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William W. Hsieh and Benyang Tang

Empirical or statistical methods have been introduced into meteorology and oceanography in four distinct stages: 1) linear regression (and correlation), 2) principal component analysis (PCA), 3) canonical correlation analysis, and recently 4) neural network (NN) models. Despite the great popularity of the NN models in many fields, there are three obstacles to adapting the NN method to meteorology–oceanography, especially in large-scale, low-frequency studies: (a) nonlinear instability with short data records, (b) large spatial data fields, and (c) difficulties in interpreting the nonlinear NN results. Recent research shows that these three obstacles can be overcome. For obstacle (a), ensemble averaging was found to be effective in controlling nonlinear instability. For (b), the PCA method was used as a prefilter for compressing the large spatial data fields. For (c), the mysterious hidden layer could be given a phase space interpretation, and spectral analysis aided in understanding the nonlinear NN relations. With these and future improvements, the nonlinear NN method is evolving to a versatile and powerful technique capable of augmenting traditional linear statistical methods in data analysis and forecasting; for example, the NN method has been used for El Niño prediction and for nonlinear PCA. The NN model is also found to be a type of variational (adjoint) data assimilation, which allows it to be readily linked to dynamical models under adjoint data assimilation, resulting in a new class of hybrid neural–dynamical models.

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W. Timothy Liu and Wenqing Tang

Abstract

Ocean surface stress, the turbulent transport of momentum, is largely derived from wind through a drag coefficient. In tropical cyclones (TCs), scatterometers have difficulty measuring strong wind and there is large uncertainty in the drag coefficient. This study postulates that the microwave backscatter from ocean surface roughness, which is in equilibrium with local stress, does not distinguish between weather systems. The reduced sensitivity of scatterometer wind retrieval algorithms under the strong wind is an air–sea interaction problem that is caused by a change in the behavior of the drag coefficient rather than a sensor problem. Under this assumption, a stress retrieval algorithm developed over a moderate wind range is applied to retrieve stress under the strong winds of TCs. Over a moderate wind range, the abundant wind measurements and the more established drag coefficient value allow for sufficient stress data to be computed from wind to develop a stress retrieval algorithm for the scatterometer. Using 0.9 million coincident stress and wind pairs, the study shows that the drag coefficient decreases with wind speed at a much steeper rate than previously revealed, for wind speeds over 25 m s−1. The result implies that the ocean applies less drag to inhibit TC intensification, and that TCs cause less ocean mixing and surface cooling than previous studies indicated.

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Youmin Tang and William W. Hsieh

Abstract

The advent of the feed-forward neural network (N) model opens the possibility of hybrid neural–dynamical models via variational data assimilation. Such a hybrid model may be used in situations where some variables, difficult to model dynamically, have sufficient data for modeling them empirically with an N. This idea of using an N to replace missing dynamical equations is tested with the Lorenz three-component nonlinear system, where one of the three Lorenz equations is replaced by an N equation. In several experiments, the 4DVAR assimilation approach is used to estimate 1) the N model parameters (26 parameters), 2) two dynamical parameters and three initial conditions for the hybrid model, and 3) the dynamical parameters, initial conditions, and the N parameters (28 parameters plus three initial conditions).

Two cases of the Lorenz model—(i) the weakly nonlinear case of quasiperiodic oscillations, and (ii) the highly nonlinear, chaotic case—were chosen to test the forecast skills of the hybrid model. Numerical experiments showed that for the weakly nonlinear case, the hybrid model can be very successful, with forecast skills similar to the original Lorenz model. For the highly nonlinear case, the hybrid model could produce reasonable predictions for at least one cycle of oscillation for most experiments, although poor results were obtained for some experiments. In these failed experiments, the data used for assimilation were often located on one wing of the Lorenz butterfly-shaped attractor, while the system moved to the second wing during the forecast period. The forecasts failed as the model had never been trained with data from the second wing.

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Paulo S. Polito, W. Timothy Liu, and Wenqing Tang

Abstract

Daily NASA Scatterometer (NSCAT) wind estimates cover about 75% of the globe. The remaining data gaps, which require interpolation, are regularly distributed in space and time. The development of this interpolation algorithm was guided by a balance between the smoothness of the end product and its fidelity to the original data. Three-dimensional matrices of autocorrelation coefficients incorporate information about the dominant propagation pattern into the interpolation program. These coefficients are continuously updated in space and time and are used as weights to interpolate each point in a regular space–time grid. For the first step, European Centre for Medium-Range Weather Forecasts (ECMWF) wind data are used to simulate the NSCAT data distribution and interpolated using two different methods: one uses a single set of coefficients from a prescribed function based on the average decorrelation scales, and the other uses the locally estimated autocorrelation coefficients. The comparison of these results with the original ECMWF maps favors those based on the autocorrelation. For the second step, daily maps of bin-averaged NSCAT wind data are compared to those interpolated by the correlation-based method and to those interpolated by successive corrections. Average differences between the original and interpolated fields are presented for the areas covered by the swath and for the gaps. The two-dimensional wavenumber spectra are also compared. The correlation-based interpolation method retains relatively more small-scale signal while significantly reducing the swath signature.

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Qiuhong Tang, Andrew W. Wood, and Dennis P. Lettenmaier

Abstract

Operational hydrologic models are typically calibrated using meteorological inputs derived from retrospective station data that are commonly not available in real time. Inconsistencies between the calibration and (generally sparser) real-time station datasets can be a source of bias, which can be addressed by expressing real-time hydrological model forcings (primarily precipitation) as percentiles for a set of index stations that report both in real time and during the retrospective calibration period, and by using the real-time percentiles to create adjusted precipitation forcings. Although hydrological model precipitation forcings typically are required at time steps of one day or shorter, percentiles can be calculated for longer averaging periods to reduce the percentile estimation errors. The authors propose an index station percentile method (ISPM) to estimate precipitation at the models input time step using percentiles, relative to a climatological period, for a set of index stations that report in real time. In general, this approach is most appropriate to situations in which the spatial correlation of precipitation is high, such as cold season rainfall in the western United States. The authors evaluate the ISPM approach, including performance sensitivity to the choice of percentile estimation period length, using the Klamath River basin, Oregon, as a case study. Relative to orographically adjusted interpolation of the real-time index station values, ISPM gives better estimates of precipitation throughout the basin. The authors find that ISPM performs best for percentile estimation periods longer than 10 days, with diminishing returns for averaging periods longer than 30 days. They also evaluate the performance of ISPM for a reduced station scenario and find that performance is relatively stable, relative to the competing methods, as the number of real-time stations diminishes.

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Denis Bourras, W. Timothy Liu, Laurence Eymard, and Wenqing Tang

Abstract

Latent heat fluxes were derived from satellite observations in the region of Structure des Echanges Mer–Atmosphère, Propriétés des Hétérogénéités Océaniques: Recherche Expérimentale (SEMAPHORE), which was conducted near the Azores islands in the North Atlantic Ocean in autumn of 1993. The satellite fluxes were compared with output fields of two atmospheric circulation models and in situ measurements. The rms error of the instantaneous satellite fluxes is between 35 and 40 W m–2 and the bias is 60–85 W m–2. The large bias is mainly attributed to a bias in satellite-derived atmospheric humidity and is related to the particular shape of the vertical humidity profiles during SEMAPHORE. The bias in humidity implies that the range of estimated fluxes is smaller than the range of ship fluxes, by 34%–38%. The rms errors for fluxes from models are 30–35 W m–2, and the biases are smaller than the biases in satellite fluxes (14–18 W m–2). Two case studies suggest that the satellites detect horizontal gradients of wind speed and specific humidity if the magnitude of the gradients exceeds a detection threshold, which is 1.27 g kg–1 (100 km)–1 for specific humidity and between 0.35 and 0.82 m s–1 (30 km)–1 for wind speed. In contrast, the accuracy of the spatial gradients of bulk variables from models always varies as a function of the location and number of assimilated observations. A comparison between monthly fluxes from satellites and models reveals that satellite-derived flux anomaly fields are consistent with reanalyzed fields, whereas operational model products lack part of the mesoscale structures present in the satellite fields.

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W. Perrie, C. L. Tang, Y. Hu, and B. M. DeTracy

Abstract

Ocean models usually estimate surface currents without explicit modeling of the ocean waves. To consider the impact of waves on surface currents, here a wave model is used in a modified Ekman layer model, which is imbedded in a diagnostic ocean model. Thus wave effects, for example, Stokes drift and wave-breaking dissipation, are explicitly considered in conjunction with the Ekman current, mean currents, and wind-driven pressure gradient currents. It is shown that the wave effect on currents is largest in rapidly developing intense storms, when wave-modified currents can exceed the usual Ekman currents by as much as 40%. A large part of this increase in velocity can be attributed to the Stokes drift. Reductions in momentum transfer to the ocean due to wind input to waves and enhancements due to wave dissipation are each of the order 20%–30%. Model results are compared with measurements from the Labrador Sea Deep Convection Experiment of 1997.

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W. Timothy Liu, Wenqing Tang, and Pearn P. Niiler

Abstract

The distribution of water vapor in the atmosphere affects climate change through radiative balance and surface evaporation. The variabilities of atmospheric humidity profile over oceans from daily to interannual time scales were examined using nine years of daily and semidaily radiosonde soundings at island stations extending from the Arctic to the South Pacific. The relative humidity profiles were found to have considerable temporal and geographic variabilities, contrary to the prevalent assumption. Principal component analysis on the profiles of specific humidity were used to examine the applicability of a relation between the surface-level humidity and the integrated water vapor; this relation has been used to estimate large-scale evaporation from satellite data. The first principal component was found to correlate almost perfectly with the integrated water vapor. The fractional variance represented by this mode increases with increasing period. It reaches approximately 90% at two weeks and decreases sharply, below one week, down to approximately 60% at the daily period. At low frequencies, the integrated water vapor appeared to be an adequate estimator of the humidity profile and the surface-level humidity. At periods shorter than a week, more than one independent estimator is needed. High-frequency surface humidity can be estimated if additional information on the vertical structure of the humidity profile is available or if the integrated water vapor in the boundary layer, instead of the entire atmospheric column, can be measured accurately by spaceborne sensors.

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Robert R. Czys, Robert W. Scott, K. C. Tang, Ronald W. Przybylinski, and Michael E. Sabones

Abstract

A nondimensional parameter is presented that can he used to help distinguish between conditions favorable for the occurrence of freezing rain and ice pellets. The parameter was derived from the well-established condition that most incidents of freezing rain and ice pellets are associated with a layer of above-freezing air elevated above a layer of below-freezing air adjacent to the earth's surface and the requirement that any cloud ice must completely melt for freezing rain, otherwise ice pellets would result. The parameter was obtained from the ratio of the time available for melting to the time required for complete melting. The parameter was tested on the mesoscale thermodynamic conditions that existed with the 1990 St. Valentine's Day ice storm that affected much of the Midwest and on a number of other episodes of freezing rain and ice pellets in the Midwest. Testing showed excellent spatial agreement between diagnosed and observed locations for freezing rain and ice pellets. An isonomogram is presented to allow the parameter to be easily used as a tool in determining winter precipitation type.

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Z. Long, W. Perrie, C. L. Tang, E. Dunlap, and J. Wang

Abstract

The authors investigate the interannual variations of freshwater content (FWC) and sea surface height (SSH) in the Beaufort Sea, particularly their increases during 2004–09, using a coupled ice–ocean model (CIOM), adapted for the Arctic Ocean to simulate the interannual variations. The CIOM simulation exhibits a (relative) salinity minimum in the Beaufort Sea and a warm Atlantic water layer in the Arctic Ocean, which is similar to the Polar Hydrographic Climatology (PHC), and captures the observed FWC maximum in the central Beaufort Sea, and the observed variation and rapid decline of total ice concentration, over the last 30 years. The model simulations of SSH and FWC suggest a significant increase in the central Beaufort Sea during 2004–09. The simulated SSH increase is about 8 cm, while the FWC increase is about 2.5 m, with most of these increases occurring in the center of the Beaufort gyre. The authors show that these increases are due to an increased surface wind stress curl during 2004–09, which increased the FWC in the Beaufort Sea by about 0.63 m yr−1 through Ekman pumping. Moreover, the increased surface wind is related to the interannual variation of the Arctic polar vortex at 500 hPa. During 2004–09, the polar vortex had significant weakness, which enhanced the Beaufort Sea high by affecting the frequency of synoptic weather systems in the region. In addition to the impacts of the polar vortex, enhanced melting of sea ice also contributes to the FWC increase by about 0.3 m yr−1 during 2004–09.

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