Search Results
You are looking at 1 - 10 of 54 items for
- Author or Editor: Dudley B. Chelton x
- Refine by Access: All Content x
Abstract
The ability to estimate surface current divergence and vorticity from space is assessed from simulated satellite Doppler radar scatterometer measurements of surface velocity with an effective footprint diameter of 5 km across an 1800-km measurement swath. The focus is on non-internal-wave contributions to divergence and vorticity. This is achieved by simulating Doppler measurements of surface velocity from a numerical model in which internal waves are weak because of high dissipation, seasonal cycle forcing and the lack of tidal forcing. Divergence is much more challenging to estimate than vorticity because the signals are weaker and restricted to smaller scales. With the measurement noise that was anticipated based on early engineering studies, divergence cannot be estimated with useful resolution. Recent advances in the understanding of how the noise in measurements of surface currents depends on the ambient wind speed have concluded that measurement noise will be substantially smaller in conditions of wind speed greater than 6 m s−1. A reassessment of the ability to estimate non-internal-wave contributions to surface current divergence in this study finds that useful estimates can be obtained in such wind conditions; the wavelength resolution capability for divergence estimates in the middle of the measurement swaths will be better than 100 km in 16-day averages. The improved measurement accuracy will also provide estimates of surface current vorticity with a resolution nearly a factor-of-2 higher than was previously thought, resulting in wavelength resolutions of about 50 km, 30 km and 20 km in snapshots, 4-day averages and 16-day averages, respectively.
Abstract
The ability to estimate surface current divergence and vorticity from space is assessed from simulated satellite Doppler radar scatterometer measurements of surface velocity with an effective footprint diameter of 5 km across an 1800-km measurement swath. The focus is on non-internal-wave contributions to divergence and vorticity. This is achieved by simulating Doppler measurements of surface velocity from a numerical model in which internal waves are weak because of high dissipation, seasonal cycle forcing and the lack of tidal forcing. Divergence is much more challenging to estimate than vorticity because the signals are weaker and restricted to smaller scales. With the measurement noise that was anticipated based on early engineering studies, divergence cannot be estimated with useful resolution. Recent advances in the understanding of how the noise in measurements of surface currents depends on the ambient wind speed have concluded that measurement noise will be substantially smaller in conditions of wind speed greater than 6 m s−1. A reassessment of the ability to estimate non-internal-wave contributions to surface current divergence in this study finds that useful estimates can be obtained in such wind conditions; the wavelength resolution capability for divergence estimates in the middle of the measurement swaths will be better than 100 km in 16-day averages. The improved measurement accuracy will also provide estimates of surface current vorticity with a resolution nearly a factor-of-2 higher than was previously thought, resulting in wavelength resolutions of about 50 km, 30 km and 20 km in snapshots, 4-day averages and 16-day averages, respectively.
Abstract
The impact of SST specification on low-level winds in the operational ECMWF numerical weather prediction model is investigated in the eastern tropical Pacific from comparisons of ECMWF wind stress fields with QuikSCAT satellite scatterometer observations of wind stress during the August–December cold seasons of 2000 and 2001. These two time periods bracket the 9 May 2001 change from the Reynolds SST analyses to the Real-Time Global SST (RTG_SST) analyses as the ocean boundary condition in the ECMWF model. The ocean–atmosphere interaction in the eastern tropical Pacific that is clearly evident in QuikSCAT wind stress divergence and curl fields is also evident in the ECMWF winds, but is more than twice as strong in the 2001 cold season as in the 2000 cold season, due primarily to the improved spatial and temporal resolution of the RTG_SST analyses compared with the Reynolds SST analyses. While a significant improvement compared with 2000, the response of the 2001 ECMWF wind stress field to SST is only about half as strong as the coupling inferred from QuikSCAT data and satellite observations of SST from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). It is concluded that the underrepresentation of the ocean–atmosphere coupling is attributable partly to underrepresentation of SST gradients in the RTG_SST fields and partly to inadequacies of the ECWMF model. The latter may be due to errors in the parameterization of boundary layer processes or to insufficient horizontal or vertical resolution in the model.
Abstract
The impact of SST specification on low-level winds in the operational ECMWF numerical weather prediction model is investigated in the eastern tropical Pacific from comparisons of ECMWF wind stress fields with QuikSCAT satellite scatterometer observations of wind stress during the August–December cold seasons of 2000 and 2001. These two time periods bracket the 9 May 2001 change from the Reynolds SST analyses to the Real-Time Global SST (RTG_SST) analyses as the ocean boundary condition in the ECMWF model. The ocean–atmosphere interaction in the eastern tropical Pacific that is clearly evident in QuikSCAT wind stress divergence and curl fields is also evident in the ECMWF winds, but is more than twice as strong in the 2001 cold season as in the 2000 cold season, due primarily to the improved spatial and temporal resolution of the RTG_SST analyses compared with the Reynolds SST analyses. While a significant improvement compared with 2000, the response of the 2001 ECMWF wind stress field to SST is only about half as strong as the coupling inferred from QuikSCAT data and satellite observations of SST from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). It is concluded that the underrepresentation of the ocean–atmosphere coupling is attributable partly to underrepresentation of SST gradients in the RTG_SST fields and partly to inadequacies of the ECWMF model. The latter may be due to errors in the parameterization of boundary layer processes or to insufficient horizontal or vertical resolution in the model.
Abstract
Wind measurements by the National Aeronautics and Space Administration (NASA) scatterometer (NSCAT) and the SeaWinds scatterometer on the NASA QuikSCAT satellite are compared with buoy observations to establish that the accuracies of both scatterometers are essentially the same. The scatterometer measurement errors are best characterized in terms of random component errors, which are about 0.75 and 1.5 m s−1 for the along-wind and crosswind components, respectively.
The NSCAT and QuikSCAT datasets provide a consistent baseline from which recent changes in the accuracies of 10-m wind analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the U.S. National Centers for Environmental Prediction (NCEP) operational numerical weather prediction (NWP) models are assessed from consideration of three time periods: September 1996–June 1997, August 1999–July 2000, and February 2002–January 2003. These correspond, respectively, to the 9.5-month duration of the NSCAT mission, the first 12 months of the QuikSCAT mission, and the first year after both ECMWF and NCEP began assimilating QuikSCAT observations. There were large improvements in the accuracies of both NWP models between the 1997 and 2000 time periods. Though modest in comparison, there were further improvements in 2002, at least partly attributable to the assimilation of QuikSCAT observations in both models.
There is no evidence of bias in the 10-m wind speeds in the NCEP model. The 10-m wind speeds in the ECMWF model, however, are shown to be biased low by about 0.4 m s−1. While it is difficult to eliminate systematic errors this small, a bias of 0.4 m s−1 corresponds to a typical wind stress bias of more than 10%. This wind stress bias increases to nearly 20% if atmospheric stability effects are not taken into account. Biases of these magnitudes will result in significant systematic errors in ocean general circulation models that are forced by ECMWF winds.
Abstract
Wind measurements by the National Aeronautics and Space Administration (NASA) scatterometer (NSCAT) and the SeaWinds scatterometer on the NASA QuikSCAT satellite are compared with buoy observations to establish that the accuracies of both scatterometers are essentially the same. The scatterometer measurement errors are best characterized in terms of random component errors, which are about 0.75 and 1.5 m s−1 for the along-wind and crosswind components, respectively.
The NSCAT and QuikSCAT datasets provide a consistent baseline from which recent changes in the accuracies of 10-m wind analyses from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the U.S. National Centers for Environmental Prediction (NCEP) operational numerical weather prediction (NWP) models are assessed from consideration of three time periods: September 1996–June 1997, August 1999–July 2000, and February 2002–January 2003. These correspond, respectively, to the 9.5-month duration of the NSCAT mission, the first 12 months of the QuikSCAT mission, and the first year after both ECMWF and NCEP began assimilating QuikSCAT observations. There were large improvements in the accuracies of both NWP models between the 1997 and 2000 time periods. Though modest in comparison, there were further improvements in 2002, at least partly attributable to the assimilation of QuikSCAT observations in both models.
There is no evidence of bias in the 10-m wind speeds in the NCEP model. The 10-m wind speeds in the ECMWF model, however, are shown to be biased low by about 0.4 m s−1. While it is difficult to eliminate systematic errors this small, a bias of 0.4 m s−1 corresponds to a typical wind stress bias of more than 10%. This wind stress bias increases to nearly 20% if atmospheric stability effects are not taken into account. Biases of these magnitudes will result in significant systematic errors in ocean general circulation models that are forced by ECMWF winds.
Abstract
The frequency-domain characteristics of the successive corrections method in one dimension are investigated through the calculation of smoother weights and filter transfer functions. The successive corrections algorithm acts as a low-pass filter that behaves similarly to noniterative smoothers. The spectral content of fixed-span successive corrections estimates depends upon the number of iterations, the selected weighting function and the grid to which the dataset is interpolated. For a given weighting function and grid, increasing the number of iterations for the fixed-span case results in filter transfer functions with increased cutoff frequency and rolloff. Within data gaps, the use of more than one iteration leads to estimates that are more likely to be contaminated by high-frequency variability in the data. It is shown that variable-span successive corrections estimates are nearly independent of the choice of weights for the initial iterations and are almost equivalent to estimates obtained using a single iteration. The greater computational requirements of multiple-iteration successive corrections is a disadvantage for general applications.
Abstract
The frequency-domain characteristics of the successive corrections method in one dimension are investigated through the calculation of smoother weights and filter transfer functions. The successive corrections algorithm acts as a low-pass filter that behaves similarly to noniterative smoothers. The spectral content of fixed-span successive corrections estimates depends upon the number of iterations, the selected weighting function and the grid to which the dataset is interpolated. For a given weighting function and grid, increasing the number of iterations for the fixed-span case results in filter transfer functions with increased cutoff frequency and rolloff. Within data gaps, the use of more than one iteration leads to estimates that are more likely to be contaminated by high-frequency variability in the data. It is shown that variable-span successive corrections estimates are nearly independent of the choice of weights for the initial iterations and are almost equivalent to estimates obtained using a single iteration. The greater computational requirements of multiple-iteration successive corrections is a disadvantage for general applications.
Abstract
Mean-squared errors of surface geostrophic velocity estimates from the crossover and parallel-track methods are calculated for altimeters in the Ocean Topography Experiment (TOPEX)/Poseidon and Jason orbits. As part of the crossover method analysis, the filtering properties and errors of cross-track speed estimates are examined. Velocity estimates from both the crossover and parallel-track methods have substantial mean-squared errors that exceed 20% of the signal standard deviation, differ systematically between the zonal and meridional components, and vary with latitude. The measurement errors on the zonal and meridional velocity component estimates from both methods increase at low latitudes owing to the inverse dependence of geostrophic velocity on the Coriolis parameter. Additional latitudinal variations result for the parallel-track method because of the poleward convergence of the satellite ground tracks and the presence of orbit error, and for the crossover method because of the changing angle between the ascending and descending ground tracks. At high latitudes, parallel-track estimates, have elevated measurement errors in both components, while only the zonal component is so affected for the crossover method. Along-track smoothing is efficient for mitigating measurement errors for crossover estimates, and the filtering properties of the smoothed estimates are simply related to the spectrum of cross-track speeds. Such smoothing is less effective for parallel-track estimates, and the filtering properties are more difficult to characterize because of the sampling geometry and the convergence of the parallel ground tracks at high latitudes.
If suitable along-track smoothing is applied in the crossover method, root-mean-squared errors (rmse's) of about 30% or less of the signal standard deviation can be obtained for each orthogonal velocity component over the latitude range 5°–60°. With 2-cm orbit errors, the parallel-track method yields estimates of the meridional velocity component with errors that exceed 40% at all latitudes. If orbit errors can be reduced to 1-cm standard deviation, the parallel-track method yields an rmse smaller than 30% in both orthogonal components for the latitude range 5°–55°.
Abstract
Mean-squared errors of surface geostrophic velocity estimates from the crossover and parallel-track methods are calculated for altimeters in the Ocean Topography Experiment (TOPEX)/Poseidon and Jason orbits. As part of the crossover method analysis, the filtering properties and errors of cross-track speed estimates are examined. Velocity estimates from both the crossover and parallel-track methods have substantial mean-squared errors that exceed 20% of the signal standard deviation, differ systematically between the zonal and meridional components, and vary with latitude. The measurement errors on the zonal and meridional velocity component estimates from both methods increase at low latitudes owing to the inverse dependence of geostrophic velocity on the Coriolis parameter. Additional latitudinal variations result for the parallel-track method because of the poleward convergence of the satellite ground tracks and the presence of orbit error, and for the crossover method because of the changing angle between the ascending and descending ground tracks. At high latitudes, parallel-track estimates, have elevated measurement errors in both components, while only the zonal component is so affected for the crossover method. Along-track smoothing is efficient for mitigating measurement errors for crossover estimates, and the filtering properties of the smoothed estimates are simply related to the spectrum of cross-track speeds. Such smoothing is less effective for parallel-track estimates, and the filtering properties are more difficult to characterize because of the sampling geometry and the convergence of the parallel ground tracks at high latitudes.
If suitable along-track smoothing is applied in the crossover method, root-mean-squared errors (rmse's) of about 30% or less of the signal standard deviation can be obtained for each orthogonal velocity component over the latitude range 5°–60°. With 2-cm orbit errors, the parallel-track method yields estimates of the meridional velocity component with errors that exceed 40% at all latitudes. If orbit errors can be reduced to 1-cm standard deviation, the parallel-track method yields an rmse smaller than 30% in both orthogonal components for the latitude range 5°–55°.
Abstract
A technique previously developed for assessing the effects of sampling errors on sea surface height (SSH) fields constructed from satellite altimeter data is extended to include measurement errors, thus providing estimates of the total mean-squared error of the SSH fields. The measurement error contribution becomes an important consideration with the greater sampling density of a coordinated tandem satellite mission. Mean-squared errors are calculated for a variety of tandem altimeter sampling patterns. The resolution capability of each sampling pattern is assessed from a subjectively chosen but consistent set of criteria for the mean value and the spatial and temporal inhomogeneity of the root-mean-squared errors computed over a representative large collection of estimation times and locations.
For a mean mapping error threshold tolerance criterion of 25% of the signal standard deviation, the filter cutoff wavelength and period defining the resolution capability of SSH fields constructed from a tandem TOPEX/Poseidon (T/P) and Jason satellite sampling pattern with evenly spaced ground tracks are about 2.2° by 20 days. This can be compared with the resolution capability of about 6° by 20 days that can be obtained from a single altimeter in the T/P orbit. A tandem T/P–Jason mission with 0.75° spacing between simultaneously sampled parallel tracks that has been suggested for estimating geostrophic velocity yields an SSH mapping resolution capability of about 3.7° by 20 days. For the anticipated factor-of-2 larger orbit errors for ENVISAT compared with Jason, the resolution capability of a tandem Jason–ENVISAT scenario is about 3° by 20 days.
For mapping the SSH field, the tandem T/P–Jason sampling patterns with evenly spaced, interleaved ground tracks and either a 5-day or a 0-day offset is far better than the other tandem altimeter mission scenarios considered here. For the highest-resolution mapping, the 5-day offset is preferable to the 0-day offset. The scientific benefits of such a tandem mission are discussed in the context of two specific examples: Rossby wave dispersion and investigation of eddy–mean flow interaction.
Abstract
A technique previously developed for assessing the effects of sampling errors on sea surface height (SSH) fields constructed from satellite altimeter data is extended to include measurement errors, thus providing estimates of the total mean-squared error of the SSH fields. The measurement error contribution becomes an important consideration with the greater sampling density of a coordinated tandem satellite mission. Mean-squared errors are calculated for a variety of tandem altimeter sampling patterns. The resolution capability of each sampling pattern is assessed from a subjectively chosen but consistent set of criteria for the mean value and the spatial and temporal inhomogeneity of the root-mean-squared errors computed over a representative large collection of estimation times and locations.
For a mean mapping error threshold tolerance criterion of 25% of the signal standard deviation, the filter cutoff wavelength and period defining the resolution capability of SSH fields constructed from a tandem TOPEX/Poseidon (T/P) and Jason satellite sampling pattern with evenly spaced ground tracks are about 2.2° by 20 days. This can be compared with the resolution capability of about 6° by 20 days that can be obtained from a single altimeter in the T/P orbit. A tandem T/P–Jason mission with 0.75° spacing between simultaneously sampled parallel tracks that has been suggested for estimating geostrophic velocity yields an SSH mapping resolution capability of about 3.7° by 20 days. For the anticipated factor-of-2 larger orbit errors for ENVISAT compared with Jason, the resolution capability of a tandem Jason–ENVISAT scenario is about 3° by 20 days.
For mapping the SSH field, the tandem T/P–Jason sampling patterns with evenly spaced, interleaved ground tracks and either a 5-day or a 0-day offset is far better than the other tandem altimeter mission scenarios considered here. For the highest-resolution mapping, the 5-day offset is preferable to the 0-day offset. The scientific benefits of such a tandem mission are discussed in the context of two specific examples: Rossby wave dispersion and investigation of eddy–mean flow interaction.
Abstract
Six different SST analyses are compared with each other and with buoy data for the period 2007–08. All analyses used different combinations of satellite data [for example, infrared Advanced Very High Resolution Radiometer (AVHRR) and microwave Advanced Microwave Scanning Radiometer (AMSR) instruments] with different algorithms, spatial resolution, etc. The analyses considered are the National Climatic Data Center (NCDC) AVHRR-only and AMSR+AVHRR, the Navy Coupled Ocean Data Assimilation (NCODA), the Remote Sensing Systems (RSS), the Real-Time Global High-Resolution (RTG-HR), and the Operational SST and Sea Ice Analysis (OSTIA); the spatial grid sizes were 
To help quantify SST analysis differences, wavenumber spectra were computed at several locations. These results suggested that the RSS is much noisier and that the RTG-HR analysis is much smoother than the other analyses. Further comparisons made using collocated buoys showed that RSS was especially noisy in the tropics and that RTG-HR had winter biases near the Aleutians region during January and February 2007. The correlation results show that NCODA and, to a somewhat lesser extent, OSTIA are strongly tuned locally to buoy data. The results also show that grid spacing does not always correlate with analysis resolution.
The AVHRR-only analysis is useful for climate studies because it is the only daily SST analysis that extends back to September 1981. Furthermore, comparisons of the AVHRR-only analysis and the AMSR+AVHRR analysis show that AMSR data can degrade the combined AMSR and AVHRR resolution in cloud-free regions while AMSR otherwise improves the resolution. These results indicate that changes in satellite instruments over time can impact SST analysis resolution.
Abstract
Six different SST analyses are compared with each other and with buoy data for the period 2007–08. All analyses used different combinations of satellite data [for example, infrared Advanced Very High Resolution Radiometer (AVHRR) and microwave Advanced Microwave Scanning Radiometer (AMSR) instruments] with different algorithms, spatial resolution, etc. The analyses considered are the National Climatic Data Center (NCDC) AVHRR-only and AMSR+AVHRR, the Navy Coupled Ocean Data Assimilation (NCODA), the Remote Sensing Systems (RSS), the Real-Time Global High-Resolution (RTG-HR), and the Operational SST and Sea Ice Analysis (OSTIA); the spatial grid sizes were
To help quantify SST analysis differences, wavenumber spectra were computed at several locations. These results suggested that the RSS is much noisier and that the RTG-HR analysis is much smoother than the other analyses. Further comparisons made using collocated buoys showed that RSS was especially noisy in the tropics and that RTG-HR had winter biases near the Aleutians region during January and February 2007. The correlation results show that NCODA and, to a somewhat lesser extent, OSTIA are strongly tuned locally to buoy data. The results also show that grid spacing does not always correlate with analysis resolution.
The AVHRR-only analysis is useful for climate studies because it is the only daily SST analysis that extends back to September 1981. Furthermore, comparisons of the AVHRR-only analysis and the AMSR+AVHRR analysis show that AMSR data can degrade the combined AMSR and AVHRR resolution in cloud-free regions while AMSR otherwise improves the resolution. These results indicate that changes in satellite instruments over time can impact SST analysis resolution.
Obtaining global sea surface temperature (SST) fields for the ocean boundary condition in numerical weather prediction (NWP) models and for climate research has long been problematic. Historically, such fields have been constructed by a blending of in situ observations from ships and buoys and satellite infrared observations from the Advanced Very High Resolution Radiometer (AVHRR) that has been operational on NOAA satellites since November 1981. The resolution of these global SST fields is limited by the sparse coverage of in situ observations in many areas of the World Ocean and cloud contamination of AVHRR observations, which can exceed 75% over the subpolar oceans. As clouds and aerosols are essentially transparent to microwave radiation, satellite microwave observations can greatly improve the sampling and resolution of global SST fields. The Advanced Microwave Scanning Radiometer on the NASA Earth Observing System (EOS) Aqua satellite (AMSR-E) is providing the first highly accurate and global satellite microwave observations of SST. The potential for AMSR-E observations to improve the sampling, resolution, and accuracy of SST fields for NWP and climate research is demonstrated from example SST fields and from an investigation of the sensitivity of NWP models to specification of the SST boundary condition.
Obtaining global sea surface temperature (SST) fields for the ocean boundary condition in numerical weather prediction (NWP) models and for climate research has long been problematic. Historically, such fields have been constructed by a blending of in situ observations from ships and buoys and satellite infrared observations from the Advanced Very High Resolution Radiometer (AVHRR) that has been operational on NOAA satellites since November 1981. The resolution of these global SST fields is limited by the sparse coverage of in situ observations in many areas of the World Ocean and cloud contamination of AVHRR observations, which can exceed 75% over the subpolar oceans. As clouds and aerosols are essentially transparent to microwave radiation, satellite microwave observations can greatly improve the sampling and resolution of global SST fields. The Advanced Microwave Scanning Radiometer on the NASA Earth Observing System (EOS) Aqua satellite (AMSR-E) is providing the first highly accurate and global satellite microwave observations of SST. The potential for AMSR-E observations to improve the sampling, resolution, and accuracy of SST fields for NWP and climate research is demonstrated from example SST fields and from an investigation of the sensitivity of NWP models to specification of the SST boundary condition.
Abstract
In a recent paper, Lanzante reviewed methods for estimating the skill and significance of screening regression models through the use of Monte Carlo simulations. The strategies reviewed have several limitations that were not specified by the author. Due to the influence of true model skill, the Monte Carlo method provides an upper bound on the expected artificial skill, not the expected artificial skill itself as assumed. Lanzante emphasizes the advantages of the use of independent (uncorrelated) predictors. However, the disadvantages of their use and the advantages of dependent predictors in a screening regression were not considered.
The review of the effects of serial correlation on estimates of skill is misleading. The assertion that the formulations developed by Davis and Chelton are erroneous is incorrect. Moreover, contrary to the implication of the review, the use of effective sample size in tests of model significance has practical utility in applications including the Monte Carlo method.
Abstract
In a recent paper, Lanzante reviewed methods for estimating the skill and significance of screening regression models through the use of Monte Carlo simulations. The strategies reviewed have several limitations that were not specified by the author. Due to the influence of true model skill, the Monte Carlo method provides an upper bound on the expected artificial skill, not the expected artificial skill itself as assumed. Lanzante emphasizes the advantages of the use of independent (uncorrelated) predictors. However, the disadvantages of their use and the advantages of dependent predictors in a screening regression were not considered.
The review of the effects of serial correlation on estimates of skill is misleading. The assertion that the formulations developed by Davis and Chelton are erroneous is incorrect. Moreover, contrary to the implication of the review, the use of effective sample size in tests of model significance has practical utility in applications including the Monte Carlo method.
Abstract
A formalism is presented for determining the wavenumber-frequency transfer function associated with an irregularly sampled multidimensional dataset. This transfer function reveals the filtering characteristics and aliasing patterns inherent in the sample design. In combination with information about the spectral characteristics of the signal, the transfer function can be used to quantify the spatial and temporal resolution capability of the dataset. Application of the method to idealized Geosat altimeter data (i.e., neglecting measurement errors and data dropouts) concludes that the Geosat orbit configuration is capable of resolving scales of about 3° in latitude and longitude by about 30 days.
Abstract
A formalism is presented for determining the wavenumber-frequency transfer function associated with an irregularly sampled multidimensional dataset. This transfer function reveals the filtering characteristics and aliasing patterns inherent in the sample design. In combination with information about the spectral characteristics of the signal, the transfer function can be used to quantify the spatial and temporal resolution capability of the dataset. Application of the method to idealized Geosat altimeter data (i.e., neglecting measurement errors and data dropouts) concludes that the Geosat orbit configuration is capable of resolving scales of about 3° in latitude and longitude by about 30 days.
