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Abstract
This study extends initial work by Sun and Penny and Sun et al. to explore the inclusion of path information from surface drifters using an augmented-state Lagrangian data assimilation based on the local ensemble transform Kalman filter (LETKF-LaDA) with vertical localization to improve analysis of the ocean. The region of interest is the Gulf of Mexico during the passage of Hurricane Isaac in the summer of 2012. Results from experiments with a regional ocean model at eddy-permitting and eddy-resolving model resolutions are used to quantify improvements to the analysis of sea surface velocity, sea surface temperature, and sea surface height in a data assimilation system. The data assimilation system assimilates surface drifter positions, as well as vertical profiles of temperature and salinity. Data were used from drifters deployed as a part of the Grand Lagrangian Deployment beginning 20 July 2012. Comparison of experiment results shows that at both eddy-permitting and eddy-resolving horizontal resolutions Lagrangian assimilation of drifter positions significantly improves analysis of the ocean state responding to hurricane conditions. These results, which should be applicable to other tropical oceans such as the Bay of Bengal, open new avenues for estimating ocean initial conditions to improve tropical cyclone forecasting.
Abstract
This study extends initial work by Sun and Penny and Sun et al. to explore the inclusion of path information from surface drifters using an augmented-state Lagrangian data assimilation based on the local ensemble transform Kalman filter (LETKF-LaDA) with vertical localization to improve analysis of the ocean. The region of interest is the Gulf of Mexico during the passage of Hurricane Isaac in the summer of 2012. Results from experiments with a regional ocean model at eddy-permitting and eddy-resolving model resolutions are used to quantify improvements to the analysis of sea surface velocity, sea surface temperature, and sea surface height in a data assimilation system. The data assimilation system assimilates surface drifter positions, as well as vertical profiles of temperature and salinity. Data were used from drifters deployed as a part of the Grand Lagrangian Deployment beginning 20 July 2012. Comparison of experiment results shows that at both eddy-permitting and eddy-resolving horizontal resolutions Lagrangian assimilation of drifter positions significantly improves analysis of the ocean state responding to hurricane conditions. These results, which should be applicable to other tropical oceans such as the Bay of Bengal, open new avenues for estimating ocean initial conditions to improve tropical cyclone forecasting.
Abstract
Deep convection that penetrates the tropopause, referred to here as overshooting convection, is capable of lifting tropospheric air well into the stratosphere. In addition to water, these overshoots also transport various chemical species, affecting chemistry and radiation in the stratosphere. It is not currently known, however, how much transport is a result of this mechanism. To better understand overshooting convection, this study aims to characterize the durations of overshooting events. To achieve this, radar data from the Next Generation Weather Radar (NEXRAD) network is composited onto a three-dimensional grid at 5-min intervals. Overshoots are identified by comparing echo-top heights with tropopause estimates derived from ERA5 reanalysis data. These overshoots are linked in space from one analysis time to the next to form tracks. This process is performed for 12 four-day sample windows in the months May–August of 2017–19. Track characteristics such as duration, overshoot area, tropopause-relative altitude, and column-maximum reflectivity are investigated. Positive correlations are found between track duration and other track characteristics. Integrated track volume is found as a product of the overshoot area, depth, and duration, and provides a measure of the potential stratospheric impact of each track. Short-lived tracks are observed to contribute the most total integrated volume when considering track duration, while tracks that overshoot by 2–3 km show the largest contribution when considering overshoot depth. A diurnal cycle is observed, with peak track initiation around 1600–1700 local time. Track-mean duration peaks a few hours earlier, while track-mean area and tropopause-relative height peak a few hours later.
Abstract
Deep convection that penetrates the tropopause, referred to here as overshooting convection, is capable of lifting tropospheric air well into the stratosphere. In addition to water, these overshoots also transport various chemical species, affecting chemistry and radiation in the stratosphere. It is not currently known, however, how much transport is a result of this mechanism. To better understand overshooting convection, this study aims to characterize the durations of overshooting events. To achieve this, radar data from the Next Generation Weather Radar (NEXRAD) network is composited onto a three-dimensional grid at 5-min intervals. Overshoots are identified by comparing echo-top heights with tropopause estimates derived from ERA5 reanalysis data. These overshoots are linked in space from one analysis time to the next to form tracks. This process is performed for 12 four-day sample windows in the months May–August of 2017–19. Track characteristics such as duration, overshoot area, tropopause-relative altitude, and column-maximum reflectivity are investigated. Positive correlations are found between track duration and other track characteristics. Integrated track volume is found as a product of the overshoot area, depth, and duration, and provides a measure of the potential stratospheric impact of each track. Short-lived tracks are observed to contribute the most total integrated volume when considering track duration, while tracks that overshoot by 2–3 km show the largest contribution when considering overshoot depth. A diurnal cycle is observed, with peak track initiation around 1600–1700 local time. Track-mean duration peaks a few hours earlier, while track-mean area and tropopause-relative height peak a few hours later.
Abstract
Improving lead time for forecasting floods is important to minimize property damage and ensure the safety of the public and emergency services during flood events. Numerical weather prediction (NWP) models are important components of flood forecasting systems and have been vital in extending forecasting lead time under complex weather and terrain conditions. However, NWP forecasts still have significant uncertainty associated with the precipitation fields that are the main inputs of the hydrologic models and thus the resulting flood forecasts. An issue often overlooked is the importance of correctly representing variability over a range of different temporal scales. To address this gap, here a new wavelet-based method for postprocessing NWP precipitation forecasts is proposed. First, precipitation forecasts are decomposed into the frequency domain using a wavelet transform, providing estimates of the amplitudes and phases of the time series at different frequencies. Quantile mapping is then used to correct bias in the amplitudes of each frequency. Randomized phases are used to generate an ensemble of realizations of the precipitation forecasts. The postprocessed precipitation forecasts are reconstructed by taking the inverse of adjusted time-frequency decompositions with the corrected amplitudes and randomized phases. The proposed method was used to postprocess NWP precipitation forecasts in the Sydney region of Australia. There is a significant improvement in postprocessed precipitation forecasts across multiple time scales in terms of bias and temporal and spatial correlation structures. The postprocessed precipitation fields can be used for the modeling of fully distributed hydrologic systems, improving runoff stimulation, flood depth estimation, and flood early warning.
Significance Statement
A new method accounting for the timing and spatial errors of NWP precipitation forecasts is proposed, and it can improve the skill of forecasts across multiple time scales, especially at short lead times. The proposed method provides a practical and effective way to correct these errors by incorporating spatiotemporal neighborhood information through the frequency domain using sophisticated wavelet transforms. With systematic timing and spatial errors removed, precipitation forecasts will be more skillful, and hydrological modeling using the postprocessed forecasts can provide higher accuracy of streamflow estimation.
Abstract
Improving lead time for forecasting floods is important to minimize property damage and ensure the safety of the public and emergency services during flood events. Numerical weather prediction (NWP) models are important components of flood forecasting systems and have been vital in extending forecasting lead time under complex weather and terrain conditions. However, NWP forecasts still have significant uncertainty associated with the precipitation fields that are the main inputs of the hydrologic models and thus the resulting flood forecasts. An issue often overlooked is the importance of correctly representing variability over a range of different temporal scales. To address this gap, here a new wavelet-based method for postprocessing NWP precipitation forecasts is proposed. First, precipitation forecasts are decomposed into the frequency domain using a wavelet transform, providing estimates of the amplitudes and phases of the time series at different frequencies. Quantile mapping is then used to correct bias in the amplitudes of each frequency. Randomized phases are used to generate an ensemble of realizations of the precipitation forecasts. The postprocessed precipitation forecasts are reconstructed by taking the inverse of adjusted time-frequency decompositions with the corrected amplitudes and randomized phases. The proposed method was used to postprocess NWP precipitation forecasts in the Sydney region of Australia. There is a significant improvement in postprocessed precipitation forecasts across multiple time scales in terms of bias and temporal and spatial correlation structures. The postprocessed precipitation fields can be used for the modeling of fully distributed hydrologic systems, improving runoff stimulation, flood depth estimation, and flood early warning.
Significance Statement
A new method accounting for the timing and spatial errors of NWP precipitation forecasts is proposed, and it can improve the skill of forecasts across multiple time scales, especially at short lead times. The proposed method provides a practical and effective way to correct these errors by incorporating spatiotemporal neighborhood information through the frequency domain using sophisticated wavelet transforms. With systematic timing and spatial errors removed, precipitation forecasts will be more skillful, and hydrological modeling using the postprocessed forecasts can provide higher accuracy of streamflow estimation.
Abstract
Forecasting mesoscale convective systems (MCSs) and precipitation over complex terrain is an ongoing challenge even for convective-permitting numerical models. Here, we show the value of combining mesoscale constraints to improve short-term MCS forecasts for two events during the North American monsoon season in 2013, including the following: 1) the initial specification of moisture, via GPS-precipitable water vapor (PWV) data assimilation (DA); 2) kinematics via modification of cumulus parameterization; and 3) microphysics via modification of cloud microphysics parameterization. A total of five convective-permitting Weather Research and Forecasting (WRF) Model experiments is conducted for each event to elucidate the impact of these constraints. Results show that combining GPS-PWV DA with a modified Kain–Fritsch scheme and double-moment microphysics provides relatively the best forecast of both North American monsoon MCSs and convective precipitation in terms of timing, location, and intensity relative to available precipitation and cloud-top temperature observations. Additional examination on the associated reflectivity, vertical wind field, equivalent potential temperature, and hydrometeor distribution of MCS events show the added value of each individual constraint to forecast performance.
Significance Statement
Forecasting thunderstorm clouds and rain over mountainous regions is challenging because of limitations in having radar and rain gauges and in resolving physical drivers in forecast models. We examine the value of considering all possible constraints by incorporating moisture into these models, and correcting physics in the model treatment of cumulus and cloud microphysics parameterizations. This study demonstrates that assimilating moisture and using modified Kain–Fritsch and double-moment microphysics schemes provides the best thunderstorm cloud and rain forecasts in terms of timing, location, and intensity. Each correction improves key properties of these storms such as vertical wind, along with distribution of water in various phases. We highlight the need to improve our efforts on effectively integrating these constraints into current and future forecasts.
Abstract
Forecasting mesoscale convective systems (MCSs) and precipitation over complex terrain is an ongoing challenge even for convective-permitting numerical models. Here, we show the value of combining mesoscale constraints to improve short-term MCS forecasts for two events during the North American monsoon season in 2013, including the following: 1) the initial specification of moisture, via GPS-precipitable water vapor (PWV) data assimilation (DA); 2) kinematics via modification of cumulus parameterization; and 3) microphysics via modification of cloud microphysics parameterization. A total of five convective-permitting Weather Research and Forecasting (WRF) Model experiments is conducted for each event to elucidate the impact of these constraints. Results show that combining GPS-PWV DA with a modified Kain–Fritsch scheme and double-moment microphysics provides relatively the best forecast of both North American monsoon MCSs and convective precipitation in terms of timing, location, and intensity relative to available precipitation and cloud-top temperature observations. Additional examination on the associated reflectivity, vertical wind field, equivalent potential temperature, and hydrometeor distribution of MCS events show the added value of each individual constraint to forecast performance.
Significance Statement
Forecasting thunderstorm clouds and rain over mountainous regions is challenging because of limitations in having radar and rain gauges and in resolving physical drivers in forecast models. We examine the value of considering all possible constraints by incorporating moisture into these models, and correcting physics in the model treatment of cumulus and cloud microphysics parameterizations. This study demonstrates that assimilating moisture and using modified Kain–Fritsch and double-moment microphysics schemes provides the best thunderstorm cloud and rain forecasts in terms of timing, location, and intensity. Each correction improves key properties of these storms such as vertical wind, along with distribution of water in various phases. We highlight the need to improve our efforts on effectively integrating these constraints into current and future forecasts.
Abstract
This paper examines the meteorological factors that led to the record-breaking heavy precipitation event in Taiwan in the early 2020 mei-yu season (15–31 May). The extreme amount of rainfall (an average of 135.9 mm per station) during the 36-h period around 22 May (hereafter Y20R) also set a record. Compared to climatology, the Pacific subtropical high was stronger and the southwesterly monsoonal flow was more intense during the first half of the 2020 mei-yu season, resulting in a stronger moisture conveyor belt over the northern Indo-China Peninsula. The record-breaking precipitation in Y20R was mainly caused by the eastward movement of a southwest vortex (SWV) generated in southwestern China. When the eastern portion of the SWV touched northern Taiwan, its associated west-southwesterly winds and the large-scale southwesterly monsoonal flow transported moisture toward the Taiwan Strait. The moisture-laden southwesterly flow was lifted by the stationary mei-yu front, leading to the heavy rainfall in southern Taiwan. When the SWV passed through northern Taiwan, it became the dominant weather system that enhanced the west-southwesterly winds and transported moisture from South China to Taiwan. The front moved southward through the Taiwan Strait during this period, with its location greatly determining the pattern of rainfall in southern Taiwan. In summary, the most critical factors leading to heavy rainfall in southern Taiwan are the strong 850-hPa southwesterly winds and moisture fluxes associated with the SWV. The other key factors include, in order of sensitivity to rainfall, the distance of the front, the distance of the SWV, the frontal speed, and the intensity of the SWV.
Abstract
This paper examines the meteorological factors that led to the record-breaking heavy precipitation event in Taiwan in the early 2020 mei-yu season (15–31 May). The extreme amount of rainfall (an average of 135.9 mm per station) during the 36-h period around 22 May (hereafter Y20R) also set a record. Compared to climatology, the Pacific subtropical high was stronger and the southwesterly monsoonal flow was more intense during the first half of the 2020 mei-yu season, resulting in a stronger moisture conveyor belt over the northern Indo-China Peninsula. The record-breaking precipitation in Y20R was mainly caused by the eastward movement of a southwest vortex (SWV) generated in southwestern China. When the eastern portion of the SWV touched northern Taiwan, its associated west-southwesterly winds and the large-scale southwesterly monsoonal flow transported moisture toward the Taiwan Strait. The moisture-laden southwesterly flow was lifted by the stationary mei-yu front, leading to the heavy rainfall in southern Taiwan. When the SWV passed through northern Taiwan, it became the dominant weather system that enhanced the west-southwesterly winds and transported moisture from South China to Taiwan. The front moved southward through the Taiwan Strait during this period, with its location greatly determining the pattern of rainfall in southern Taiwan. In summary, the most critical factors leading to heavy rainfall in southern Taiwan are the strong 850-hPa southwesterly winds and moisture fluxes associated with the SWV. The other key factors include, in order of sensitivity to rainfall, the distance of the front, the distance of the SWV, the frontal speed, and the intensity of the SWV.
Abstract
The national upgrade of the operational weather radar network to include polarimetric capabilities has led to numerous studies focusing on polarimetric radar signatures commonly observed in supercells. One such signature is the horizontal separation of regions of enhanced differential reflectivity (Z DR) and specific differential phase (K DP) values due to hydrometeor size sorting. Recent observational studies have shown that the orientation of this separation tends to be more perpendicular to storm motion in supercells that produce tornadoes. Although this finding has potential operational utility, the physical relationship between this observed radar signature and tornadic potential is not known. This study uses an ensemble of supercell simulations initialized with tornadic and nontornadic environments to investigate this connection. The tendency for tornadic supercells to have a more perpendicular separation orientation was reproduced, although to a lesser degree. This difference in orientation angles was caused by stronger rearward storm-relative flow in the nontornadic supercells, leading to a rearward shift of precipitation and, therefore, the enhanced K DP region within the supercell. Further, this resulted in an unfavorable rearward shift of the negative buoyancy region, which led to an order of magnitude less baroclinic generation of circulation in the nontornadic simulations compared to tornadic simulations.
Abstract
The national upgrade of the operational weather radar network to include polarimetric capabilities has led to numerous studies focusing on polarimetric radar signatures commonly observed in supercells. One such signature is the horizontal separation of regions of enhanced differential reflectivity (Z DR) and specific differential phase (K DP) values due to hydrometeor size sorting. Recent observational studies have shown that the orientation of this separation tends to be more perpendicular to storm motion in supercells that produce tornadoes. Although this finding has potential operational utility, the physical relationship between this observed radar signature and tornadic potential is not known. This study uses an ensemble of supercell simulations initialized with tornadic and nontornadic environments to investigate this connection. The tendency for tornadic supercells to have a more perpendicular separation orientation was reproduced, although to a lesser degree. This difference in orientation angles was caused by stronger rearward storm-relative flow in the nontornadic supercells, leading to a rearward shift of precipitation and, therefore, the enhanced K DP region within the supercell. Further, this resulted in an unfavorable rearward shift of the negative buoyancy region, which led to an order of magnitude less baroclinic generation of circulation in the nontornadic simulations compared to tornadic simulations.
Abstract
This study evaluates the impact of assimilating Global Navigation Satellite System (GNSS) radio occultation (RO) bending angles from Formosa Satellite Mission-7/Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) receiver satellites on Hurricane Weather Research and Forecasting (HWRF) Model tropical cyclone (TC) forecasts. Launched in June 2019, the COSMIC-2 mission provides significantly higher tropics data coverage compared to its predecessor COSMIC constellation. GNSS RO measurements yield information about atmospheric pressure, temperature, and water vapor profiles. HWRF is cycled with and without COSMIC-2 bending angle data assimilation for six 2020 Atlantic hurricane cases. COSMIC-2 assimilation has little impact on HWRF track forecasts, consistent with HWRF’s design limiting cycled data assimilation impacts on surrounding large-scale flows; however, COSMIC-2 assimilation results in a statistically significant ∼8%–12% mean absolute forecast error reduction in minimum central sea level pressure for t = 36-, 54-, 60-, and 108–120-h lead times. Forecasts initialized from analyses assimilating COSMIC-2 observations also have a 1%–4% smaller 600–700-hPa specific humidity (SPFH) root-mean-squared deviation compared to radiosondes and dropwindsondes for most lead times. While not all HWRF intensity forecasts benefit from COSMIC-2 assimilation, a few show notable improvement. For example, assimilating two COSMIC-2 profiles within the inner core of developing Hurricane Hanna (2020) increases 800-hPa SPFH by up to 1 g kg−1 locally, helping to correct a dry bias. The forecast initialized from this analysis better captures Hanna’s observed intensification rate, likely because its moister inner core facilitates development of persistent deep convection near the TC center, where diabatic heating is more efficiently converted to cyclonic wind kinetic energy.
Significance Statement
Tropical cyclone (TC) intensification can be strongly sensitive to the lower-to-midtropospheric water vapor distribution near the storm. The COSMIC-2 GNSS radio occultation (RO) receiver satellite mission provides denser spatial coverage of atmospheric water vapor and temperature profiles over the tropics compared to other GNSS RO observation platforms. Herein, using six 2020 Atlantic TC cases, we evaluate the impacts of assimilating COSMIC-2 RO bending angles into a regional forecast model that already assimilates clear-sky satellite radiances. It is shown that COSMIC-2 assimilation yields a modest ∼10% intensity forecast skill improvement for several lead times, although more substantial intensity forecast improvement is found for a few forecasts where the COSMIC-2 observation assimilation helps correct a lower-to-midtropospheric water vapor bias.
Abstract
This study evaluates the impact of assimilating Global Navigation Satellite System (GNSS) radio occultation (RO) bending angles from Formosa Satellite Mission-7/Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) receiver satellites on Hurricane Weather Research and Forecasting (HWRF) Model tropical cyclone (TC) forecasts. Launched in June 2019, the COSMIC-2 mission provides significantly higher tropics data coverage compared to its predecessor COSMIC constellation. GNSS RO measurements yield information about atmospheric pressure, temperature, and water vapor profiles. HWRF is cycled with and without COSMIC-2 bending angle data assimilation for six 2020 Atlantic hurricane cases. COSMIC-2 assimilation has little impact on HWRF track forecasts, consistent with HWRF’s design limiting cycled data assimilation impacts on surrounding large-scale flows; however, COSMIC-2 assimilation results in a statistically significant ∼8%–12% mean absolute forecast error reduction in minimum central sea level pressure for t = 36-, 54-, 60-, and 108–120-h lead times. Forecasts initialized from analyses assimilating COSMIC-2 observations also have a 1%–4% smaller 600–700-hPa specific humidity (SPFH) root-mean-squared deviation compared to radiosondes and dropwindsondes for most lead times. While not all HWRF intensity forecasts benefit from COSMIC-2 assimilation, a few show notable improvement. For example, assimilating two COSMIC-2 profiles within the inner core of developing Hurricane Hanna (2020) increases 800-hPa SPFH by up to 1 g kg−1 locally, helping to correct a dry bias. The forecast initialized from this analysis better captures Hanna’s observed intensification rate, likely because its moister inner core facilitates development of persistent deep convection near the TC center, where diabatic heating is more efficiently converted to cyclonic wind kinetic energy.
Significance Statement
Tropical cyclone (TC) intensification can be strongly sensitive to the lower-to-midtropospheric water vapor distribution near the storm. The COSMIC-2 GNSS radio occultation (RO) receiver satellite mission provides denser spatial coverage of atmospheric water vapor and temperature profiles over the tropics compared to other GNSS RO observation platforms. Herein, using six 2020 Atlantic TC cases, we evaluate the impacts of assimilating COSMIC-2 RO bending angles into a regional forecast model that already assimilates clear-sky satellite radiances. It is shown that COSMIC-2 assimilation yields a modest ∼10% intensity forecast skill improvement for several lead times, although more substantial intensity forecast improvement is found for a few forecasts where the COSMIC-2 observation assimilation helps correct a lower-to-midtropospheric water vapor bias.
Abstract
Accurate atmospheric-state analysis is essential for understanding and prediction of the atmosphere and is a difficult scientific problem due to the chaotic nature of the atmosphere; namely, small atmospheric perturbations (APs) grow rapidly in nonlinear processes. The key to atmospheric-state analysis is knowing the structure of the APs. We analyzed the AP structure in terms of network theory using a 192-member AP ensemble. The AP ensemble was generated by an ensemble of variational data assimilation (DA) with the perturbed observation method using the operational numerical weather prediction system at the Japan Meteorological Agency. The generated APs captured flow-dependent AP structures corresponding to atmospheric normal modes, and their use in DA improved accuracy of atmospheric-state predictions. These show the usefulness of the APs. The network property of the APs are as follows. The atmosphere has a small average network distance compared with the square root of the number of nodes, and a large clustering coefficient (about 0.6). These show that the APs have small-world network properties. The degree distribution of APs shows the heavy-tailed structure. These three properties of APs are common to various complex networks in other systems. Hubs in the AP network correspond to atmospheric disturbances. The network community detection using network modularity shows about 18 communities with 0.8 modularity. These basic network properties of APs represent efficient information exchange in the atmosphere, which provides a complementary atmospheric picture to its traditional physical picture based on fluid dynamics and thermodynamics, and would be basic information for atmospheric sciences and extension of application target of the network theory.
Significance Statement
The purpose of this paper is to analyze properties of atmospheric perturbations using the network theory and an accurate ensemble of the atmospheric perturbations. This is important for atmospheric-state estimation and forecasting because the atmosphere is chaotic and small perturbations grow rapidly. Our results show that the atmosphere has a small average network distance and a large clustering coefficient, which are the properties of a small-world network, and a heavy-tailed degree distribution. These three properties of atmospheric perturbations are common to various complex networks in other systems.
Abstract
Accurate atmospheric-state analysis is essential for understanding and prediction of the atmosphere and is a difficult scientific problem due to the chaotic nature of the atmosphere; namely, small atmospheric perturbations (APs) grow rapidly in nonlinear processes. The key to atmospheric-state analysis is knowing the structure of the APs. We analyzed the AP structure in terms of network theory using a 192-member AP ensemble. The AP ensemble was generated by an ensemble of variational data assimilation (DA) with the perturbed observation method using the operational numerical weather prediction system at the Japan Meteorological Agency. The generated APs captured flow-dependent AP structures corresponding to atmospheric normal modes, and their use in DA improved accuracy of atmospheric-state predictions. These show the usefulness of the APs. The network property of the APs are as follows. The atmosphere has a small average network distance compared with the square root of the number of nodes, and a large clustering coefficient (about 0.6). These show that the APs have small-world network properties. The degree distribution of APs shows the heavy-tailed structure. These three properties of APs are common to various complex networks in other systems. Hubs in the AP network correspond to atmospheric disturbances. The network community detection using network modularity shows about 18 communities with 0.8 modularity. These basic network properties of APs represent efficient information exchange in the atmosphere, which provides a complementary atmospheric picture to its traditional physical picture based on fluid dynamics and thermodynamics, and would be basic information for atmospheric sciences and extension of application target of the network theory.
Significance Statement
The purpose of this paper is to analyze properties of atmospheric perturbations using the network theory and an accurate ensemble of the atmospheric perturbations. This is important for atmospheric-state estimation and forecasting because the atmosphere is chaotic and small perturbations grow rapidly. Our results show that the atmosphere has a small average network distance and a large clustering coefficient, which are the properties of a small-world network, and a heavy-tailed degree distribution. These three properties of atmospheric perturbations are common to various complex networks in other systems.
Abstract
A set of control parameters is introduced in the fully elastic nonhydrostatic Euler equations formulated in the mass-based vertical coordinate of Laprise. Contrary to the classical approach, the hydrostatic limit is represented by a subspace of control parameters, instead of a single point. By finding a suitable path from the fully compressible equations to the hydrostatic subspace, we are able to construct a blended system with acoustic modes slowed down and gravity modes nearly unaffected. Numerical stability of the discretized system is thus improved, and the solution remains essentially the fully compressible one. Alternatively, control parameters can be used to redefine the linear model of the constant coefficients semi-implicit time scheme, increasing the numerical stability of the fully compressible system. With a careful choice of the control parameters in both, the linear model used in the semi-implicit temporal scheme, and in the full model, the blended system does not deteriorate the compressible solution while its semi-implicit temporal discretization is more stable. We illustrate the potential of the method in several simple examples and in real case studies using the ALADIN system.
Abstract
A set of control parameters is introduced in the fully elastic nonhydrostatic Euler equations formulated in the mass-based vertical coordinate of Laprise. Contrary to the classical approach, the hydrostatic limit is represented by a subspace of control parameters, instead of a single point. By finding a suitable path from the fully compressible equations to the hydrostatic subspace, we are able to construct a blended system with acoustic modes slowed down and gravity modes nearly unaffected. Numerical stability of the discretized system is thus improved, and the solution remains essentially the fully compressible one. Alternatively, control parameters can be used to redefine the linear model of the constant coefficients semi-implicit time scheme, increasing the numerical stability of the fully compressible system. With a careful choice of the control parameters in both, the linear model used in the semi-implicit temporal scheme, and in the full model, the blended system does not deteriorate the compressible solution while its semi-implicit temporal discretization is more stable. We illustrate the potential of the method in several simple examples and in real case studies using the ALADIN system.
