Statistical relationships between higher-order moments of probability density functions (PDFs) ar... more Statistical relationships between higher-order moments of probability density functions (PDFs) are used to analyze top-of-atmosphere radiance measurements made by the Atmospheric Infrared Sounder (AIRS) and radiance calculations from the ECMWF Re-Analysis (ERA) and the Modern-Era Retrospective Analysis for Research and Applications (MERRA) over a 10-yr period. The statistical analysis used in this paper has previously been applied to sea surface temperature, and here the authors show that direct satellite radiance observations of atmospheric variability also exhibit stochastic forcing characteristics. The authors have chosen six different AIRS channels based on the sensitivity of their measured radiances to a variety of geophysical properties. In each of these channels, the authors have found evidence of correlated additive and multiplicative (CAM) stochastic forcing. In general, channels sensitive to tropospheric humidity and surface temperature show the strongest evidence of CAM forcing, while those sensitive to stratospheric temperature and ozone exhibit the weakest forcing. Radiance calculations from ERA and MERRA agree well with AIRS measurements in the Gaussian part of the PDFs but show some differences in the tails, indicating that the reanalyses may be missing some extrema there. The CAM forcing is investigated through numerical simulation of simple stochastic differential equations (SDEs). The authors show how measurements agree better with weaker CAM forcing, achieved by reducing the multiplicative forcing or by increasing the spatial correlation of the added noise in the case of an SDE with one spatial dimension. This indicates that atmospheric models could be improved by adjusting nonlinear terms that couple long and short time scales.
S U M M A R Y We have developed a new geomagnetic data assimilation approach which uses the minim... more S U M M A R Y We have developed a new geomagnetic data assimilation approach which uses the minimum variance' estimate for the analysis state, and which models both the forecast (or model output) and observation errors using an empirical approach and parameter tuning. This system is used in a series of assimilation experiments using Gauss coefficients (hereafter referred to as observational data) from the GUFM1 and CM4 field models for the years 1590–1990. We show that this assimilation system could be used to improve our knowledge of model parameters, model errors and the dynamical consistency of observation errors, by comparing forecasts of the magnetic field with the observations every 20 yr. Statistics of differences between observation and forecast (O − F) are used to determine how forecast accuracy depends on the Rayleigh number, forecast error correlation length scale and an observation error scale factor. Experiments have been carried out which demonstrate that a Rayleigh number of 30 times the critical Rayleigh number produces better geomagnetic forecasts than lower values, with an Ekman number of E = 1.25 Ă— 10 −6 , which produces a modified magnetic Reynolds number within the parameter domain with an 'Earth like' geodynamo. The optimal forecast error correlation length scale is found to be around 90 per cent of the thickness of the outer core, indicating a significant bias in the forecasts. Geomagnetic forecasts are also found to be highly sensitive to estimates of modelled observation errors: Errors that are too small do not lead to the gradual reduction in forecast error with time that is generally expected in a data assimilation system while observation errors that are too large lead to model divergence. Finally, we show that assimilation of L ≤ 3 (or large scale) gauss coefficients can help to improve forecasts of the L > 5 (smaller scale) coefficients, and that these improvements are the result of corrections to the velocity field in the geodynamo model.
Atmospheric CO2 retrievals with peak sensitivity
in the mid- to lower troposphere from the Atmosp... more Atmospheric CO2 retrievals with peak sensitivity in the mid- to lower troposphere from the Atmospheric Infrared Sounder (AIRS) have been assimilated into the GEOS- 5 (Goddard Earth Observing System Model, Version 5) constituent assimilation system for the period 1 January 2005 to 31 December 2006. A corresponding model simulation, using identical initial conditions, circulation, and CO2 boundary fluxes was also completed. The analyzed and simulated CO2 fields are compared with surface measurements globally and aircraft measurements over North America. Surface level monthly mean CO2 values show a marked improvement due to the assimilation in the Southern Hemisphere, while less consistent improvements are seen in the Northern Hemisphere. Mean differences with aircraft observations are reduced at all levels, with the largest decrease occurring in the mid-troposphere. The difference standard deviations are reduced slightly at all levels over the ocean, and all levels except the surface layer over land. These initial experiments indicate that the used channels contain useful information on CO2 in the middle to lower troposphere. However, the benefits of assimilating these data are reduced over the land surface, where concentrations are dominated by uncertain local fluxes and where the observation density is quite low. Away from these regions, the study demonstrates the power of the data assimilation technique for evaluating data that are not co-located, in that the improvements in mid-tropospheric CO2 by the sparsely distributed partial-column retrievals are transported by the model to the fixed in situ surface observation locations in more remote areas.
Numerical simulations of unsteady mixed convection involving interface tracking between two
immis... more Numerical simulations of unsteady mixed convection involving interface tracking between two immiscible fluids have been carried out, using spectral methods. A periodic oscillating flow is created by combining forced and natural convection with spatially periodic heating. The fluid motion that results is found to contain unsteady vortices in the flow which cause the stretching and folding that is required for efficient mixing processes. The interface between the two fluids is found to grow exponentially when the flow is unsteady, and the individual particles move with chaotically varying velocities. The interface growth rate is found to increase with increasing Prandtl number.
Statistical relationships between higher-order moments of probability density functions (PDFs) ar... more Statistical relationships between higher-order moments of probability density functions (PDFs) are used to analyze top-of-atmosphere radiance measurements made by the Atmospheric Infrared Sounder (AIRS) and radiance calculations from the ECMWF Re-Analysis (ERA) and the Modern-Era Retrospective Analysis for Research and Applications (MERRA) over a 10-yr period. The statistical analysis used in this paper has previously been applied to sea surface temperature, and here the authors show that direct satellite radiance observations of atmospheric variability also exhibit stochastic forcing characteristics. The authors have chosen six different AIRS channels based on the sensitivity of their measured radiances to a variety of geophysical properties. In each of these channels, the authors have found evidence of correlated additive and multiplicative (CAM) stochastic forcing. In general, channels sensitive to tropospheric humidity and surface temperature show the strongest evidence of CAM forcing, while those sensitive to stratospheric temperature and ozone exhibit the weakest forcing. Radiance calculations from ERA and MERRA agree well with AIRS measurements in the Gaussian part of the PDFs but show some differences in the tails, indicating that the reanalyses may be missing some extrema there. The CAM forcing is investigated through numerical simulation of simple stochastic differential equations (SDEs). The authors show how measurements agree better with weaker CAM forcing, achieved by reducing the multiplicative forcing or by increasing the spatial correlation of the added noise in the case of an SDE with one spatial dimension. This indicates that atmospheric models could be improved by adjusting nonlinear terms that couple long and short time scales.
S U M M A R Y We have developed a new geomagnetic data assimilation approach which uses the minim... more S U M M A R Y We have developed a new geomagnetic data assimilation approach which uses the minimum variance' estimate for the analysis state, and which models both the forecast (or model output) and observation errors using an empirical approach and parameter tuning. This system is used in a series of assimilation experiments using Gauss coefficients (hereafter referred to as observational data) from the GUFM1 and CM4 field models for the years 1590–1990. We show that this assimilation system could be used to improve our knowledge of model parameters, model errors and the dynamical consistency of observation errors, by comparing forecasts of the magnetic field with the observations every 20 yr. Statistics of differences between observation and forecast (O − F) are used to determine how forecast accuracy depends on the Rayleigh number, forecast error correlation length scale and an observation error scale factor. Experiments have been carried out which demonstrate that a Rayleigh number of 30 times the critical Rayleigh number produces better geomagnetic forecasts than lower values, with an Ekman number of E = 1.25 Ă— 10 −6 , which produces a modified magnetic Reynolds number within the parameter domain with an 'Earth like' geodynamo. The optimal forecast error correlation length scale is found to be around 90 per cent of the thickness of the outer core, indicating a significant bias in the forecasts. Geomagnetic forecasts are also found to be highly sensitive to estimates of modelled observation errors: Errors that are too small do not lead to the gradual reduction in forecast error with time that is generally expected in a data assimilation system while observation errors that are too large lead to model divergence. Finally, we show that assimilation of L ≤ 3 (or large scale) gauss coefficients can help to improve forecasts of the L > 5 (smaller scale) coefficients, and that these improvements are the result of corrections to the velocity field in the geodynamo model.
Atmospheric CO2 retrievals with peak sensitivity
in the mid- to lower troposphere from the Atmosp... more Atmospheric CO2 retrievals with peak sensitivity in the mid- to lower troposphere from the Atmospheric Infrared Sounder (AIRS) have been assimilated into the GEOS- 5 (Goddard Earth Observing System Model, Version 5) constituent assimilation system for the period 1 January 2005 to 31 December 2006. A corresponding model simulation, using identical initial conditions, circulation, and CO2 boundary fluxes was also completed. The analyzed and simulated CO2 fields are compared with surface measurements globally and aircraft measurements over North America. Surface level monthly mean CO2 values show a marked improvement due to the assimilation in the Southern Hemisphere, while less consistent improvements are seen in the Northern Hemisphere. Mean differences with aircraft observations are reduced at all levels, with the largest decrease occurring in the mid-troposphere. The difference standard deviations are reduced slightly at all levels over the ocean, and all levels except the surface layer over land. These initial experiments indicate that the used channels contain useful information on CO2 in the middle to lower troposphere. However, the benefits of assimilating these data are reduced over the land surface, where concentrations are dominated by uncertain local fluxes and where the observation density is quite low. Away from these regions, the study demonstrates the power of the data assimilation technique for evaluating data that are not co-located, in that the improvements in mid-tropospheric CO2 by the sparsely distributed partial-column retrievals are transported by the model to the fixed in situ surface observation locations in more remote areas.
Numerical simulations of unsteady mixed convection involving interface tracking between two
immis... more Numerical simulations of unsteady mixed convection involving interface tracking between two immiscible fluids have been carried out, using spectral methods. A periodic oscillating flow is created by combining forced and natural convection with spatially periodic heating. The fluid motion that results is found to contain unsteady vortices in the flow which cause the stretching and folding that is required for efficient mixing processes. The interface between the two fluids is found to grow exponentially when the flow is unsteady, and the individual particles move with chaotically varying velocities. The interface growth rate is found to increase with increasing Prandtl number.
Uploads
Papers by Andy Tangborn
in the mid- to lower troposphere from the Atmospheric Infrared
Sounder (AIRS) have been assimilated into the GEOS-
5 (Goddard Earth Observing System Model, Version 5) constituent
assimilation system for the period 1 January 2005 to
31 December 2006. A corresponding model simulation, using
identical initial conditions, circulation, and CO2 boundary
fluxes was also completed. The analyzed and simulated
CO2 fields are compared with surface measurements globally
and aircraft measurements over North America. Surface
level monthly mean CO2 values show a marked improvement
due to the assimilation in the Southern Hemisphere,
while less consistent improvements are seen in the Northern
Hemisphere. Mean differences with aircraft observations are
reduced at all levels, with the largest decrease occurring in
the mid-troposphere. The difference standard deviations are
reduced slightly at all levels over the ocean, and all levels
except the surface layer over land. These initial experiments
indicate that the used channels contain useful information on
CO2 in the middle to lower troposphere. However, the benefits
of assimilating these data are reduced over the land surface,
where concentrations are dominated by uncertain local
fluxes and where the observation density is quite low.
Away from these regions, the study demonstrates the power
of the data assimilation technique for evaluating data that are
not co-located, in that the improvements in mid-tropospheric
CO2 by the sparsely distributed partial-column retrievals are
transported by the model to the fixed in situ surface observation
locations in more remote areas.
immiscible fluids have been carried out, using spectral methods. A periodic oscillating flow is created by
combining forced and natural convection with spatially periodic heating. The fluid motion that results
is found to contain unsteady vortices in the flow which cause the stretching and folding that is required
for efficient mixing processes. The interface between the two fluids is found to grow exponentially when
the flow is unsteady, and the individual particles move with chaotically varying velocities. The interface
growth rate is found to increase with increasing Prandtl number.
in the mid- to lower troposphere from the Atmospheric Infrared
Sounder (AIRS) have been assimilated into the GEOS-
5 (Goddard Earth Observing System Model, Version 5) constituent
assimilation system for the period 1 January 2005 to
31 December 2006. A corresponding model simulation, using
identical initial conditions, circulation, and CO2 boundary
fluxes was also completed. The analyzed and simulated
CO2 fields are compared with surface measurements globally
and aircraft measurements over North America. Surface
level monthly mean CO2 values show a marked improvement
due to the assimilation in the Southern Hemisphere,
while less consistent improvements are seen in the Northern
Hemisphere. Mean differences with aircraft observations are
reduced at all levels, with the largest decrease occurring in
the mid-troposphere. The difference standard deviations are
reduced slightly at all levels over the ocean, and all levels
except the surface layer over land. These initial experiments
indicate that the used channels contain useful information on
CO2 in the middle to lower troposphere. However, the benefits
of assimilating these data are reduced over the land surface,
where concentrations are dominated by uncertain local
fluxes and where the observation density is quite low.
Away from these regions, the study demonstrates the power
of the data assimilation technique for evaluating data that are
not co-located, in that the improvements in mid-tropospheric
CO2 by the sparsely distributed partial-column retrievals are
transported by the model to the fixed in situ surface observation
locations in more remote areas.
immiscible fluids have been carried out, using spectral methods. A periodic oscillating flow is created by
combining forced and natural convection with spatially periodic heating. The fluid motion that results
is found to contain unsteady vortices in the flow which cause the stretching and folding that is required
for efficient mixing processes. The interface between the two fluids is found to grow exponentially when
the flow is unsteady, and the individual particles move with chaotically varying velocities. The interface
growth rate is found to increase with increasing Prandtl number.