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Abstract
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Abstract
The numerical model of air-sea interaction previously described in Jacobs (1978), Pandolfo and Jacobs (1972) and Pandolfo (1969) is inserted at one horizontal grid point in the GATE III Gridded Global Data Set to calculate a model-generated, local interface temperature over a two-day interval (0000 GMT 4 September-0000 GMT 6 September 1974) of GATE Period III.
The experiment provides a preliminary demonstration of the accuracy achievable in predicting sea-surface temperature over multi-day scales with limited-domain models nested within global data sets. It also demonstrates the degree of sensitivity of the model-generated sea-surface temperature to the inclusion of parameterized convective adjustments in the oceanic and atmospheric sub-layers under the general conditions prevailing during the period studied.
Initial and boundary data were provided to the local model on a relatively coarse vertical grid and with relatively coarse (12 h) temporal resolution. Linear spatial and temporal interpolation was used to produce the higher resolution data required by the model. (A 6 min time step and grid intervals as small as 1 m were used in the experiments described in this paper.) Therefore, the nested local model provides, in this preliminary experiment, increased resolution only in the vertical and temporal dimensions. It also adds greater physical complexity to the global-scale model used in the generation of the GATE III gridded data set (and described in Miyakoda et al., 1980) by coupling the atmosphere-ocean boundary layers to allow the prediction (rather than the prespecification) of sea-surface temperature, and by taking into account model-generated temporal variations in the vertical structures of the atmospheric transmissivity with regard to solar and infrared radiation.
The two-day period used for this demonstration is characterized by moderately disturbed tropical marine conditions with intermittent periods of light wind as contrasted to the generally steady trade-wind and midlatitude conditions previously treated in the papers cited above. Nevertheless, the air-sea interaction model, when suitably refined to include parameterized convective adjustment in the, coupled air-ocean layers, again yields model-generated sea-surface temperatures which generally differ from those observed by less than the uncertainty of measurement, and with accuracy well within that estimated in Charney et al. (1966) as required in order to extend the temporal range of weather forecasts in numerical models of the atmosphere.
In one model run of the experiment the atmospheric convective adjustment was eliminated from the model. The result is an unrealistic accumulation of heat in the ocean surface layer. In another model run of the experiment the ocean-surface layer convective adjustment was eliminated from the model. The result is a somewhat cooler model-generated nighttime interface temperature.
Interaction between the parameterized convective processes of the coupled air-sea model layers is also evident from the results. When the parameterized atmospheric convective adjustment is omitted from the model, significant alteration of the model-generated oceanic “convection depth” takes place; conversely when the parameterized oceanic convective adjustment is omitted, there occurs a substantial alteration of the model-generated atmospheric “convective condensation level.”
Abstract
The numerical model of air-sea interaction previously described in Jacobs (1978), Pandolfo and Jacobs (1972) and Pandolfo (1969) is inserted at one horizontal grid point in the GATE III Gridded Global Data Set to calculate a model-generated, local interface temperature over a two-day interval (0000 GMT 4 September-0000 GMT 6 September 1974) of GATE Period III.
The experiment provides a preliminary demonstration of the accuracy achievable in predicting sea-surface temperature over multi-day scales with limited-domain models nested within global data sets. It also demonstrates the degree of sensitivity of the model-generated sea-surface temperature to the inclusion of parameterized convective adjustments in the oceanic and atmospheric sub-layers under the general conditions prevailing during the period studied.
Initial and boundary data were provided to the local model on a relatively coarse vertical grid and with relatively coarse (12 h) temporal resolution. Linear spatial and temporal interpolation was used to produce the higher resolution data required by the model. (A 6 min time step and grid intervals as small as 1 m were used in the experiments described in this paper.) Therefore, the nested local model provides, in this preliminary experiment, increased resolution only in the vertical and temporal dimensions. It also adds greater physical complexity to the global-scale model used in the generation of the GATE III gridded data set (and described in Miyakoda et al., 1980) by coupling the atmosphere-ocean boundary layers to allow the prediction (rather than the prespecification) of sea-surface temperature, and by taking into account model-generated temporal variations in the vertical structures of the atmospheric transmissivity with regard to solar and infrared radiation.
The two-day period used for this demonstration is characterized by moderately disturbed tropical marine conditions with intermittent periods of light wind as contrasted to the generally steady trade-wind and midlatitude conditions previously treated in the papers cited above. Nevertheless, the air-sea interaction model, when suitably refined to include parameterized convective adjustment in the, coupled air-ocean layers, again yields model-generated sea-surface temperatures which generally differ from those observed by less than the uncertainty of measurement, and with accuracy well within that estimated in Charney et al. (1966) as required in order to extend the temporal range of weather forecasts in numerical models of the atmosphere.
In one model run of the experiment the atmospheric convective adjustment was eliminated from the model. The result is an unrealistic accumulation of heat in the ocean surface layer. In another model run of the experiment the ocean-surface layer convective adjustment was eliminated from the model. The result is a somewhat cooler model-generated nighttime interface temperature.
Interaction between the parameterized convective processes of the coupled air-sea model layers is also evident from the results. When the parameterized atmospheric convective adjustment is omitted from the model, significant alteration of the model-generated oceanic “convection depth” takes place; conversely when the parameterized oceanic convective adjustment is omitted, there occurs a substantial alteration of the model-generated atmospheric “convective condensation level.”
Abstract
A numerical analysis of the nonlinear heat diffusion equation has been carted out to bring to light a heretofore little-understood type of instability that can be encountered in many numerical modeling applications. The nature of the instability is such that the error remains bounded but becomes large enough to prevent proper assessment of model results. For the sample problem under investigation, the nonlinearity is introduced through a diffusion coefficient that depends on the Richardson number which, in turn, is a function of the dependent variable. Our analysis shows that the interaction of short-wavelength and inter-mediate-wavelength solution components can induce nonlinear instability if the amplitude of either component is sufficiently large. Since the unstable solution may not wander far from the true solution, the error can be difficult to detect. A criterion, given in terms of a restriction on the Richardson number, guarantees local (short-term) stability of the numerical scheme whenever the criterion is satisfied. Numerical results obtained using a boundary-layer model with GATE Phase III data are presented to support the theoretical conclusions.
Abstract
A numerical analysis of the nonlinear heat diffusion equation has been carted out to bring to light a heretofore little-understood type of instability that can be encountered in many numerical modeling applications. The nature of the instability is such that the error remains bounded but becomes large enough to prevent proper assessment of model results. For the sample problem under investigation, the nonlinearity is introduced through a diffusion coefficient that depends on the Richardson number which, in turn, is a function of the dependent variable. Our analysis shows that the interaction of short-wavelength and inter-mediate-wavelength solution components can induce nonlinear instability if the amplitude of either component is sufficiently large. Since the unstable solution may not wander far from the true solution, the error can be difficult to detect. A criterion, given in terms of a restriction on the Richardson number, guarantees local (short-term) stability of the numerical scheme whenever the criterion is satisfied. Numerical results obtained using a boundary-layer model with GATE Phase III data are presented to support the theoretical conclusions.
Abstract
The advection-diffusion equation is often solved by implicit finite-difference schemes that are unconditionally stable when the grid interval is uniform. When such schemes are generalized to account for nonuniform grid spacing, instability can result. The cause of this difficulty is identified and a procedure given to reclaim stability. An example is provided to show that similar computational problems can be encountered in the use of explicit differencing schemes.
Abstract
The advection-diffusion equation is often solved by implicit finite-difference schemes that are unconditionally stable when the grid interval is uniform. When such schemes are generalized to account for nonuniform grid spacing, instability can result. The cause of this difficulty is identified and a procedure given to reclaim stability. An example is provided to show that similar computational problems can be encountered in the use of explicit differencing schemes.
Abstract
A procedure is given here that allows two finite-difference schemes having dissimilar time-differencing operators (say, a horizontal advection-diffusion scheme and a vertical diffusion scheme) to be merged into a single equation at the cost of increasing storage requirements through the introduction of an additional time level. lie accuracy and stability of the combined scheme are investigated.
Abstract
A procedure is given here that allows two finite-difference schemes having dissimilar time-differencing operators (say, a horizontal advection-diffusion scheme and a vertical diffusion scheme) to be merged into a single equation at the cost of increasing storage requirements through the introduction of an additional time level. lie accuracy and stability of the combined scheme are investigated.
Abstract
Abstract
Abstract
The numerical model of air-sea interaction previously described in Brown et al. (1982), Pandolfo and Jacobs (1972) and Pandolfo (1969) is applied over a limited horizontal portion of the GATE III Gridded Global Data set (including continental grid points) to calculate a model-generated interface temperature field over a two-day period of GATE Period III.
The experiment provides a further estimate of the accuracy achievable in predicting sea-surface temperature over multi-day scales with limited-domain models nested within global data sets. It also demonstrates the degree of sensitivity of the model solutions to the inclusion of three additional atmospheric radiators (viz., an hypothesized tropical haze over the entire area simulated, a Saharan dust layer over its northern portions, and model-generated cloud); and to the thermodynamic effects of the parameterized cloud and rain-generating mechanism.
The initial oceanic temperature field was subjectively analyzed from GATE ship data and supplemented by climatological data. The sea-surface temperatures thus derived were qualitatively consistent in pattern with independent analysts of daily mean temperature based on GATE satellite and ship data. Both analyses show a belt of maximum temperature extending from the western boundary of the simulated area north-eastward to the African coast. In both analyses sea-surface temperatures decrease rapidly toward the southeast of the axis of maximum temperature. In our synoptic field it decreases more slowly toward the northwest. Actual values of analyzed temperature may differ locally by up to 2°C at locations sparse in ship data, but by less than the 0.50°C accuracy suggested by Krishnamurti et al. (1976) in data-rich portions of the limited area.
When the haze and model-generated cloud are included in the numerical simulation, model-generated daily mean temperatures change from the first to the second day of simulation in a manner that is also qualitatively consistent with that exhibited by day-to-day changes of the independently analyzed mean temperature. In the absence of these additional radiators the model-generated temperatures exhibit unrealistic warming of sea-surface temperatures. The sensitivity of daily average model-generated interface temperature to the presence of individual radiators shows patterns of difference similar in intensity and scale to those of the day-to-day changes.
Model-generated hourly-average temperature fields show isolated, shallow, cool-water pools at locations with intense model-generated cloud and rain and at data-sparse locations of the limited area simulated. At their most intense, they are similar in scale and intensity to a feature observed at another time, and under similar conditions, in the vicinity of the AB-scale GATE array. Their presence in the model-generated solutions is directly attributable to inclusion of the salinity-stabilization mechanism suggested by Katsaros (1976). These features appear with greatest intensity when all three atmospheric radiators are included, and diminish noticeably in intensity as the atmospheric dust is removed. They are completely absent in a simulation in which model-generated cloud and rain are also omitted.
In that simulation, an isolated, shallow, warm-water pool appears in the presence of generally strong insulation, and at a location with light surface wind. It is similar in scale and intensity to a feature observed at another time, and under similar conditions, within the GATE-AB scale array (Peters, 1978).
A noticeable nocturnal temperature maximum in the northern coastal regions of the simulated area is present in the initial data, and is repeated in the model-generated nighttime temperature fields thereafter. It is complemented by a repeated model-generated coastal daytime temperature minimum slightly to the south. Observational data are not available to confirm this most pronounced diurnally-varying feature of the simulated sea-surface temperature fields.
Abstract
The numerical model of air-sea interaction previously described in Brown et al. (1982), Pandolfo and Jacobs (1972) and Pandolfo (1969) is applied over a limited horizontal portion of the GATE III Gridded Global Data set (including continental grid points) to calculate a model-generated interface temperature field over a two-day period of GATE Period III.
The experiment provides a further estimate of the accuracy achievable in predicting sea-surface temperature over multi-day scales with limited-domain models nested within global data sets. It also demonstrates the degree of sensitivity of the model solutions to the inclusion of three additional atmospheric radiators (viz., an hypothesized tropical haze over the entire area simulated, a Saharan dust layer over its northern portions, and model-generated cloud); and to the thermodynamic effects of the parameterized cloud and rain-generating mechanism.
The initial oceanic temperature field was subjectively analyzed from GATE ship data and supplemented by climatological data. The sea-surface temperatures thus derived were qualitatively consistent in pattern with independent analysts of daily mean temperature based on GATE satellite and ship data. Both analyses show a belt of maximum temperature extending from the western boundary of the simulated area north-eastward to the African coast. In both analyses sea-surface temperatures decrease rapidly toward the southeast of the axis of maximum temperature. In our synoptic field it decreases more slowly toward the northwest. Actual values of analyzed temperature may differ locally by up to 2°C at locations sparse in ship data, but by less than the 0.50°C accuracy suggested by Krishnamurti et al. (1976) in data-rich portions of the limited area.
When the haze and model-generated cloud are included in the numerical simulation, model-generated daily mean temperatures change from the first to the second day of simulation in a manner that is also qualitatively consistent with that exhibited by day-to-day changes of the independently analyzed mean temperature. In the absence of these additional radiators the model-generated temperatures exhibit unrealistic warming of sea-surface temperatures. The sensitivity of daily average model-generated interface temperature to the presence of individual radiators shows patterns of difference similar in intensity and scale to those of the day-to-day changes.
Model-generated hourly-average temperature fields show isolated, shallow, cool-water pools at locations with intense model-generated cloud and rain and at data-sparse locations of the limited area simulated. At their most intense, they are similar in scale and intensity to a feature observed at another time, and under similar conditions, in the vicinity of the AB-scale GATE array. Their presence in the model-generated solutions is directly attributable to inclusion of the salinity-stabilization mechanism suggested by Katsaros (1976). These features appear with greatest intensity when all three atmospheric radiators are included, and diminish noticeably in intensity as the atmospheric dust is removed. They are completely absent in a simulation in which model-generated cloud and rain are also omitted.
In that simulation, an isolated, shallow, warm-water pool appears in the presence of generally strong insulation, and at a location with light surface wind. It is similar in scale and intensity to a feature observed at another time, and under similar conditions, within the GATE-AB scale array (Peters, 1978).
A noticeable nocturnal temperature maximum in the northern coastal regions of the simulated area is present in the initial data, and is repeated in the model-generated nighttime temperature fields thereafter. It is complemented by a repeated model-generated coastal daytime temperature minimum slightly to the south. Observational data are not available to confirm this most pronounced diurnally-varying feature of the simulated sea-surface temperature fields.
Abstract
Average statistics for periods of large positive 500 mb height anomalies are compared to statistics for all other situations using NMC data for the 15 Januaries from 1963 to 1977. The 500 mb heights and geostrophic streamfunctions are represented as surface spherical harmonics, and energy and enstrophy spectra along with nonlinear wave-wave interaction statistics are computed.
Differences in 500 mb geopotential height variance, kinetic energy and enstrophy spectra occur between large positive anomaly events and other days in the two-dimensional spectral index band from roughly n=6 to n=9, where n is the degree of the associated Legendre function. The same index band experiences a reversal of both the usual kinetic energy and enstrophy cascades during large positive anomaly events. That is, the 6≤n≤9 band gains energy and enstrophy from wave-wave interactions during the anomaly events and loses energy and enstrophy by the same process at other times. The source of this energy and enstrophy is higher index (smaller two-dimensional scale) waves. The indication is that the Atlantic cases are more Subject to this cascade reversal than are Pacific events.
Our results suggest that the smaller scale, transient eddies may play a regime-dependent role in interactions with atmospheric circulation modes on the scale of the persistent anomalies. When interacting with larger-scale features, the role of smaller-scale transients may not always be dissipative.
Abstract
Average statistics for periods of large positive 500 mb height anomalies are compared to statistics for all other situations using NMC data for the 15 Januaries from 1963 to 1977. The 500 mb heights and geostrophic streamfunctions are represented as surface spherical harmonics, and energy and enstrophy spectra along with nonlinear wave-wave interaction statistics are computed.
Differences in 500 mb geopotential height variance, kinetic energy and enstrophy spectra occur between large positive anomaly events and other days in the two-dimensional spectral index band from roughly n=6 to n=9, where n is the degree of the associated Legendre function. The same index band experiences a reversal of both the usual kinetic energy and enstrophy cascades during large positive anomaly events. That is, the 6≤n≤9 band gains energy and enstrophy from wave-wave interactions during the anomaly events and loses energy and enstrophy by the same process at other times. The source of this energy and enstrophy is higher index (smaller two-dimensional scale) waves. The indication is that the Atlantic cases are more Subject to this cascade reversal than are Pacific events.
Our results suggest that the smaller scale, transient eddies may play a regime-dependent role in interactions with atmospheric circulation modes on the scale of the persistent anomalies. When interacting with larger-scale features, the role of smaller-scale transients may not always be dissipative.
Abstract
Tropical cyclones are some of the most devastating natural hazards and the “three beasts”—Harvey, Irma, and Maria—during the Atlantic hurricane season 2017 are recent examples. The European Centre for Medium-Range Weather Forecasts (ECMWF) is working on fulfilling its 2016–25 strategy in which early warnings for extreme events will be made possible by a high-resolution Earth system ensemble forecasting system. Several verification reports acknowledge deterministic and probabilistic tropical cyclone tracks from ECMWF as world leading. However, producing reliable intensity forecasts is still a difficult task for the ECMWF global forecasting model, especially regarding maximum wind speed. This article will put the ECMWF strategy into a tropical cyclone perspective and highlight some key research activities, using Harvey, Irma, and Maria as examples. We describe the observation usage around tropical cyclones in data assimilation and give examples of their impact. From a model perspective, we show the impact of running at 5-km resolution and also the impact of applying ocean coupling. Finally, we discuss the future challenges to tackle the errors in intensity forecasts for tropical cyclones.
Abstract
Tropical cyclones are some of the most devastating natural hazards and the “three beasts”—Harvey, Irma, and Maria—during the Atlantic hurricane season 2017 are recent examples. The European Centre for Medium-Range Weather Forecasts (ECMWF) is working on fulfilling its 2016–25 strategy in which early warnings for extreme events will be made possible by a high-resolution Earth system ensemble forecasting system. Several verification reports acknowledge deterministic and probabilistic tropical cyclone tracks from ECMWF as world leading. However, producing reliable intensity forecasts is still a difficult task for the ECMWF global forecasting model, especially regarding maximum wind speed. This article will put the ECMWF strategy into a tropical cyclone perspective and highlight some key research activities, using Harvey, Irma, and Maria as examples. We describe the observation usage around tropical cyclones in data assimilation and give examples of their impact. From a model perspective, we show the impact of running at 5-km resolution and also the impact of applying ocean coupling. Finally, we discuss the future challenges to tackle the errors in intensity forecasts for tropical cyclones.
Abstract
Accurate cloud and precipitation forecasts are a fundamental component of short-range data assimilation/model prediction systems such as the NOAA 3-km High-Resolution Rapid Refresh (HRRR) or the 13-km Rapid Refresh (RAP). To reduce cloud and precipitation spinup problems, a nonvariational assimilation technique for stratiform clouds was developed within the Gridpoint Statistical Interpolation (GSI) data assimilation system. One goal of this technique is retention of observed stratiform cloudy and clear 3D volumes into the subsequent model forecast. The cloud observations used include cloud-top data from satellite brightness temperatures, surface-based ceilometer data, and surface visibility. Quality control, expansion into spatial information content, and forward operators are described for each observation type. The projection of data from these observation types into an observation-based cloud-information 3D gridded field is accomplished via identification of cloudy, clear, and cloud-unknown 3D volumes. Updating of forecast background fields is accomplished through clearing and building of cloud water and cloud ice with associated modifications to water vapor and temperature. Impact of the cloud assimilation on short-range forecasts is assessed with a set of retrospective experiments in warm and cold seasons using the RAPv5 model. Short-range (1–9 h) forecast skill is improved in both seasons for cloud ceiling and visibility and for 2-m temperature in daytime and with mixed results for other measures. Two modifications were introduced and tested with success: use of prognostic subgrid-scale cloud fraction to condition cloud building (in response to a high bias) and removal of a WRF-based rebalancing.
Abstract
Accurate cloud and precipitation forecasts are a fundamental component of short-range data assimilation/model prediction systems such as the NOAA 3-km High-Resolution Rapid Refresh (HRRR) or the 13-km Rapid Refresh (RAP). To reduce cloud and precipitation spinup problems, a nonvariational assimilation technique for stratiform clouds was developed within the Gridpoint Statistical Interpolation (GSI) data assimilation system. One goal of this technique is retention of observed stratiform cloudy and clear 3D volumes into the subsequent model forecast. The cloud observations used include cloud-top data from satellite brightness temperatures, surface-based ceilometer data, and surface visibility. Quality control, expansion into spatial information content, and forward operators are described for each observation type. The projection of data from these observation types into an observation-based cloud-information 3D gridded field is accomplished via identification of cloudy, clear, and cloud-unknown 3D volumes. Updating of forecast background fields is accomplished through clearing and building of cloud water and cloud ice with associated modifications to water vapor and temperature. Impact of the cloud assimilation on short-range forecasts is assessed with a set of retrospective experiments in warm and cold seasons using the RAPv5 model. Short-range (1–9 h) forecast skill is improved in both seasons for cloud ceiling and visibility and for 2-m temperature in daytime and with mixed results for other measures. Two modifications were introduced and tested with success: use of prognostic subgrid-scale cloud fraction to condition cloud building (in response to a high bias) and removal of a WRF-based rebalancing.
