Testing a new Free Core Nutation empirical model

The Free Core Nutation (FCN) is a free mode of the Earth's rotation caused by the different material characteristics of the Earth's core and mantle. This causes the rotational axes of those layers to slightly diverge from each other, resulting in a wobble of the Earth's rotation axis comparable to nutations. In this paper we focus on estimating empirical FCN models using the observed nutations derived from the VLBI sessions between 1993 and 2013. Assuming a fixed value for the oscillation period, the time-variable amplitudes and phases are estimated by means of multiple sliding window analyses. The effects of using different a priori Earth Rotation Parameters (ERP) in the derivation of models are also addressed. The optimal choice of the fundamental parameters of the model, namely the window width and step-size of its shift, is searched by performing a thorough experimental analysis using real data. The former analyses lead to the derivation of a model with a temporal resolution higher than the one used in the models currently available, with a sliding window reduced to 400 days and a day-by-day shift. It is shown that this new model increases the accuracy of the modeling of the observed Earth's rotation. Besides, empirical models determined from USNO Finals as a priori ERP present a slightly lower Weighted Root Mean Square (WRMS) of residuals than IERS 08 C04 along the whole period of VLBI observations, according to our computations. The model is also validated through comparisons with other recognized models. The level of agreement among them is satisfactory. Let us remark that our estimates give rise to the lowest residuals and seem to reproduce the FCN signal in more detail.

Gakara region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4673-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Gakara. Printed in: 1994. Covers portions of Gakara region, Burundi. Sheet: 4673-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Bubanza region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4674-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Bubanza. Printed in: 1994. Covers portions of Bubanza region, Burundi. Sheet: 4674-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Bujumbura region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4674-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Bujumbura. Printed in: 1994. Covers portions of Bujumbura region, Burundi. Sheet: 4674-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Butahana region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Butahana. Printed in: 1994. Covers portions of Butahana region, Burundi. Sheet: 4675-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Ndora region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Ndora. Printed in: 1994. Covers portions of Ndora region, Burundi. Sheet: 4675-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Cibitoke region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-III (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Cibitoke. Printed in: 1994. Covers portions of Cibitoke region, Burundi. Sheet: 4675-III. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Mabayi region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4675-IV (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Mabayi. Printed in: 1994. Covers portions of Mabayi region, Burundi. Sheet: 4675-IV. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Mabanda region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4772-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Mabanda. Printed in: 1994. Covers portions of Mabanda region, Burundi. Sheet: 4772-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Nyanza-Lac region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4772-III (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Nyanza-Lac. Printed in: 1994. Covers portions of Nyanza-Lac region, Burundi. Sheet: 4772-III. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Mutambara region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4772-IV (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Mutambara. Printed in: 1994. Covers portions of Mutambara region, Burundi. Sheet: 4772-IV. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Bukirasazi region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4773-I (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Bukirasazi. Printed in: 1994. Covers portions of Bukirasazi region, Burundi. Sheet: 4773-I. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Rutana region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4773-II (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Rutana. Printed in: 1994. Covers portions of Rutana region, Burundi. Sheet: 4773-II. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Bururi region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4773-III (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Bururi. Printed in: 1994. Covers portions of Bururi region, Burundi. Sheet: 4773-III. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.

Mwaro region, Burundi, 1994, Defense Mapping Agency (DMA) Series Z724, Sheet 4773-IV (Raster Image)

This layer is a georeferenced raster image of the United States Defense Mapping Agency (DMA) Series Z724, Burundi, 1:50,000 Topographic Line Map (TLM) Series sheet map entitled: Mwaro. Printed in: 1994. Covers portions of Mwaro region, Burundi. Sheet: 4773-IV. Edition statement: Ed. 1 - DMA. The image inside the map neatline is georeferenced to the surface of the earth and fit to World Geodetic System (1984) coordinates. All map collar information is also available as part of the raster image. Burundi 1:50:000 Series Z724 maps are in English and French (legends also include Rundi). Each source map in the series is printed in color at a scale of 1:50,000. Series source sheets were published in 1994-1995 by the United States Defense Mapping Agency, Hydrographic/Topographic Center. The source map was scanned and georeferenced for Harvard University's Center for Geographic Analysis' AfricaMap project by East View Cartographic. Individual TLM sheets covering Burundi (40 sheets in total) were selected from the TLM worldwide series. DMA Topographic Line Map series maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 20 meters, with some sheets having supplemental meter contours, form lines, hachures, shading, and/or spot heights. Depths shown by bathymetric isolines. Please pay close attention to map collar information on projections, spheroid, compilation dates, legend information, and keys to grid numbering and other numbers which appear inside the neatline.