-text

Generalized Background Error covariance matrix model (GEN_BE v2.0)

Geoscientific Model Development Discussions ◽

10.5194/gmdd-7-4291-2014 ◽

2014 ◽

Vol 7 (4) ◽

pp. 4291-4352

Author(s):

G. Descombes ◽

T. Auligné ◽

F. Vandenberghe ◽

D. M. Barker

Keyword(s):

Data Assimilation ◽

Covariance Matrix ◽

Chemical Species ◽

Variational Data Assimilation ◽

Control Variables ◽

Background Error ◽

Error Covariance Matrix ◽

Background Error Covariance ◽

Error Covariance ◽

The Impact

Abstract. The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model to allow for a simpler, flexible, robust, and community-oriented framework that gathers methods used by meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks and showing some of the new features on data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to involve new control variables. While the generation of the background errors statistics code has been first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily extended to other domains of science and be chosen as a testbed for diagnostic and new modeling of B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

Download Full-text

A Study of the Error Covariance Matrix of Radar Rainfall Estimates in Stratiform Rain

Weather and Forecasting ◽

10.1175/2008waf2222134.1 ◽

2008 ◽

Vol 23 (6) ◽

pp. 1085-1101 ◽

Cited By ~ 48

Author(s):

Marc Berenguer ◽

Isztar Zawadzki

Keyword(s):

Covariance Matrix ◽

Drop Size ◽

Size Distributions ◽

Radar Rainfall ◽

Error Covariance Matrix ◽

Error Covariance ◽

Drop Size Distributions ◽

The Impact ◽

Dependent Error ◽

Rainfall Estimates

Abstract The contribution of various physical sources of uncertainty affecting radar rainfall estimates at the ground is quantified toward deriving and understanding the error covariance matrix of these estimates. The focus here is on stratiform precipitation at a resolution of 15 km, which is most relevant for data assimilation onto mesoscale numerical models. In the characterization of the error structure, the following contributions are considered: (i) the individual effect of the range-dependent error (associated with beam broadening and increasing height of radar measurements with range), (ii) the error associated with the transformation from reflectivity to rain rate due to the variability of drop size distributions, and (iii) the interaction of the first two, that is, the term resulting from the cross correlation between the effects of the range-dependent error and the uncertainty related to the variability of drop size distributions (DSDs). For this purpose a large database of S-band radar observations at short range (where reflectivity near the ground is measured and the beam is narrow) is used to characterize the range-dependent error within a simulation framework, and disdrometric measurements collocated with the radar data are used to assess the impact of the variability of DSDs. It is noted that these two sources of error are well correlated in the vicinity of the melting layer as result of the physical processes that determine the density of snow (e.g., riming), which affect both the DSD variability and the vertical profile of reflectivity.

Download Full-text

Impact of a time-dependent background error covariance matrix on air quality analysis

Geoscientific Model Development ◽

10.5194/gmd-5-1075-2012 ◽

2012 ◽

Vol 5 (5) ◽

pp. 1075-1090 ◽

Cited By ~ 14

Author(s):

E. Jaumouillé ◽

S. Massart ◽

A. Piacentini ◽

D. Cariolle ◽

V.-H. Peuch

Keyword(s):

Covariance Matrix ◽

Surface Ozone ◽

Winter Season ◽

Quality Analysis ◽

Background Error ◽

Error Covariance Matrix ◽

Background Error Covariance ◽

Error Covariance ◽

Seasonal Characteristics ◽

The Impact

Abstract. In this article we study the influence of different characteristics of our assimilation system on surface ozone analyses over Europe. Emphasis is placed on the evaluation of the background error covariance matrix (BECM). Data assimilation systems require a BECM in order to obtain an optimal representation of the physical state. A posteriori diagnostics are an efficient way to check the consistency of the used BECM. In this study we derived a diagnostic to estimate the BECM. On the other hand, an increasingly used approach to obtain such a covariance matrix is to estimate it from an ensemble of perturbed assimilation experiments. We applied this method, combined with variational assimilation, while analysing the surface ozone distribution over Europe. We first show that the resulting covariance matrix is strongly time (hourly and seasonally) and space dependent. We then built several configurations of the background error covariance matrix with none, one or two of its components derived from the ensemble estimation. We used each of these configurations to produce surface ozone analyses. All the analyses are compared between themselves and compared to assimilated data or data from independent validation stations. The configurations are very well correlated with the validation stations, but with varying regional and seasonal characteristics. The largest correlation is obtained with the experiments using time- and space-dependent correlation of the background errors. Results show that our assimilation process is efficient in bringing the model assimilations closer to the observations than the direct simulation, but we cannot conclude which BECM configuration is the best. The impact of the background error covariances configuration on four-days forecasts is also studied. Although mostly positive, the impact depends on the season and lasts longer during the winter season.

Download Full-text

Impact of a time-dependent background error covariance matrix on air quality analysis

Geoscientific Model Development Discussions ◽

10.5194/gmdd-5-873-2012 ◽

2012 ◽

Vol 5 (2) ◽

pp. 873-916

Author(s):

E. Jaumouillé ◽

S. Massart ◽

A. Piacentini ◽

D. Cariolle ◽

V.-H. Peuch

Keyword(s):

Covariance Matrix ◽

Surface Ozone ◽

Winter Season ◽

Quality Analysis ◽

Background Error ◽

Error Covariance Matrix ◽

Background Error Covariance ◽

Error Covariance ◽

Seasonal Characteristics ◽

The Impact

Abstract. In this article we study the influence of different characteristics of our assimilation system on the surface ozone analyses over Europe. Emphasis is placed on the evaluation of the background error covariance matrix (BECM). Data assimilation systems require a BECM in order to obtain an optimal representation of the physical state. A posteriori diagnostics are an efficient way to check the consistency of the used BECM. In this study we derived a diagnostic to estimate the BECM. On the other hand an increasingly used approach to obtain such a covariance matrix is to estimate it from an ensemble of perturbed assimilation experiments. We applied this method, combined with variational assimilation, while analysing the surface ozone distribution over Europe. We first show that the resulting covariance matrix is strongly time (hourly and seasonally) and space dependent. We then built several configurations of the background error covariance matrix with none, one or two of its components derived from the ensemble estimation. We used each of these configurations to produce surface ozone analyses. All the analyses are compared between themselves and compared to assimilated data or data from independent validation stations. The configurations are very well correlated with the validation stations, but with varying regional and seasonal characteristics. The largest correlation is obtained with the experiments using time and space dependent correlation of the background errors. Results show that our assimilation process is efficient in bringing the model assimilations closer to the observations than the direct simulation, but we cannot conclude which BECM configuration is the best. The impact of the background error covariances configuration on four-days forecasts is also studied. Although mostly positive, the impact depends on the season and lasts longer during the winter season.

Download Full-text

Greenland land-terminating glaciers velocity trends during the last two decades

10.5194/egusphere-egu21-2084 ◽

2021 ◽

Author(s):

Paul Halas ◽

Jeremie Mouginot ◽

Basile de Fleurian ◽

Petra Langebroek

Keyword(s):

Water Pressure ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Surface Melting ◽

Limited Area ◽

Ice Dynamics ◽

Basal Sliding ◽

Surface Melt ◽

Ice Sheet Dynamics ◽

The Impact

<div> <p>Ice losses from the Greenland Ice Sheet have been increasing in the last two decades, leading to a larger contribution to the global sea level rise.&#160;Roughly 40% of the contribution comes from ice-sheet dynamics, mainly regulated by basal sliding.&#160;The sliding component&#160;of glaciers has been observed to be strongly related to surface melting, as water&#160;can eventually&#160;reach the bed and impact&#160;the subglacial water pressure, affecting the basal sliding.&#160;&#160;</p> </div><div> <p>The link between ice velocities and surface melt on multi-annual time scale is still not totally understood&#160;even though it&#160;is of major importance with expected increasing surface melting.&#160;Several studies showed&#160;some&#160;correlation between an increase in surface melt and a slowdown in&#160;velocities, but&#160;there is no&#160;consensus&#160;on those trends.&#160;Moreover&#160;those&#160;investigations&#160;only&#160;presented results&#160;in a limited area over&#160;Southwest&#160;Greenland.&#160;&#160;</p> </div><div> <p>Here we present the ice motion over many land-terminating glaciers on the Greenland Ice Sheet for the period 2000 - 2020. This type of glacier is ideal for studying processes at the interface between the bed and the ice since they are exempted from interactions with the sea while still being relevant for all glaciers since they share the same basal friction laws. The velocity data was obtained using optical Landsat 7 & 8 imagery and feature-tracking algorithm. We attached importance keeping the starting date of our image pairs similar, and avoided stacking pairs starting before and after melt seasons, resulting in multiple velocity products for each year.&#160;&#160;</p> </div><div> <p>Our results show similar velocity trends for previously studied areas with a slowdown until 2012 followed by an acceleration.&#160;This trend however does not seem to be observed on the whole ice sheet and is probably&#160;specific&#160;to&#160;this region&#8217;s&#160;climate forcing.&#160;</p> </div><div> <p>Moreover comparison between ice velocities from different parts of Greenland allows us to observe the impact of different climatic trends on ice dynamics.</p> </div>

Download Full-text

Early Holocene ocean conditions off the Zachariæ Isstrøm, Northeast Greenland

10.5194/egusphere-egu21-15076 ◽

2021 ◽

Author(s):

Joanna Davies ◽

Anders Møller Mathiasen ◽

Kristiane Kristensen ◽

Christof Pearce ◽

Marit-Solveig Seidenkrantz

Keyword(s):

Climate Change ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Atlantic Water ◽

The Arctic ◽

Future Climate Change ◽

Polar Regions ◽

Ice Shelf ◽

Outlet Glacier ◽

The Impact

<p>The polar regions exhibit some of the most visible signs of climate change globally; annual mass loss from the Greenland Ice Sheet (GrIS) has quadrupled in recent decades, from 51 &#177; 65 Gt yr<sup>&#8722;1</sup> (1992-2001) to 211 &#177; 37 Gt yr<sup>&#8722;1</sup> (2002-2011). This can partly be attributed to the widespread retreat and speed-up of marine-terminating glaciers. The Zachariae Isstr&#248;m (ZI) is an outlet glacier of the Northeast Greenland Ice Steam (NEGIS), one of the largest ice streams of the GrIS (700km), draining approximately 12% of the ice sheet interior. Observations show that the ZI began accelerating in 2000, resulting in the collapse of the floating ice shelf between 2002 and 2003. By 2014, the ice shelf extended over an area of 52km<sup>2</sup>, a 95% decrease in area since 2002, where it extended over 1040km<sup>2</sup>. Paleo-reconstructions provide an opportunity to extend observational records in order to understand the oceanic and climatic processes governing the position of the grounding zone of marine terminating glaciers and the extent of floating ice shelves. Such datasets are thus necessary if we are to constrain the impact of future climate change projections on the Arctic cryosphere.</p><p>A multi-proxy approach, involving grain size, geochemical, foraminiferal and sedimentary analysis was applied to marine sediment core DA17-NG-ST8-92G, collected offshore of the ZI, on &#160;the Northeast Greenland Shelf. The aim was to reconstruct changes in the extent of the ZI and the palaeoceanographic conditions throughout the Early to Mid Holocene (c.a. 12,500-5,000 cal. yrs. BP). Evidence from the analysis of these datasets indicates that whilst there has been no grounded ice at the site over the last 12,500 years, the ice shelf of the ZI extended as a floating ice shelf over the site between 12,500 and 9,200 cal. yrs. BP, with the grounding line further inland from our study site. This was followed by a retreat in the ice shelf extent during the Holocene Thermal Maximum; this was likely to have been governed, in part, by basal melting driven by Atlantic Water (AW) recirculated from Svalbard or from the Arctic Ocean. Evidence from benthic foraminifera suggest that there was a shift from the dominance of AW to Polar Water at around 7,500 cal. yrs. BP, although the ice shelf did not expand again despite of this cooling of subsurface waters.</p>

Download Full-text

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

Monthly Weather Review ◽

10.1175/mwr-d-18-0093.1 ◽

2018 ◽

Vol 146 (12) ◽

pp. 3949-3976 ◽

Cited By ~ 2

Author(s):

Herschel L. Mitchell ◽

P. L. Houtekamer ◽

Sylvain Heilliette

Keyword(s):

Covariance Matrix ◽

Background Error ◽

Error Covariance Matrix ◽

Background Error Covariance ◽

Error Covariance ◽

Microwave Sounding Unit ◽

The Matrix ◽

Microwave Sounding ◽

Background Temperature ◽

The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

Download Full-text

Last Interglacial climate and sea-level evolution from a coupled ice sheet–climate model

Climate of the Past ◽

10.5194/cp-12-2195-2016 ◽

2016 ◽

Vol 12 (12) ◽

pp. 2195-2213 ◽

Cited By ~ 22

Author(s):

Heiko Goelzer ◽

Philippe Huybrechts ◽

Marie-France Loutre ◽

Thierry Fichefet

Keyword(s):

Surface Temperature ◽

Sea Level ◽

Ice Sheets ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Last Interglacial ◽

A Minor ◽

The Antarctic ◽

The Impact ◽

And Sea Level

Abstract. As the most recent warm period in Earth's history with a sea-level stand higher than present, the Last Interglacial (LIG, ∼  130 to 115 kyr BP) is often considered a prime example to study the impact of a warmer climate on the two polar ice sheets remaining today. Here we simulate the Last Interglacial climate, ice sheet, and sea-level evolution with the Earth system model of intermediate complexity LOVECLIM v.1.3, which includes dynamic and fully coupled components representing the atmosphere, the ocean and sea ice, the terrestrial biosphere, and the Greenland and Antarctic ice sheets. In this setup, sea-level evolution and climate–ice sheet interactions are modelled in a consistent framework.Surface mass balance change governed by changes in surface meltwater runoff is the dominant forcing for the Greenland ice sheet, which shows a peak sea-level contribution of 1.4 m at 123 kyr BP in the reference experiment. Our results indicate that ice sheet–climate feedbacks play an important role to amplify climate and sea-level changes in the Northern Hemisphere. The sensitivity of the Greenland ice sheet to surface temperature changes considerably increases when interactive albedo changes are considered. Southern Hemisphere polar and sub-polar ocean warming is limited throughout the Last Interglacial, and surface and sub-shelf melting exerts only a minor control on the Antarctic sea-level contribution with a peak of 4.4 m at 125 kyr BP. Retreat of the Antarctic ice sheet at the onset of the LIG is mainly forced by rising sea level and to a lesser extent by reduced ice shelf viscosity as the surface temperature increases. Global sea level shows a peak of 5.3 m at 124.5 kyr BP, which includes a minor contribution of 0.35 m from oceanic thermal expansion. Neither the individual contributions nor the total modelled sea-level stand show fast multi-millennial timescale variations as indicated by some reconstructions.

Download Full-text