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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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Anthony G. Barnston
and
Huug M. van den Dool

Abstract

Highly negative skill scores may occur in regression-based experimental forecast trials in which the data being forecast are withheld in turn from a fixed sample, and the remaining data are used to develop regression relationships-that is, exhaustive cross-validation methods. A small negative bias in skill is amplified when forecasts are verified using the correlation between forecasts and actual data. The same outcome occurs when forecasts are amplitude-inflated in conversion to a categorical system and scored in a “number of hits” framework. The effect becomes severe when predictor-predictand relationships are weak, as is often the case in climate prediction. Some basic characteristics of this degeneracy are explored for regression-based cross-validation.

Simulations using both randomized and designed datasets indicate that the correlation skill score degeneracy becomes important when nearly all of the available sample is used to develop forecast equations for the remaining (very few) points, and when the predictability in the full dependent sample falls short of the conventional requirement for statistical significance for the sample size. The undesirable effects can be reduced with one of the following methodological adjustments: 1) excluding more than a very small portion of the sample from the development group for each cross-validation forecast trial or 2) redefining the “total available sample” within one cross-validation exercise. A more complete elimination of the effects is achieved by 1) downward adjusting the magnitude of negative correlation skills in proportion to forecast amplitude, 2) regarding negative correlation skills as zero, or 3) using a forecast verification measure other than correlation such as root-mean-square error.

When the correlation skill score degeneracy is acknowledged and treated appropriately, cross-validation remains an effective and valid technique for estimating predictive skill for independent data.

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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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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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Huug van den Dool
,
Emily Becker
,
Li-Chuan Chen
, and
Qin Zhang

Abstract

An ordinary regression of predicted versus observed probabilities is presented as a direct and simple procedure for minimizing the Brier score (BS) and improving the attributes diagram. The main example applies to seasonal prediction of extratropical sea surface temperature by a global coupled numerical model. In connection with this calibration procedure, the probability anomaly correlation (PAC) is developed. This emphasizes the exact analogy of PAC and minimizing BS to the widely used anomaly correlation (AC) and minimizing mean squared error in physical units.

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Yueyue Yu
,
Ming Cai
,
Rongcai Ren
, and
Huug M. van den Dool

Abstract

This study investigates dominant patterns of daily surface air temperature anomalies in winter (November–February) and their relationship with the meridional mass circulation variability using the daily Interim ECMWF Re-Analysis in 1979–2011. Mass circulation indices are constructed to measure the day-to-day variability of mass transport into the polar region by the warm air branch aloft and out of the polar region by the cold air branch in the lower troposphere. It is shown that weaker warm airmass transport into the upper polar atmosphere is accompanied by weaker equatorward advancement of cold air in the lower troposphere. As a result, the cold air is largely imprisoned within the polar region, responsible for anomalous warmth in midlatitudes and anomalous cold in high latitudes. Conversely, stronger warm airmass transport into the upper polar atmosphere is synchronized with stronger equatorward discharge of cold polar air in the lower troposphere, resulting in massive cold air outbreaks in midlatitudes and anomalous warmth in high latitudes. There are two dominant geographical patterns of cold air outbreaks during the cold air discharge period (or 1–10 days after a stronger mass circulation across 60°N). One represents cold air outbreaks in midlatitudes of both North America and Eurasia, and the other is the dominance of cold air outbreaks only over one of the two continents with abnormal warmth over the other continent. The first pattern mainly corresponds to the first and fourth leading empirical orthogonal functions (EOFs) of daily surface air temperature anomalies in winter, whereas the second pattern is related to the second EOF mode.

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Emily J. Becker
,
Huug van den Dool
, and
Malaquias Peña

Abstract

Forecasts for extremes in short-term climate (monthly means) are examined to understand the current prediction capability and potential predictability. This study focuses on 2-m surface temperature and precipitation extremes over North and South America, and sea surface temperature extremes in the Niño-3.4 and Atlantic hurricane main development regions, using the Climate Forecast System (CFS) global climate model, for the period of 1982–2010. The primary skill measures employed are the anomaly correlation (AC) and root-mean-square error (RMSE). The success rate of forecasts is also assessed using contingency tables.

The AC, a signal-to-noise skill measure, is routinely higher for extremes in short-term climate than those when all forecasts are considered. While the RMSE for extremes also rises, especially when skill is inherently low, it is found that the signal rises faster than the noise. Permutation tests confirm that this is not simply an effect of reduced sample size. Both 2-m temperature and precipitation forecasts have higher anomaly correlations in the area of South America than North America; credible skill in precipitation is very low over South America and absent over North America, even for extremes. Anomaly correlations for SST are very high in the Niño-3.4 region, especially for extremes, and moderate to high in the Atlantic hurricane main development region. Prediction skill for forecast extremes is similar to skill for observed extremes. Assessment of the potential predictability under perfect-model assumptions shows that predictability and prediction skill have very similar space–time dependence. While prediction skill is higher in CFS version 2 than in CFS version 1, the potential predictability is not.

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Emily J. Becker
,
Huug van den Dool
, and
Malaquias Peña
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Huug M. Van Den Dool
,
Peter J. Lamb
, and
Randy A. Peppler

Abstract

The procedure to calculate the active layer depth of the upper ocean, as proposed by Van den Dool and Horel (DH), was applied to the Atlantic Ocean from 20°S to 70°N. In this method, the observed climatological annual cycle in SST is employed to invert a simple linear energy balance. The results for the Atlantic are similar to those for the Pacific Ocean in several ways. The active layer is considerably shallower than the annual mean mixed layer (which is calculated from in situ sea temperature profiles). Just as for the Pacific, however, the patterns of active and mixed layer depth show a remarkable spatial match.

Using Bunker's datasets for SST and heat transfer over the Atlantic Ocean, the forcing used in the energy balance equation was made increasingly more realistic, from (i) astronomical solar radiation, through (ii) empirical estimates of absorbed solar radiation including the modifying effect of clouds to (iii) the complete empirically determined net ocean surface heat gain. No matter what forcing was used, the calculated active layer is always much shallower than the mixed layer depth. The best pattern match was found using the simplest forcing of all—the astronomical solar forcing.

Increasingly, atmospheric models are being coupled to an oceanic slab in which the SST evolves in response to local heat gains and losses. The key question is how deep that slab should be. Our study implies that, in order to match the observed annual cycle in SST, the oceanic stab should be quite shallow, and certainly shallower than the mixed layer depth. The shallowness of the active layer implies that ocean heat transport contributes to the forcing of the annual cycle in SST in the midlatitudes of the Atlantic Ocean.

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Åke Johansson
,
Anthony Barnston
,
Suranjana Saha
, and
Huug van den Dool

Abstract

This study examines the level and origin of seasonal forecast skill of surface air temperature in northern Europe. The forecasts are based on an empirical methodology, canonical correlation analysis (CCA), which is a method designed to find correlated patterns between predictor and predictand fields. A modified form of CCA is used where a prefiltering step precedes the CCA as proposed by T. P. Barnett and R. Preisendorfer. The predictive potential of four fields is investigated, namely, (a) surface air temperature (i.e., the predictand field itself), (b) local sea surface temperature (SST) in the northern European area on a dense grid, (c) Northern Hemisphere 700-hPa geopotential height, and (d) quasi-global SST on a coarse grid. The design is such that four contiguous predictor periods (of 3 months each) are followed by a lead time and then a single predictand period (3 months long). The shortest lead time is 1 month and the longest is 15 months. The skill of the CCA- based forecasts is estimated for the 39-yr time period 1955–93, using cross-validated hindcasting. Skill estimates are expressed as the temporal correlation between the forecasts and the respective verifying observations.

The forecasts are most skillful in the winter seasons with a secondary weaker skill maximum during summer. During winter the geopotential height field produces the highest skill scores of the four predictor fields. The dominant predictor pattern of the geopotential height field is confined to the predictor period that is closest to a preceding core winter season and resembles the North Atlantic Oscillation (NAO) teleconnection pattern. The time series of the expansion coefficients of this dominant predictor pattern correlates well with a low-pass filtered time series of an NAO index. The obtained skill is similar to what is found in the United States, both with regard to seasonal distribution and level of skill. The origin of skill is however different. In the United States it is the El Niño–Southern Oscillation (ENSO) with its predominantly interannual character that is the main source of skill in winter. In northern Europe it is instead the NAO that contributes the most, and especially the lower frequency part of the NAO (periods between 4 and 10 yr).

Spatially sparse station data of surface pressure extending back to the middle of the nineteenth century suggests a nonstationarity in the NAO behavior. The implications of this nonstationarity for the obtained results of this study is briefly discussed. Because finely resolved field data are not readily available for this earlier period, the level of skill realizable for that period using a pattern relationship technique such as CCA remains an open question.

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