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- Author or Editor: Suranjana Saha x
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Abstract
We describe an extensive nudging (within-integration correction) experiment with a large and sophisticated atmospheric model. The model is an R30 version of the National Meteorological Center (NMC) T80 operational global medium-range forecast model. The purpose is to combat the systematic-error growth right from the start of the integration process by adding artificial sources and sinks (the corrections) of heat, momentum, and mass. The corrections derived from 30 antecedent 24-h integrations (by subtracting the forecasts from their verifying initial conditions) are applied to 30 subsequent independent 5-day forecasts from 1 July 1988 to 30 July 1988. Verification statistics over these 30 5-day forecasts are computed for the control cases, the nudged cases, and for forecasts corrected after the fact.
The main results show that the nudging process, when carefully designed, does not lead to any technical problems and the model accepts the applied corrections quite faithfully. Both nudging and after-the-fact corrected forecasts have greatly reduced systematic errors. In terms of forecast accuracy, nudging is, on the whole, not better than after-the-fact correction. However, for forecast lead times beyond 10 days, where after-the-fact corrections are currently not possible, nudging is an attractive alternative. The physical process most affected by the nudging process is precipitation. In the nudged model atmosphere without the traditional “cold bias,” both large-scale and convective precipitation is reduced detrimentally relative to the control runs, possibly due to tuning of the model.
Abstract
We describe an extensive nudging (within-integration correction) experiment with a large and sophisticated atmospheric model. The model is an R30 version of the National Meteorological Center (NMC) T80 operational global medium-range forecast model. The purpose is to combat the systematic-error growth right from the start of the integration process by adding artificial sources and sinks (the corrections) of heat, momentum, and mass. The corrections derived from 30 antecedent 24-h integrations (by subtracting the forecasts from their verifying initial conditions) are applied to 30 subsequent independent 5-day forecasts from 1 July 1988 to 30 July 1988. Verification statistics over these 30 5-day forecasts are computed for the control cases, the nudged cases, and for forecasts corrected after the fact.
The main results show that the nudging process, when carefully designed, does not lead to any technical problems and the model accepts the applied corrections quite faithfully. Both nudging and after-the-fact corrected forecasts have greatly reduced systematic errors. In terms of forecast accuracy, nudging is, on the whole, not better than after-the-fact correction. However, for forecast lead times beyond 10 days, where after-the-fact corrections are currently not possible, nudging is an attractive alternative. The physical process most affected by the nudging process is precipitation. In the nudged model atmosphere without the traditional “cold bias,” both large-scale and convective precipitation is reduced detrimentally relative to the control runs, possibly due to tuning of the model.
Abstract
The paper presents die results of a study of the thermal budget of a monsoon depression that developed over the Bay of Bengal during the period 3–8 July 1979. The complete thermodynamic energy equation is considered, to examine the possible role of the various terms and to evaluate the total diabatic heating. In the west-southwest quadrant of the monsoon depression where there is considerable rainfall, latent heat released by precipitation appears to account for about 80% of the total diabatic heating. This heating appears to be offset by cooling due to strong upward motion; however, the total diabatic beating over an area immediately to the north-northeast of the depression center appears to be negative, suggesting downward air motion and adiabatic warming. It is suggested that this warm sector to the north-northeast of the depression center, which is maintained by subsidence warming may serve as an effective tropospheric energy source for the monsoon depression.
Abstract
The paper presents die results of a study of the thermal budget of a monsoon depression that developed over the Bay of Bengal during the period 3–8 July 1979. The complete thermodynamic energy equation is considered, to examine the possible role of the various terms and to evaluate the total diabatic heating. In the west-southwest quadrant of the monsoon depression where there is considerable rainfall, latent heat released by precipitation appears to account for about 80% of the total diabatic heating. This heating appears to be offset by cooling due to strong upward motion; however, the total diabatic beating over an area immediately to the north-northeast of the depression center appears to be negative, suggesting downward air motion and adiabatic warming. It is suggested that this warm sector to the north-northeast of the depression center, which is maintained by subsidence warming may serve as an effective tropospheric energy source for the monsoon depression.
Abstract
The budget of the systematic component of the short-range forecast error in the National Meteorological Center's Medium-Range Forecast Model (NMC MRF) is examined. The budget is computed for the spectral coefficients and the variances of vorticity, divergence, virtual temperature, and specific humility at every time step during the 24-h model integration. Two months in winter and three months in summer, totaling 150 cases, were integrated with the budget diagnostics. The results of the budget of the spectral coefficients—that is, the budget of mean error—showed compensation among large terms except near the model boundary; therefore, it is difficult to point to a significant source of the systematic error in the free atmosphere. Near the model lower boundaries, dynamics cannot fully compensate physical forcing, and estimation of some physical processes responsible for the mean errors is possible. In contrast, the budget of the variance of the coefficients—that is, the energy budget—is more interesting and informative. The most apparent problem found in the model is a loss of rotational kinetic energy in the medium (total wavenumber n = 11–40) and small (n = 41–80) scales in the free atmosphere. About 50% of the loss is explained by the excessive horizontal and vertical diffusion. There is a strong indication that the rest of the loss of kinetic energy is related to the insufficient generation of available potential energy in the medium scale.
To isolate further the cause of the error in the energetics, several forecasts with budget diagnostics were performed. The experiments showed complex interactions between the physics and dynamics and among the different physical processes. Particularly noteworthy are (a) the compensation between horizontal and vertical diffusion and (b) the balance among horizontal/vertical diffusion, the barotropic scale interaction, and the baroclinic conversion terms in the rotational kinetic energy equation. The results of this study guided the design and implementation of changes in the NMC model in the horizontal diffusion and the cumulus parameterization.
Abstract
The budget of the systematic component of the short-range forecast error in the National Meteorological Center's Medium-Range Forecast Model (NMC MRF) is examined. The budget is computed for the spectral coefficients and the variances of vorticity, divergence, virtual temperature, and specific humility at every time step during the 24-h model integration. Two months in winter and three months in summer, totaling 150 cases, were integrated with the budget diagnostics. The results of the budget of the spectral coefficients—that is, the budget of mean error—showed compensation among large terms except near the model boundary; therefore, it is difficult to point to a significant source of the systematic error in the free atmosphere. Near the model lower boundaries, dynamics cannot fully compensate physical forcing, and estimation of some physical processes responsible for the mean errors is possible. In contrast, the budget of the variance of the coefficients—that is, the energy budget—is more interesting and informative. The most apparent problem found in the model is a loss of rotational kinetic energy in the medium (total wavenumber n = 11–40) and small (n = 41–80) scales in the free atmosphere. About 50% of the loss is explained by the excessive horizontal and vertical diffusion. There is a strong indication that the rest of the loss of kinetic energy is related to the insufficient generation of available potential energy in the medium scale.
To isolate further the cause of the error in the energetics, several forecasts with budget diagnostics were performed. The experiments showed complex interactions between the physics and dynamics and among the different physical processes. Particularly noteworthy are (a) the compensation between horizontal and vertical diffusion and (b) the balance among horizontal/vertical diffusion, the barotropic scale interaction, and the baroclinic conversion terms in the rotational kinetic energy equation. The results of this study guided the design and implementation of changes in the NMC model in the horizontal diffusion and the cumulus parameterization.
Abstract
Atmospheric budget calculations suffer from various observational and numerical errors. This paper demonstrates that all budget calculations applied to a large number of samples suffer from additional errors originating from systematic tendency errors of the budget equation used. Quantitative evaluation of this systematic tendency error for various types of budget computations showed that the systematic tendency errors are generally comparable in magnitude to the leading terms in the budget equations. Because of this error, the calculated budget does not satisfy conservation properties under steady conditions.
Abstract
Atmospheric budget calculations suffer from various observational and numerical errors. This paper demonstrates that all budget calculations applied to a large number of samples suffer from additional errors originating from systematic tendency errors of the budget equation used. Quantitative evaluation of this systematic tendency error for various types of budget computations showed that the systematic tendency errors are generally comparable in magnitude to the leading terms in the budget equations. Because of this error, the calculated budget does not satisfy conservation properties under steady conditions.
Abstract
Use general question considered in this is study is: To what extent does the maintenance of a correctly simulated quasi-stationary flow in a model influence the simulation of the transient part of the flow? and, in particular, the question. To what extent does the existence of systematic errors influence the growth of random errors? As an initial approach toward addressing this question, a simple model is used to generate a sequence of realizations. The model is based on the equivalent barotropic equation with orography, forcing and dissipation included and is applied to the whole globe with a spectral representation of the fields, truncated triangularly at T25. Dissipation is in the form of a Rayleigh friction term and a fourth-order dissipation term. The forcing is calculated from observed data in such a way as to balance the time-mean Jacobian term and the dissipation. The data from these relations are called the control data. A perturbation of the model is purposely introduced and integrations are made with this perturbed model starting from the same initial data point of each realization of the control run. The data from these realizations of the perturbed model are called the perturbed data. Comparison of statistics compiled from the two datasets reveals a drift of the climate of the perturbed model away from the climate of the control model. The difference between the perturbed and control runs constitutes the error field. The systematic part of this error field is used to correct another sequence of forecasts made with the perturbed model. The corrections are made in two ways. First, all the forecasts are corrected at each forecast lead time after the entire integration is made. Second, all the forecasts are corrected every 12 hours during the integration so that the quasi-stationary part of the flow is repeatedly adjusted back to the climatology of the control run. Both types of corrections practically wipe out the systematic error. The main result of this paper is that, for this model, the recurrent corrections are also able to decrease the growth of the random error substantially, which indicates that the transient part of the flow is quite sensitive to the accuracy with which the quasi-stationary flow is simulated. Possible mechanisms in the model responsible for this behavior are briefly discussed.
Abstract
Use general question considered in this is study is: To what extent does the maintenance of a correctly simulated quasi-stationary flow in a model influence the simulation of the transient part of the flow? and, in particular, the question. To what extent does the existence of systematic errors influence the growth of random errors? As an initial approach toward addressing this question, a simple model is used to generate a sequence of realizations. The model is based on the equivalent barotropic equation with orography, forcing and dissipation included and is applied to the whole globe with a spectral representation of the fields, truncated triangularly at T25. Dissipation is in the form of a Rayleigh friction term and a fourth-order dissipation term. The forcing is calculated from observed data in such a way as to balance the time-mean Jacobian term and the dissipation. The data from these relations are called the control data. A perturbation of the model is purposely introduced and integrations are made with this perturbed model starting from the same initial data point of each realization of the control run. The data from these realizations of the perturbed model are called the perturbed data. Comparison of statistics compiled from the two datasets reveals a drift of the climate of the perturbed model away from the climate of the control model. The difference between the perturbed and control runs constitutes the error field. The systematic part of this error field is used to correct another sequence of forecasts made with the perturbed model. The corrections are made in two ways. First, all the forecasts are corrected at each forecast lead time after the entire integration is made. Second, all the forecasts are corrected every 12 hours during the integration so that the quasi-stationary part of the flow is repeatedly adjusted back to the climatology of the control run. Both types of corrections practically wipe out the systematic error. The main result of this paper is that, for this model, the recurrent corrections are also able to decrease the growth of the random error substantially, which indicates that the transient part of the flow is quite sensitive to the accuracy with which the quasi-stationary flow is simulated. Possible mechanisms in the model responsible for this behavior are briefly discussed.
Abstract
The authors have investigated the climatological annual cycle in surface pressure on the Tibetan Plateau in relation to the annual cycle in surface pressure at the lower surroundings (India and China). It is found that surface pressure on the plateau is low (high) when the surrounding Asian continent has high (low) pressure. This out-of-phase relationship is evident in the NMC analyses and in long runs made with the NMC's global model. The authors have also found a few station observations on the plateau that have partially confirmed these opposing annual cycles in surface pressure. The authors believe this contrast to be real and operative over other parts of the globe as well. Near mean sea level, the surface pressure is low (high) when the temperature is high (low) (relative to its surroundings). At higher elevations, pressure is low (high) when temperatures are low (high). Also, in the datasets studied, the authors found no evidence for a thermal low on top of the plateau in summer.
Abstract
The authors have investigated the climatological annual cycle in surface pressure on the Tibetan Plateau in relation to the annual cycle in surface pressure at the lower surroundings (India and China). It is found that surface pressure on the plateau is low (high) when the surrounding Asian continent has high (low) pressure. This out-of-phase relationship is evident in the NMC analyses and in long runs made with the NMC's global model. The authors have also found a few station observations on the plateau that have partially confirmed these opposing annual cycles in surface pressure. The authors believe this contrast to be real and operative over other parts of the globe as well. Near mean sea level, the surface pressure is low (high) when the temperature is high (low) (relative to its surroundings). At higher elevations, pressure is low (high) when temperatures are low (high). Also, in the datasets studied, the authors found no evidence for a thermal low on top of the plateau in summer.
Abstract
The climate drift of various quantities associated with deep, planetary-scale, equilibrated, transient Rossby waves are estimated for the Southern Hemisphere extratropical summer as revealed by the DERF II (Dynamical Extended Range Forecasting) dataset. It is found that the vertical structures of these waves systematically become too baroclinic during the course of integration. There are two time scales associated with this climate drift. There is one very short time scale, estimated to be of the order of one day, when the waves become more barotropic. It is followed by a period when the wave baroclinicity monotonically increases, and after roughly 10 days the model structures appear to have reached their statistically equilibrated state.
In the meantime, the kinetic energy of the transient waves decreases substantially to roughly half the observed value. After this initial drop, however, the transient kinetic energy increases again, and it is not clear if an equilibrium value has been reached after 30 days, which is the limit of the DERF II dataset. This third time scale is not found in the quantities directly associated with the vertical structures per se, but it is hypothesized to be a consequence of these errors.
A theory is utilized that in a simplified way takes into account the processes that determine the vertical structure of baroclinic waves as well as their robustness as a means of understanding the processes leading to these errors. The implications from this theory are that the formulation and magnitude of the dissipative and diffusive processes in the model are the most likely problem, but there are other possibilities.
Abstract
The climate drift of various quantities associated with deep, planetary-scale, equilibrated, transient Rossby waves are estimated for the Southern Hemisphere extratropical summer as revealed by the DERF II (Dynamical Extended Range Forecasting) dataset. It is found that the vertical structures of these waves systematically become too baroclinic during the course of integration. There are two time scales associated with this climate drift. There is one very short time scale, estimated to be of the order of one day, when the waves become more barotropic. It is followed by a period when the wave baroclinicity monotonically increases, and after roughly 10 days the model structures appear to have reached their statistically equilibrated state.
In the meantime, the kinetic energy of the transient waves decreases substantially to roughly half the observed value. After this initial drop, however, the transient kinetic energy increases again, and it is not clear if an equilibrium value has been reached after 30 days, which is the limit of the DERF II dataset. This third time scale is not found in the quantities directly associated with the vertical structures per se, but it is hypothesized to be a consequence of these errors.
A theory is utilized that in a simplified way takes into account the processes that determine the vertical structure of baroclinic waves as well as their robustness as a means of understanding the processes leading to these errors. The implications from this theory are that the formulation and magnitude of the dissipative and diffusive processes in the model are the most likely problem, but there are other possibilities.
Abstract
A 10-year run was made with a reduced resolution (T40) version of NMC's medium range forecast model. The 12 monthly mean surface pressure fields averaged over 10 years are used to study the climatological seasonal redistribution of mass associated with the annual cycle in heating in the model. The vertically integrated divergent mass flux required to account for the surface pressure changes is presented in 2D vector form. The primary outcome is a picture of mass flowing between land and sea on planetary scales. The divergent mass fluxes are small in the Southern Hemisphere and tropics but larger in the midlatitudes of the Northern Hemisphere, although, when expressed as a velocity, nowhere larger than a few millimeters per second. Although derived from a model, the results are interesting because we have described aspects of the global monsoon system that are very difficult to determine from observations.
Two additional features are discussed, one physical, the other due to postprocessing. First, we show that the local imbalance between the mass of precipitation and evaporation implies a divergent water mass flux that is large in the aforementioned context (i.e., cm s−1). Omission of surface pressure tendencies due to the imbalance of evaporation and precipitation (order 10–30 mb per month) may therefore be a serious obstacle in the correct simulation of the annual cycle. Within the context of the model world it is also shown that the common conversion from surface to sea level pressure creates very large errors in the mass budget over land. In some areas the annual cycles of surface and sea level pressure are 180° out of phase.
Abstract
A 10-year run was made with a reduced resolution (T40) version of NMC's medium range forecast model. The 12 monthly mean surface pressure fields averaged over 10 years are used to study the climatological seasonal redistribution of mass associated with the annual cycle in heating in the model. The vertically integrated divergent mass flux required to account for the surface pressure changes is presented in 2D vector form. The primary outcome is a picture of mass flowing between land and sea on planetary scales. The divergent mass fluxes are small in the Southern Hemisphere and tropics but larger in the midlatitudes of the Northern Hemisphere, although, when expressed as a velocity, nowhere larger than a few millimeters per second. Although derived from a model, the results are interesting because we have described aspects of the global monsoon system that are very difficult to determine from observations.
Two additional features are discussed, one physical, the other due to postprocessing. First, we show that the local imbalance between the mass of precipitation and evaporation implies a divergent water mass flux that is large in the aforementioned context (i.e., cm s−1). Omission of surface pressure tendencies due to the imbalance of evaporation and precipitation (order 10–30 mb per month) may therefore be a serious obstacle in the correct simulation of the annual cycle. Within the context of the model world it is also shown that the common conversion from surface to sea level pressure creates very large errors in the mass budget over land. In some areas the annual cycles of surface and sea level pressure are 180° out of phase.
Abstract
An objective and practical limit of predictability for NWP models is proposed. The time T 0 is said to be the limit of predictability if model forecast beyond T 0 has no extra skill over persisting the T 0 forecast. The “skill” is measured here in terms of standard rms and anomaly correlation scores. For the NMC medium-range forecast model, T 0 is found to be 5–6 days for 250, 500 and 1000 mb height forecasts for the period 5 May–25 July 1987. The T 0 can also be interpreted as the time at which them is no longer skill in the prediction of the time derivative of the quantity under consideration.
Abstract
An objective and practical limit of predictability for NWP models is proposed. The time T 0 is said to be the limit of predictability if model forecast beyond T 0 has no extra skill over persisting the T 0 forecast. The “skill” is measured here in terms of standard rms and anomaly correlation scores. For the NMC medium-range forecast model, T 0 is found to be 5–6 days for 250, 500 and 1000 mb height forecasts for the period 5 May–25 July 1987. The T 0 can also be interpreted as the time at which them is no longer skill in the prediction of the time derivative of the quantity under consideration.
Abstract
A method is proposed to calculate measures of forecast skill for high, medium and low temporal frequency variations in the atmosphere. This method is applied to a series of 128 consecutive 1 to 10-day forecasts produced at NMC with their operational global medium-range-forecast model during 1 May–5 September 1988. It is found that over this period, more than 50% of the variance in observed 500 mb height fields is found at periods of 18 days or longer. The. intuitive notion that the predictability time of a phenomenon should be proportional to its lifetime is found to be qualitatively correct; i.e., the low frequencies are predicted (at a given skill level) over a longer time than high frequencies. However, the current prediction skill in low frequencies is far below its potential if one assumes that for any frequency the predictability time scale ought to be equal to the lifetime scale. In the high frequencies, however, the current prediction skill has already reached its potential; i.e., cyclones are being predicted over a time comparable to their lifetime; i.e. 3 to 4 days. We offer some speculations as to why the low frequency variations in the atmosphere are so poorly predicted by our current state-of-the-art models. The conclusions are tested, and found to hold up, on a more recent dataset covering 10 December 1988–16 April 1989.
Abstract
A method is proposed to calculate measures of forecast skill for high, medium and low temporal frequency variations in the atmosphere. This method is applied to a series of 128 consecutive 1 to 10-day forecasts produced at NMC with their operational global medium-range-forecast model during 1 May–5 September 1988. It is found that over this period, more than 50% of the variance in observed 500 mb height fields is found at periods of 18 days or longer. The. intuitive notion that the predictability time of a phenomenon should be proportional to its lifetime is found to be qualitatively correct; i.e., the low frequencies are predicted (at a given skill level) over a longer time than high frequencies. However, the current prediction skill in low frequencies is far below its potential if one assumes that for any frequency the predictability time scale ought to be equal to the lifetime scale. In the high frequencies, however, the current prediction skill has already reached its potential; i.e., cyclones are being predicted over a time comparable to their lifetime; i.e. 3 to 4 days. We offer some speculations as to why the low frequency variations in the atmosphere are so poorly predicted by our current state-of-the-art models. The conclusions are tested, and found to hold up, on a more recent dataset covering 10 December 1988–16 April 1989.
