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M. Cheng and R. Brown

Abstract

Methods of optimizing the Lovejoy and Austin technique to delineate areas of precipitation using visible and infrared satellite data are investigated. The technique involves training the satellite data by correlation with real-time radar data. The choice of statistical measures to define the precipitation/no-precipitation boundary between satellite classes is investigated. Subjective evaluation of the satellite-diagnosed precipitation fields indicates that minimizing the difference between the observed and diagnosed number of precipitation pixels produces the most realistic results. Maximization of some standard skill scores tends to overestimate the areas extent of the precipitation. Examples of the variability of the accuracy of the technique and the variation in optimum boundary or threshold are given. Cases illustrating the improvement produced by using different correlation tables for different synoptic systems are presented. Use of time-averaged correlation tables is investigated and found to be nearly as accurate as use of tables formed at one time, when evaluated within the training area. Fixed predefined tables were rather less accurate when evaluated within the training area, especially with respect to the diagnosed areal extent. A method is presented to combine the use of instantaneous and time-averaged correlation tables, together with a predefined table. Ideally, the method should incorporate the use of different correlation tables for different synoptic systems.

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Xinhua Cheng and John M. Wallace

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Hierarchical cluster analysis based on the method of Ward is performed on the Northern Hemisphere wintertime 10-day low-pass-filtered 500-hPa height field, using the NMC operational analyses for the period 1946–85. Input data are gridded fields at 5-day intervals, a total of 702 maps, each with 445 grid points. The measure of similarity between maps is the squared height difference, averaged over all grid points; that is, the squared “distance” between the maps in multidimensional phase space. The closest two of the 702 maps are merged to form a cluster that, in subsequent calculations, replaces the maps from which it was formed. This procedure (modified slightly, to deal with the differing numbers of maps in the clusters) is repeated 701 times until all the maps have been merged to form a single cluster whose centroid corresponds to the climatological mean map. The two clusters involved in the final merger, the pair of smaller clusters that merged to form each of them, and so on, are represented in terms of a “family tree” that is traced back to the point where the clusters become too small to be of practical interest. The reproducibility of the larger clusters is compared by seeing how well various ones are replicated when the analysis is repeated on randomly chosen halves of the dataset in an ensemble of 50 runs.

The three most reproducible clusters, which together account for ∼⅓ of the 702 maps in the dataset, can be reconstructed remarkably well from linear combinations of the two leading EOFs of the covariance matrix. They are related to features of the probability density function (PDF) in a two-dimensional phase space defined by the expansion coefficients of these EOFs. One is marked by a closed anticyclone over the southern tip of Greenland, one by a ridge over the Gulf of Alaska, and one by a ridge over the Rockies. In comparison to other clusters of comparable size, their centroids are conspicuously far from the climatological mean map. Positive 500-hPa height anomalies in excess of 200 m are observed in association with the first two clusters, over regions of large variance and strong positive skewness of the 500-hPa height field. Occurrences of these two clusters have often been marked by extreme cold over parts of North America. Similar clusters are obtained when the analysis is performed on the Pacific/North American and Atlantic/European sectors of the hemisphere. The results are compared with those obtained in other studies, based on a variety of analysis techniques.

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M. Cheng and C. G. Collier

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In this paper, a simple objective method for recognizing and correcting the effects of the radar bright band in weather radar images is presented. The method is based upon the finding that area-average rainfall rate can be estimated from a fractional area of rainfall rate using a threshold value of 2 mm and excluding radar data contaminated by bright band. The observed area-average rainfall rate is much larger than that estimated for brightband cases. It is shown by case studies that the method is successful for frontal rainfall systems. A simple objective method of deriving a rainfall rate within arm affected by bright band is also proposed.

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Y. Cheng and V. M. Canuto

Abstract

A model is presented to compute the turbulent kinetic energy dissipation length scale lε in a stably stratified shear flow. The expression for lε is derived from solving the spectral balance equation for the turbulent kinetic energy. The buoyancy spectrum entering such equation is constructed using a Lagrangian timescale with modifications due to stratification. The final result for lε is given in algebraic form as a function of the Froude number Fr and the flux Richardson number Rf, lε = lε(Fr, Rf). The model predicts that for Rf < Rfc, lε decreases with stratification or shear; for Rf > Rfc, which may occur in subgrid-scale models, lε increases with stratification. An attractive feature of the present model is that it encompasses, as special cases, some seemingly different models for lε that have been proposed in the past by Deardorff, Hunt et al., Weinstock, and Canuto and Minotti. An alternative form for the dissipation rate ε is also discussed that may be useful when one uses a prognostic equation for the heat flux. The present model is applicable to subgrid-scale models, which are needed in large eddy simulations (LES), as well as to ensemble average models.

The model is applied to predict the variation of lε with height z in the planetary boundary layer. The resulting lε versus z profile reproduces very closely the nonmonotonic profile of lε exhibited by many LES calculations, beginning with the one by Deardorff in 1974.

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V. M. Canuto and Y. Cheng

Abstract

The mesoscale contribution to subduction in the Southern Ocean was studied by Sallée and Rintoul in 2011 (SR11) using the following mesoscale model. The adiabatic (A) regime was modeled with the Gent–McWilliams streamfunction, the diabatic (D) regime was modeled with tapering functions, the D–A interface was taken to be at the mixed layer depth, and the mesoscale diffusivity either was a constant or was given by a 2D model. Since the resulting subductions were an order of magnitude smaller than the data of ±200 m yr−1 as reported by Mazloff et al. in 2010, SR11 showed that if, instead of the above model-dependent mesoscale diffusivities, they employed the ones reported in 2008 by Sallée et al. from surface drifter observations, the subductions compared significantly better to the data. On those grounds, SR11 suggested a 10-fold increase of the diffusivity. In this work, we suggest that, since the mesoscale diffusivity is but one component of a much large mesoscale parameterization, one should first assess the latter’s overall performance followed by an assessment of the predicted Antarctic Circumpolar Current (ACC) subduction. We employ the mesoscale model formulated by Canuto et al. in 2018 and 2019 that includes recent theoretical and observational advances and that was assessed against a variety of data, including the output of 17 other OGCMs. The ACC diffusivities compare well to drifter data from Sallée et al., and the ACC subduction rates are in agreement with the data.

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L. Cheng, M. English, and R. Wong

Abstract

From ten storms, 184 time-resolved hailstone samples have been collected at the ground in Alberta. For each of the samples collected, hailstone size and concentration were determined and a truncated exponential distribution was fitted to the data. From the fitted size distributions an intercept parameter N 0 and slope parameter Λ were obtained for each hail sample. It was found that the intercept parameters are related to the slope parameters by a power relationship of the form N 0 = AΛb and that such a relationship applies to each storm individually. Furthermore, it appears that the exponent parameter of the power law b is constant from storm to storm, whereas the coefficient parameter A depends upon the storm thermodynamics. Relationships between the coefficient parameter A and cloud base temperature and maximum water mass flux are derived.

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M. Cheng, R. Brown, and C. C. Collier

Abstract

The relationship between precipitation and infrared and visible satellite data is investigated in the vicinity of the United Kingdom. The investigation uses histograms of Meteosat data, built up from many half-hourly fields, which represent the frequency distribution of the pixels as a function of temperature and brightness. Separate histograms are produced for pixels classified as “precipitation” and “no precipitation” by coincident radar observations. The study is conducted separately for four distinct synoptic types: cold fronts, warm fronts, cold-air convection, and mesoscale convective systems (MCSs). A method is presented that uses this information to delineate areas of precipitation.

It is found that the use of combined infrared and visible satellite data yields better results than using infrared alone for all four synoptic types and is better than visible date alone for the majority. Use of visible data alone is better than using infrared data by itself, except for warm-front cases. The results indicate that the ability of the satellite data to delineate precipitation decreases in the following order of synoptic regime: cold frontal, MCS, warm frontal. The most difficult regime to delineate is cold-air convection.

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V. M. Canuto, Y. Cheng, and A. Howard

Abstract

Turbulent convection is inherently a nonlocal phenomenon and a primary condition for a successful treatment of the convective boundary layer is a reliable model of nonlocality. In the dynamic equations governing the convective flux, the turbulent kinetic energy, etc., nonlocality is represented by the third-order moments (TOMs). Since the simplest form, the so-called down gradient approximation (DGA), severely underestimates the TOMs (up to an order of magnitude), a more physical model is needed. In 1994, an analytical model was presented that was derived directly from the dynamical equations for the TOMs. It considerably improved the DGA but was a bit cumbersome to use and, more importantly, it was based on the quasi-normal (QN) approximation for the fourth-order moments.

Here, we present a new analytic expression for the TOMs that is structurally simpler than the 1994 expression and avoids the QN approximation. The resulting fit to the LES data is superior to that of the 1994 model.

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Xinhua Cheng, Gregor Nitsche, and John M. Wallace

Abstract

The robustness of low-frequency circulation patterns defined by unrotated and rotated empirical orthogonal functions (E0Fs) are compared based on the Northern Hemisphere 10-day low-pass filtered wintertime 500-hPa height field. The Pacific/North American pattern and the North Atlantic Oscillation are the most prominent modes of low-frequency variability in the data. The reproducibility of the spatial patterns derived from EOF and rotated EOF analysis is assessed by repeating the analysis on 50 subsets of the data, each comprised of the maps belonging to 22 randomly selected winters from the 44 winters in the total record. The results indicate that rotated spatial patterns are less sensitive to sampling fluctuations than their unrotated counterparts.

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V. M. Canuto, Y. Cheng, and A. M. Howard

Abstract

The goal of this paper is to derive the equation for the turbulence dissipation rate ε for a shear-driven flow. In 1961, Davydov used a one-point closure model to derive the ε equation from first principles but the final result contained undetermined terms and thus lacked predictive power. Both in 1987 (Schiestel) and in 2001 (Rubinstein and Zhou), attempts were made to derive the ε equation from first principles using a two-point closure, but their methods relied on a phenomenological assumption. The standard practice has thus been to employ a heuristic form of the ε equation that contains three empirical ingredients: two constants, c 1,ε and c 2,ε, and a diffusion term D ε. In this work, a two-point closure is employed, yielding the following results: 1) the empirical constants get replaced by c 1, c 2, which are now functions of K and ε; 2) c 1 and c 2 are not independent because a general relation between the two that are valid for any K and ε are derived; 3) c 1, c 2 become constant with values close to the empirical values c 1,ε, c 2,ε (i.e., homogenous flows); and 4) the empirical form of the diffusion term D ε is no longer needed because it gets substituted by the K–ε dependence of c 1, c 2, which plays the role of the diffusion, together with the diffusion of the turbulent kinetic energy DK, which now enters the new ε equation (i.e., inhomogeneous flows). Thus, the three empirical ingredients c 1,ε, c 2,ε, D ε are replaced by a single function c 1(K, ε) or c 2(K, ε), plus a DK term. Three tests of the new equation for ε are presented: one concerning channel flow and two concerning the shear-driven planetary boundary layer (PBL).

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