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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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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
Suranjana Saha

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.

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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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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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Huug M. Van Den Dool
and
Robert M. Chervin

Abstract

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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Wilbur Y. Chen
and
Huug M. van den Dool

Abstract

A series of 90-day integrations by a low-resolution version (T40) of the National Meteorological Center's global spectral model was analyzed for its performance as well as its low-frequency variability behavior. In particular, 5-day mean 500-mb forecasts with leads up to 88 days were examined and compared with the observations. The forecast mean height decreased rapidly as forecast lead increased. A severe negative bias of the mean height in the Tropics was caused by a negative temperature bias and a drop of the surface pressure of about 2 mb. The forecast variance also dropped rapidly to a minimum of 75% of the atmospheric standard deviation before being stabilized at day 18. The model could not maintain large anomalous flows from the atmospheric initial conditions. However, it is quite capable of generating and maintaining large anomalies after drifting to its own climatology and temporal variability.

At extended ranges, the model showed better skill over the North Pacific than North Atlantic when the season advanced to the colder period of the DERF90 (dynamical extended-range forecasts 1990) experiments. The model also displayed dependence on circulation regimes, although the skill fluctuated widely from day to day in general. Blocking flows in the forecast were found to systematically retrogress to the Baffin Island area from the North Atlantic. Therefore, improvements of the model's systematic errors, including its drift, appear to be essential in order to achieve a higher level of forecast performance. However, no generalization can be made due to the usage of a low-resolution model and the experiments being carried out over a rather short time span, from only 3 May to 6 December 1990.

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Wilbur Y. Chen
and
Huug M. van den Dool

Abstract

A substantial asymmetric impact of tropical Pacific SST anomalies on the internal variability of the extratropical atmosphere is found. A variety of diagnoses is performed to help reveal the dynamical processes leading to the large impact. Thirty-five years of geopotential heights and 29 years of wind fields analyzed operationally at the National Centers for Environmental Prediction (NCEP), formerly the National Meteorological Center, and three sets of 10-yr-long perpetual January integrations run with a low-resolution NCEP global spectral model are investigated in detail for the impact of the SST anomalies on the blocking flows over the North Pacific. The impact on large-scale deep trough flows is also examined.

Both the blocking and deep trough flows develop twice as much over the North Pacific during La Niña as during El Niño winters. Consequently, the internal dynamics associated low-frequency variability (LFV), with timescales between 7 and 61 days examined in this study, display distinct characteristics: much larger magnitude for the La Niña than the El Niño winters over the eastern North Pacific, where the LFV is highest in general.

The diagnosis of the localized Eliassen–Palm fluxes and their divergence reveals that the high-frequency transient eddies (1–7 days) at high latitudes are effective in forming and maintaining the large-scale blocking flows, while the midlatitude transients are less effective. The mean deformation field over the North Pacific is much more diffluent for the La Niña than the El Niño winters, resulting in more blocking flows being developed and maintained during La Niña by the high-frequency transients over the central North Pacific.

In addition to the above dynamical process operating on the high-frequency end of the spectrum, the local barotropic energy conversion between the LFV components and the time-mean flows is also operating and playing a crucial role. The kinetic energy conversion represented by the scalar product between the E vector of the low-frequency components and the deformation D vector of the time-mean flow reveals that, on average, the low-frequency components extract energy from the time-mean flow during La Niña winters while they lose energy to the time-mean flow during El Niño winters. This local barotropic energy conversion on the low-frequency end of the spectrum, together with the forcing of the high-frequency transients on blocking flows on the high-frequency end, explain why there is a large difference in the magnitude of low-frequency variability between the La Niña and the El Niño winters.

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Jin Huang
,
Huug M. van den Dool
, and
Konstantine P. Georgarakos

Abstract

A long time series of monthly soil moisture data during the period of 1931–1993 over the entire U.S. continent has been created with a one-layer soil moisture model. The model is based on the water budget in the soil and uses monthly temperature and monthly precipitation as input. The data are for 344 U.S. climate divisions during the period of 1931–1993. The main goals of this paper are 1) to improve our understanding of soil moisture and its effects on the atmosphere and 2) to apply the calculated soil moisture toward long-range temperature forecasts.

In this study, the model parameters are estimated using observed precipitation, temperature, and runoff in Oklahoma (1960–1989) and applied to the entire United States. The comparison with the 8-yr (1984–1991) observed soil moisture in Illinois indicates that the model gives a reasonable simulation of soil moisture with both climatology and interannual variability.

The analyses of the calculated soil moisture show that the climatological soil moisture is high in the east and low in the west (except the West Coast), which is determined by the climatological precipitation amounts. The annual cycle of soil moisture, however, is determined largely by evaporation. Anomalies in soil moisture are driven by precipitation anomalies, but their timescales are to first order determined by both climatological temperature (through evaporation) and climatological precipitation. The soil moisture anomaly persistence is higher where normal temperature and precipitation are low, which is the case in the west in summer. The spatial scale of soil moisture anomalies has been analyzed and found to be larger than that of precipitation but smaller than that of temperature.

Authors found that generally in the U.S. evaporation anomalies are much smaller in magnitude than precipitation anomalies. Furthermore, observed and calculated soil moisture anomalies have a broad frequency distribution but not the strongly bimodal distribution indicative of water recycling.

Compared to antecedent precipitation, soil moisture is a better predictor for future monthly temperature. Soil moisture can provide extra skill in predicting temperature in large areas of interior continent in summer, particularly at longer leads. The predictive skill of soil moisture is even higher when the predictand is daily maximum temperature instead of daily mean temperature.

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