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- Author or Editor: H. M. van den Dool x

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## Abstract

An empirical study based on three years (1981–83) of monthly mean data revealed that colocated anomalies in precipitation (^PP) and vertical motion at 500 mb (^ω) are moderately well correlated over the United States,in winter. The ^PP data are spatial averages in 344 Climate Divisions while the ω, are derived from initialized fields of the ECMWF and NMC NWP models. To a first-order approximation the deficit of rain associated with anomalous downward motion is just as large as the surplus of rain associated with anomalous upward motion. Therefore, it should be possible to generate some of the latent heat of condensation in a linear model for the time mean atmosphere by expressing ^PP linearly in ^ω Monthly mean ω of the ECMWF and NMC are highly correlated with each other and relate about equally well to rainfall over the United States. The empirical constant *a* in the relation PP=*a*&omega turns out to be about − −0.6 mm day^{−1}/(10^{−2}N m^{−2}s^{−1}, which is on the same order of magnitude as the theoretical amount of precipitation produced by diabatic ascent of magnitude 10^{−2}2 S^{2}s^{−1}. Attempts to empirically extract the role of atmospheric moisture in the relation between ^PP and ^ω were made by comparing summer to winter, high latitudes to lower latitudes and the United States to India but the results are at best modest.

Implementation of parameterized latent had sources and sinks in a linear steady state anomaly model for the time mean atmosphere is equivalent to reducing its static stability by a sizable amount. This leads to increased response to a prescribed forcing.

## Abstract

An empirical study based on three years (1981–83) of monthly mean data revealed that colocated anomalies in precipitation (^PP) and vertical motion at 500 mb (^ω) are moderately well correlated over the United States,in winter. The ^PP data are spatial averages in 344 Climate Divisions while the ω, are derived from initialized fields of the ECMWF and NMC NWP models. To a first-order approximation the deficit of rain associated with anomalous downward motion is just as large as the surplus of rain associated with anomalous upward motion. Therefore, it should be possible to generate some of the latent heat of condensation in a linear model for the time mean atmosphere by expressing ^PP linearly in ^ω Monthly mean ω of the ECMWF and NMC are highly correlated with each other and relate about equally well to rainfall over the United States. The empirical constant *a* in the relation PP=*a*&omega turns out to be about − −0.6 mm day^{−1}/(10^{−2}N m^{−2}s^{−1}, which is on the same order of magnitude as the theoretical amount of precipitation produced by diabatic ascent of magnitude 10^{−2}2 S^{2}s^{−1}. Attempts to empirically extract the role of atmospheric moisture in the relation between ^PP and ^ω were made by comparing summer to winter, high latitudes to lower latitudes and the United States to India but the results are at best modest.

Implementation of parameterized latent had sources and sinks in a linear steady state anomaly model for the time mean atmosphere is equivalent to reducing its static stability by a sizable amount. This leads to increased response to a prescribed forcing.

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## Abstract

The influence of cloud amount on the earth's climate is studied with an energy balance climate model. Planetary albedo and infrared radiation are parameterized in terms of cloud amount and surface temperature. For the present climate a prescribed change in cloud amount (independent of latitude) leads to a negligible change in the global mean temperature (∂T̄/∂*A*
_{c}≈0). For global temperatures lower than present ∂T̄/∂*A*
_{c}, becomes positive rapidly; higher temperatures lead to. negative values of ∂T̄/∂*A*
_{c}. The sensitivity of the global mean temperature to a 1% change in the solar constant (∂T̄/∂S) is ∼ 1.5 K. With reduced cloud amount ∂T̄/∂S becomes larger because the snow-ice feedback is active in the larger cloud-free portion; with increased cloud amount ∂T̄/∂S becomes smaller. Due to the strong absorption of solar radiation by clouds deep freeze solutions are possible only for very low values of the solar constant. The response of the model to changes in cloud amount or incoming radiation should be studied as a function of latitude. Two expressions that quantify the sensitivity to changes In the solar constant and cloud amount as a function of latitude are defined. If cloud amount is assumed to increase with temperature in a certain latitude belt and to decrease with temperature elsewhere, ∂T̄/∂S (as a function of latitude) and ∂T̄/∂S can change considerably.

## Abstract

The influence of cloud amount on the earth's climate is studied with an energy balance climate model. Planetary albedo and infrared radiation are parameterized in terms of cloud amount and surface temperature. For the present climate a prescribed change in cloud amount (independent of latitude) leads to a negligible change in the global mean temperature (∂T̄/∂*A*
_{c}≈0). For global temperatures lower than present ∂T̄/∂*A*
_{c}, becomes positive rapidly; higher temperatures lead to. negative values of ∂T̄/∂*A*
_{c}. The sensitivity of the global mean temperature to a 1% change in the solar constant (∂T̄/∂S) is ∼ 1.5 K. With reduced cloud amount ∂T̄/∂S becomes larger because the snow-ice feedback is active in the larger cloud-free portion; with increased cloud amount ∂T̄/∂S becomes smaller. Due to the strong absorption of solar radiation by clouds deep freeze solutions are possible only for very low values of the solar constant. The response of the model to changes in cloud amount or incoming radiation should be studied as a function of latitude. Two expressions that quantify the sensitivity to changes In the solar constant and cloud amount as a function of latitude are defined. If cloud amount is assumed to increase with temperature in a certain latitude belt and to decrease with temperature elsewhere, ∂T̄/∂S (as a function of latitude) and ∂T̄/∂S can change considerably.

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## Abstract

An attempt is made to estimate the thermal inertia of the upper ocean, relevant to climatic change. This is done by assuming that the annual variation in sea surface temperature (SST) can, to a first-order approximation, be described by a simple energy-balance equation. From the observed climatological annual variation in SST and in absorbed solar radiation we can estimate then a typical value of the heat capacity (*C*) of the active layer of the ocean. Also we can estimate how fast the SST is damped towards an equilibrium value (damping coefficient *b*). Within the same theoretical framework the decay time of SST anomalies allows us to estimate the seasonality of *C*/*b*.

The method is first tested on SST at six ocean weather ships and two coastal stations. The calculated depth of the active layer looks reasonable though somewhat small and it is encouraging that the seasonality in *C*/*b*, derived from daily SST data at one station, is similar to the observed seasonality in mixed layer depth. One of the problems seems to be that we need rather precise observations concerning solar radiation reaching the earth's surface. At many places such knowledge is not available. The spatial distribution of calculated active layer depth over the North Pacific is very similar to that of observed annual mean mixed layer depth but the mixed layer seems to be twice as deep as the active layer. Also the effective mixed layer defined and used by Manabe and Stouffer is substantially deeper than our calculated active layer.

The results are discussed in the context of both the surface energy balance and the vertically averaged energy balance. One of the interesting findings of this study is that the layer of the ocean involved in the annual cycle should be taken as 20–50 m rather than the more customary 60–80 m. Another conclusion is that the SST seems to damp (towards equilibrium) at least five times faster than the vertically integrated energy content of the climate system as a whole (including the ocean!).

## Abstract

An attempt is made to estimate the thermal inertia of the upper ocean, relevant to climatic change. This is done by assuming that the annual variation in sea surface temperature (SST) can, to a first-order approximation, be described by a simple energy-balance equation. From the observed climatological annual variation in SST and in absorbed solar radiation we can estimate then a typical value of the heat capacity (*C*) of the active layer of the ocean. Also we can estimate how fast the SST is damped towards an equilibrium value (damping coefficient *b*). Within the same theoretical framework the decay time of SST anomalies allows us to estimate the seasonality of *C*/*b*.

The method is first tested on SST at six ocean weather ships and two coastal stations. The calculated depth of the active layer looks reasonable though somewhat small and it is encouraging that the seasonality in *C*/*b*, derived from daily SST data at one station, is similar to the observed seasonality in mixed layer depth. One of the problems seems to be that we need rather precise observations concerning solar radiation reaching the earth's surface. At many places such knowledge is not available. The spatial distribution of calculated active layer depth over the North Pacific is very similar to that of observed annual mean mixed layer depth but the mixed layer seems to be twice as deep as the active layer. Also the effective mixed layer defined and used by Manabe and Stouffer is substantially deeper than our calculated active layer.

The results are discussed in the context of both the surface energy balance and the vertically averaged energy balance. One of the interesting findings of this study is that the layer of the ocean involved in the annual cycle should be taken as 20–50 m rather than the more customary 60–80 m. Another conclusion is that the SST seems to damp (towards equilibrium) at least five times faster than the vertically integrated energy content of the climate system as a whole (including the ocean!).

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## Abstract

A zonally averaged Climate model of the energy-balance type is examined. Recently published satellite measurements were used to improve existing parameterizations of planetary albedo and outgoing radiation in term of surface and sea level temperature. A realistic constant for the diffusion of energy was found by tuning the model to the present climate. For the actual solar constant both the present climate and an ice-covered earth are solutions of the model. They are extremely stable for temperature perturbations.

The effect of variation of the solar constant was investigated in detail. If the solar constant is decreased by 9–10% the warm solution (partial ice cover) jumps to the cold one (complete ice cover). Transition from the cold to the warm solution requires an increase of the solar constant to 109–110% of its present value. Therefore, we conclude that the model climate is much more stable with regard to variations in the solar input than has been assumed so far. This is caused mainly by our updated formulation of the outgoing radiation. Further experiments showed that our model is much more sensitive to changes in the outgoing radiation than to changes in the diffusivity for energy.

## Abstract

A zonally averaged Climate model of the energy-balance type is examined. Recently published satellite measurements were used to improve existing parameterizations of planetary albedo and outgoing radiation in term of surface and sea level temperature. A realistic constant for the diffusion of energy was found by tuning the model to the present climate. For the actual solar constant both the present climate and an ice-covered earth are solutions of the model. They are extremely stable for temperature perturbations.

The effect of variation of the solar constant was investigated in detail. If the solar constant is decreased by 9–10% the warm solution (partial ice cover) jumps to the cold one (complete ice cover). Transition from the cold to the warm solution requires an increase of the solar constant to 109–110% of its present value. Therefore, we conclude that the model climate is much more stable with regard to variations in the solar input than has been assumed so far. This is caused mainly by our updated formulation of the outgoing radiation. Further experiments showed that our model is much more sensitive to changes in the outgoing radiation than to changes in the diffusivity for energy.

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## Abstract

A linear steady-state primitive equation model has been developed for the computation of stationary atmospheric waves that are forced by anomalies in surface conditions. The model has two levels in the vertical. In the zonal direction the variables are represented by Fourier series, while in the meridional direction a grid-point representation is used. The equations governing atmospheric motion are linearized around a zonally symmetric state which depends on latitude and height according to Oort (1980).

We have studied the amplitude and phase relations of the model response as a function of latitude for a very simple beating, which is sinusoidal in the zonal direction, with zonal wavenumber *m* (*m*=1, 10) and constant in the meridional direction, using February mean conditions.

The response of the model indicates that a heating in the tropics can have a substantial influence on the middle and high latitudes, provided that part of the heating is in the westerlies. We have compared the model response for such a heating with the results of similar experiments with GCM and a linear barotropic model and also with mean anomaly patterns at middle and high latitudes derived from observations for Northern Hemispheric winters with a warm equatorial Pacific. In all cases we find strong similarities of hemispheric wave patterns.

We plan to test the model for the prediction of that part of the anomalies in the monthly or seasonal mean circulation that comes from persistent abnormal surface conditions In order to predict more than a persistent atmospheric response, such an anomaly in the surface conditions must have different effects in different months or seasons. We have tested the hypothesis that due to a changing zonally symmetric state, the response to a prescribed beating will be different in the four seasons. This effect is computed for a heating in the tropics and in the middle latitudes. Both in amplitude and phase the response to exactly the same heating can change significantly from one season to the next.

## Abstract

A linear steady-state primitive equation model has been developed for the computation of stationary atmospheric waves that are forced by anomalies in surface conditions. The model has two levels in the vertical. In the zonal direction the variables are represented by Fourier series, while in the meridional direction a grid-point representation is used. The equations governing atmospheric motion are linearized around a zonally symmetric state which depends on latitude and height according to Oort (1980).

We have studied the amplitude and phase relations of the model response as a function of latitude for a very simple beating, which is sinusoidal in the zonal direction, with zonal wavenumber *m* (*m*=1, 10) and constant in the meridional direction, using February mean conditions.

The response of the model indicates that a heating in the tropics can have a substantial influence on the middle and high latitudes, provided that part of the heating is in the westerlies. We have compared the model response for such a heating with the results of similar experiments with GCM and a linear barotropic model and also with mean anomaly patterns at middle and high latitudes derived from observations for Northern Hemispheric winters with a warm equatorial Pacific. In all cases we find strong similarities of hemispheric wave patterns.

We plan to test the model for the prediction of that part of the anomalies in the monthly or seasonal mean circulation that comes from persistent abnormal surface conditions In order to predict more than a persistent atmospheric response, such an anomaly in the surface conditions must have different effects in different months or seasons. We have tested the hypothesis that due to a changing zonally symmetric state, the response to a prescribed beating will be different in the four seasons. This effect is computed for a heating in the tropics and in the middle latitudes. Both in amplitude and phase the response to exactly the same heating can change significantly from one season to the next.

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## Abstract

A diagnostic study has been performed to investigate the prospects for developing a time-averaged statistical-dynamical model for making long-range weather forecasts. Estimates are made of nearly all terms in the equations describing the evolution of the time-mean quantities (ū, v̄, T̄, ω¯) and the horizontal second-order eddy statistics (*u*′^{2}¯, *v*′^{2}¯, *u*′*v*′¯, *u*′*T*′¯) and *v*′*T*′¯. These calculations were performed over northwestern Europe, using radiosonde observations of wind, temperature and height for the winter of 1976/11977. Geostrophic winds were estimated from objective analyses, while vertical velocities were determined with a quasi-geostrophic baroclinic model. For each equation, approximate balances are presented on the basis of these estimates.

In the equations for the mean quantities the time derivatives are more than one order of magnitude smaller than the unknown second-order eddy statistics. The same holds for the time derivatives of second-order eddy statistics compared with the unknown third-order and ageostrophic terms in the equations for these eddy fluxes. We therefore conclude that the system of time-averaged equations has no capability of describing the evolution of the atmosphere from one specific mean state to another mean state in the future–since for this purpose a closure of the system or a parameterization of second- order or third-order terms has to be extremely accurate. Even in the case in which only the stationary waves of the mean flow are treated, a higher order closure scheme does not seem to be feasible, for third-order terms and ageostrophic second-order terms are probably large and very difficult to parameterize. This implies that a preferable approach is to explore in greater depth the possibility of parameterizing the second-order statistics directly.

## Abstract

A diagnostic study has been performed to investigate the prospects for developing a time-averaged statistical-dynamical model for making long-range weather forecasts. Estimates are made of nearly all terms in the equations describing the evolution of the time-mean quantities (ū, v̄, T̄, ω¯) and the horizontal second-order eddy statistics (*u*′^{2}¯, *v*′^{2}¯, *u*′*v*′¯, *u*′*T*′¯) and *v*′*T*′¯. These calculations were performed over northwestern Europe, using radiosonde observations of wind, temperature and height for the winter of 1976/11977. Geostrophic winds were estimated from objective analyses, while vertical velocities were determined with a quasi-geostrophic baroclinic model. For each equation, approximate balances are presented on the basis of these estimates.

In the equations for the mean quantities the time derivatives are more than one order of magnitude smaller than the unknown second-order eddy statistics. The same holds for the time derivatives of second-order eddy statistics compared with the unknown third-order and ageostrophic terms in the equations for these eddy fluxes. We therefore conclude that the system of time-averaged equations has no capability of describing the evolution of the atmosphere from one specific mean state to another mean state in the future–since for this purpose a closure of the system or a parameterization of second- order or third-order terms has to be extremely accurate. Even in the case in which only the stationary waves of the mean flow are treated, a higher order closure scheme does not seem to be feasible, for third-order terms and ageostrophic second-order terms are probably large and very difficult to parameterize. This implies that a preferable approach is to explore in greater depth the possibility of parameterizing the second-order statistics directly.