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Ming Cai and Huug M. Van Den Dool

Abstract

A nearly complete vorticity equation is used to diagnose the tendency components of the low-frequency variations of the 500-mb streamfunction induced by various internal linear-nonlinear interaction processes. With the aid of a special composite technique (“phase-shifting” method) that effectively records the observations in a coordinate system moving with an identifiable low-frequency pattern, the authors are able to separate the internal interactions that primarily act to make low-frequency waves propagate from those that are mostly responsible for development/maintenance/decay (“maintenance” for brevity) of low-frequency transients. It is found that the low-frequency transients are maintained primarily by two nonlinear interaction processes: one is the vorticity flux of high-frequency eddies and the other is the interaction of low-frequency transients and stationary waves. It is also found that an individual propagation tendency component may be much larger than a maintenance tendency component. In particular, the beta effect and the advection of the low-frequency vorticity by the zonally averaged climatological wind are the dominant terms among the propagation tendency components. But there is a great deal of cancellation among the propagation tendency components. As a result, the net magnitude of the tendency components describing propagation is only slightly larger than those relating to maintenance of low-frequency waves. From a forecast point of view, both propagation and forcing terms are equally important if an accurate forecast beyond a few days is required.

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Huug M. van den Dool and Suranjana Saha

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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.

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Huug M. Van Den Dool and Zoltan Toth

Abstract

It has been observed by many that skill of categorical forecasts, when decomposed into the contributions from each category separately, tends to be low, if not absent or negative, in the “near normal” (N) category. We have witnessed many discussions as to why it is so difficult to forecast near normal weather, without a satisfactory explanation ever having reached the literature. After presenting some fresh examples, we try to explain this remarkable fact from a number of statistical considerations and from the various definitions of skill. This involves definitions of rms error and skill that are specific for a given anomaly amplitude. There is low skill in the N-class of a 3-category forecast system because a) our forecast methods tend to have an rms error that depends little on forecast amplitude, while the width of the categories for predictands with a near Gaussian distribution is very narrow near the center, and b) it is easier, for the verifying observation, to ‘escape’ from the closed N-class (2-sided escape chance) than from the open ended outer classes. At a different level of explanation, there is lack of skill near the mean because in the definition of skill we compare the method in need of verification to random forecasts as the reference. The latter happens to perform, in the rms sense, best near the mean. Lack of skill near the mean is not restricted to categorical forecasts or to any specific lead time.

Rather than recommending a solution, we caution against the over-interpretation of the notion of skill-by-class. It appears that low skill near the mean is largely a matter of definition and may therefore not require a physical-dynamical explanation. We note that the whole problem is gone when one replaces the random reference forecast by persistence.

We finally note that low skill near the mean has had an element of applying the notion forecasting forecast skill in practice long before it was deduced that we were making a forecast of that skill. We show analytically that as long as the forecast anomaly amplitude is small relative to the forecast rms error, one has to expect the anomaly correlation to increase linearly with forecast magnitude. This has been found empirically by Tracton et al. (1989).

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Ming Cai and Huug M. van den Dool

Abstract

We have documented with the observed Northern Hemispheric 500 mb geopotential height data for ten winter seasons that traveling storm tracks exist downstream of the troughs of traveling low-frequency waves. The relation between the low-frequency flow and the traveling storm tracks is discovered with a novel observational technique that records high-frequency activity in a framework traveling along with an identifiable low-frequency structure. The vorticity flux of the high-frequency eddies associated with the traveling storm tracks acts both to reinforce the low-frequency waves and to retard their propagation.

These findings strongly indicate that a substantial amount of the low-frequency variability of the midlatitude atmospheric circulation is attributable to the forcing of the high-frequency eddies. These low-frequency waves organize the high-frequency eddies in such a way that the latter tend to intensify preferentially downstream of the troughs of the former. The symbiotic relation between the low-frequency flow and the traveling storm tracks is dynamically equivalent to the relation between the stationary waves and the stationary storm tracks. This mutual relationship is a necessary although not sufficient condition to parameterize high-frequency eddies in terms of low-frequency flow.

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Jin Huang and Huug M. van den Dool

Abstract

The monthly mean precipitation-air temperature (MMP-MMAT) relation over the United States has been examined by analyzing the observed MMP and MMAT during the period of 1931–87. The authors’ main purpose is to examine the possibility of using MMP as a second predictor in addition to the MMAT itself in predicting the next month's MMAT and to shed light on the physical relationship between MMP and MMAT. Both station and climate division data are used.

It was found that the lagged MMP-MMAT correlation with MMP leading by a month is generally negative, with the strongest negative correlation in summer and in the interior United States continent. Over large areas of the interior United States in summer, predictions of MMAT based on either antecedent MMP alone or on a combination of antecedent MMP and MMAT are better than a Prediction scheme based on MMAT alone. On the whole, even in the interior United States though, including MMP as a second predictor does not improve the skill of MMAT forecasts on either dependent or independent data dramatically because the first predictor (temperature persistence) has accounted for most of the MMP's predictive variance. For a verification performed separately for antecedent wet and dry months, much larger skill was found following wet than dry Julys for both one- and two-predictor schemes. Upon further analysis, we attribute this to the differences in the climate between the dependent (1931–60) and independent (1961–87) periods (the second being considerably colder in August) rather than to a true wetness dependence in the predictability.

We found some evidence for the role of soil moisture in explaining negative MMP-MMAT and positive MMAT-MMAT lagged correlations both from observed data and from output of multiyear runs with the National Meteorological Center model. This suggests that we should use some direct measure of soil moisture to improve MMAT forecasts instead of using the MMP as a proxy.

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Ming Cai and Huug M. Van Den Dool

Abstract

A special composite technique (“phase shifting” method) that records both the low- and high-frequency transient activity throughout the troposphere in a framework moving with an individual low-frequency wave of 500-mb geopotential height at 50°N was used to document the three-dimensional structure of the planetary-scale low-frequency waves as well as the attendant traveling storm tracks from the NMC twice-daily analyses of geopotential height and temperature at pressure levels 850, 700, 500, 300, and 200 mb for the ten winters 1967/68 through 1976/77.

The following are the main characteristics of the Northern Hemisphere midlatitude planetary-scale low-frequency waves (zonal wavenumber m = 1, 2, 3, and 4) in winter: (i) The amplitude of the planetary scale low-frequency waves is nearly constant with the zonal wavenumber m, and has a maximum at 300 mb for geopotential height and at 850 mb for temperature; (ii) All low-frequency waves have a nearly equivalent barotropic structure (much more so than the stationary waves); (iii) The instantaneous zonal phase speed of an individual low-frequency wave is nearly independent of height and latitude so that we may identify the three-dimensional structure of a low-frequency wave by following that wave at just one pressure level and one latitude in either geopotential height or temperature.

The traveling storm tracks, defined as the local maxima on the rms map of the phase-shifted high-frequency eddies, are identifiable from both geopotential height and temperature data throughout the troposphere. They are located over the trough regions of the low-frequency waves. The barotropic feedback (i.e., the geopotential tendency due to the vorticity flux) of the traveling storm tracks tends to reinforce the low-frequency waves and to retard their propagation throughout the troposphere. The baroclinic feedback (i.e., the temperature tendency due to the heat flux) of the traveling storm tracks appears to have an out-of-phase relation with the low-frequency waves in temperature from 850 mb to 300 mb. At 200 mb, the baroclinic feedback is nearly in phase with the low-frequency waves in the temperature field.

The mutual dependence between the low-frequency flow and their attendant traveling storm tracks dynamically resembles that between the climatological stationary waves and the climatological storm tracks. Therefore, our observational study seems to lend support for the local instability theory that accounts for the existence of the stationary/traveling storm tracks as the consequence of the zonal inhomogeneity of the climatological mean/low-frequency flow.

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Huug M. Van Den Dool and Robert M. Chervin

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The output of a 20-year integration of an annual cycle (AC) version of the NCAR Community Climate Model in which the external conditions went through 20 prescribed identical annual cycles is used to study mouth-to-month persistence of anomalies in monthly mean atmospheric circulation fields on a global and a hemispheric scale. Of all fields considered, the height fields (1000–300 mb) are the most persistent and the transient eddy flux fields the least persistent. Persistence in height field anomalies is largest in winter and small throughout the rest of the year. For the area north of 20°N, a comparison is made with the persistence of months mean height and temperature fields observed in the real world (RW) during a 28-yeu interval. On a pooled all month-pairs basis, RW height anomaly fields are significantly more persistent than those appearing in AC but, from a practical point of view, the difference is small. The differences in persistence are larger for temperature anomalies (500–1000 mb thickness) than for height. Differences between RW and AC monthly persistence over the area north of 20°N are largest in summer when the RW has a local maximum in persistence. On the assumption that the model and atmosphere have the same internal dynamics, the differences just described can be attributed to the interaction of the atmosphere with external or boundary conditions (e.g., ocean surface temperature), which was purposely omitted from the AC integration. Interaction with the lower boundary in summer seems, therefore, to be quite important to explain the observed level of month-to-month persistence in circulation anomalies. In winter, however, the internal dynamics of the atmosphere alone produces the required observed level of month-to-month persistence. The output of a 15-year integration of the same model in which the sea surface temperature, on a global scale, had realistic interannual variability, is used to interpret further the differences between RW and AC.

As a by-product of this study we have calculated the spatial degrees of freedom (dof) associated with time mean anomaly fields. The dof for global monthly mean anomaly height fields in the AC model are quite low, i.e., 25–35 on a yearly pooled basis. Over the area north of 20°N, the dof associated with monthly mean anomaly height fields of the AC model and the RW are quite close, varying from 15–20 in winter months to about 40 in summer.

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Jeffrey L. Anderson and Huug M. van den Dool

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The skill of a set of extended-range dynamical forecasts made with a modern numerical forecast model is examined. A forecast is said to be skillful if it produces a high quality forecast by correctly modeling some aspects of the dynamics of the real atmosphere; high quality forecasts may also occur by chance. The dangers of making a conclusion about model skill by verifying a single long-range forecast are pointed out by examples of apparently high “skill” verifications between extended-range forecasts and observed fields from entirely different years.

To avoid these problems, the entire distribution of forecast quality for a large set of forecasts as a function of lead time is examined. A set of control forecasts that clearly have no skill is presented. The quality distribution for the extended-range forecasts is compared to the distributions of quality for the no-skill control forecast set.

The extended-range forecast quality distributions are found to be essentially indistinguishable from those for the no-skill control at leads somewhat greater than 12 days. A search for individual forecasts with a “return of skill” at extended ranges is also made. Although it is possible to find individual forecasts that have a return of quality, a comparison to the no-skill controls demonstrates that these return of skill forecasts occur only as often as is expected by chance.

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Anthony G. Barnston and Huug M. van den Dool

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The field of standard deviation of monthly mean 700-mb geopotential height in the Northern Hemisphere for each of the 12 months over the 1950–1991 period, among other auxiliary statistics, is compiled in an atlas to which this paper is companion. Some of the major features found in the atlas are highlighted and extended here. A comparison is also made to the same statistics derived from a 10-year run of the NMC model.

There are three distinct regions of peak standard deviation (up to 85 geopotential meters in winter), all of which are located over water. Two of them remain positionally relatively stationary throughout the year in the high-latitude Pacific and Atlantic oceans, respectively. A portion of the Pacific region's winter variability comes from interdecadal fluctuations. The third region is over the Arctic Ocean and exhibits some large seasonal changes in location. A roughly north-to-south troughlike minimum in standard deviation (down to less than 20 geopotential meters in summer) is found in west central North America throughout most of the year.

The standard deviation maxima (minima) coincide largely with areas with a high (low) frequency of occurrence of height anomaly centers of both signs. Many of these anomaly centers occur in spatial coherence with other centers, forming familiar teleconnection and principal component patterns. While the high (low) standard deviation areas invest greater (lesser) amounts of variance in these coherent variability clusters than the surrounding regions, their involvement in terms of the strength of the relationships is not substantially greater (smaller). The standard deviation field does not move north and south with the changes in season as do the jets, storm tracks, and the mean flow. In summer the standard deviation peaks are largely detached from spatially coherent variability patterns, suggesting that they may be caused in large part by local interactions related to permanent (spatially fixed) features of the lower boundary at all times of the year.

The observed monthly mean 700-mb flow and the quasi-stationary locations of its interannual standard deviation maxima and minima are reproduced in approximate form in a 10-year run of the NMC medium-range forecast model. This helps provide evidence that the field of standard deviation is related, directly or indirectly, to some of the geographically fixed boundary conditions across the globe such SST, ocean-land interfaces, and terrain.

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Yun Fan, Huug M. van den Dool, and Wanru Wu

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Several land surface datasets, such as the observed Illinois soil moisture dataset; three retrospective offline run datasets from the Noah land surface model (LSM), Variable Infiltration Capacity (VIC) LSM, and Climate Prediction Center leaky bucket soil model; and three reanalysis datasets (North American Regional Reanalysis, NCEP/Department of Energy Global Reanalysis, and 40-yr ECMWF Re-Analysis), are used to study the spatial and temporal variability of soil moisture and its response to the major components of land surface hydrologic cycles: precipitation, evaporation, and runoff. Detailed analysis was performed on the evolution of the soil moisture vertical profile. Over Illinois, model simulations are compared to observations, but for the United States as a whole some impressions can be gained by comparing the multiple soil moisture–precipitation–evaporation–runoff datasets to one another. The magnitudes and partitioning of major land surface water balance components on seasonal–interannual time scales have been explored. It appears that evaporation has the most prominent annual cycle but its interannual variability is relatively small. For other water balance components, such as precipitation, runoff, and surface water storage change, the amplitudes of their annual cycles and interannual variations are comparable. This study indicates that all models have a certain capability to reproduce observed soil moisture variability on seasonal–interannual time scales, but offline runs are decidedly better than reanalyses (in terms of validation against observations) and more highly correlated to one another (in terms of intercomparison) in general. However, noticeable differences are also observed, such as the degree of simulated drought severity and the locations affected—this is due to the uncertainty in model physics, input forcing, and mode of running (interactive or offline), which continue to be major issues for land surface modeling.

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