An evaluation of the accuracy of some radar wind profiling techniques

Major advances in Doppler radar measurement in optically clear air have made it feasible to monitor radial velocities in the troposphere and lower stratosphere. For most applications the three dimensional wind vector is monitored rather than the radial velocity. Measurement of the wind vector with a single radar can be made assuming a spatially linear, time invariant wind field. The components and derivatives of the wind are estimated by the parameters of a linear regression of the radial velocities on functions of their spatial locations. The accuracy of the wind measurement thus depends on the locations of the radial velocities. The suitability is evaluated of some of the common retrieval techniques for simultaneous measurement of both the vertical and horizontal wind components. The techniques considered for study are fixed beam, azimuthal scanning (VAD) and elevation scanning (VED)

Power-Law Persistence in the Atmosphere: Analysis and Applications

We review recent results on the appearance of long-term persistence in climatic records and their relevance for the evaluation of global climate models and rare events.The persistence can be characterized, for example, by the correlation C(s) of temperature variations separated by s days.We show that, contrary to previous expectations, C(s) decays for large s as a power law, C(s) ~ s^(-gamma). For continental stations, the exponent gamma is always close to 0.7, while for stations on islands gamma is around 0.4. In contrast to the temperature fluctuations, the fluctuations of the rainfall usually cannot be characterized by long-term power-law correlations but rather by pronounced short-term correlations. The universal persistence law for the temperature fluctuations on continental stations represents an ideal (and uncomfortable) test-bed for the state of-the-art global climate models and allows us to evaluate their performance. In addition, the presence of long-term correlations leads to a novel approach for evaluating the statistics of rare events.Comment: 12 pages, 6 included EPS figures, added chapter

Phase Synchronization in Temperature and Precipitation Records

We study phase synchronization between atmospheric variables such as daily mean temperature and daily precipitation records. We find significant phase synchronization between records of Oxford and Vienna as well as between the records of precipitation and temperature in each city. To find the time delay in the synchronization between the records we study the time lag phase synchronization when the records are shifted by a variable time interval of days. We also compare the results of the method with the classical cross-correlation method and find that in certain cases the phase synchronization yields more significant results.Comment: 11 pages including 8 figure

Appropriateness of correlated first order auto-regressive processes for modeling daily temperature records

The present study investigates linear and volatile (nonlinear) correlations of first-order autoregressive process with uncorrelated AR (1) and long-range correlated CAR (1) Gaussian innovations as a function of the process parameter ($\theta$). In the light of recent findings \cite{jano}, we discuss the choice of CAR (1) in modeling daily temperature records. We demonstrate that while CAR (1) is able to capture linear correlations it is unable to capture nonlinear (volatile) correlations in daily temperature records.Comment: Accepted for publication in Physica

An application of stochastic forecasting to monthly averaged 700 mb heights.

One month dependent and independent forecasts of the standardized height anomalies are made and compared to similar forecasts made climatologically. The multivariate autoregressive model is found to perform better on the average than climatology. Several month forecasts are also made and examined for retrogression of anomalies. For the single case studied, the model is found to move features both eastward and westward.The statistical forecast method of multivariate autoregression is applied to a 27 year record of monthly averaged 700 mb heights. According to the theorem of predictive decomposition, a stationary series can be represented as the sum of deterministic and stochastic parts that are uncorrelated. Hence the deterministic annual cycle is removed and the statistical model applied to standardized anomalies of the 700 mb heights.A complementary study to the numerical modeling of climate is the statistical modeling of existing climatic records. Such statistical models can be used to forecast climate variations without the physical understanding needed in the dynamical approach. Since most climatic records cover only several decades, these statistical methods are feasible for forecast periods of weeks or months.The field of height anomalies is represented by 504 gridded values, which is far too large a dimension for multivariate autoregressive modeling. Therefore, 95 of these values representing equal areas are selected for modeling. Principal component analysis is then used to further reduce the 95 values to twenty. These twenty principal components are modeled by an objectively selected, third order multivariate autoregressive model

Volatility in atmospheric temperature variability

Using detrended fluctuation analysis (DFA), we study the scaling properties of the volatility time series $V_i=| T_{i+1}-T_i|$ of daily temperatures $T_i$ for ten chosen sites around the globe. We find that the volatility is long range power-law correlated with an e xponent $\gamma$ close to 0.8 for all sites considered here. We use this result to test the scaling performance of several state-of-the art global climate models and find that the models do not reproduce the observed scaling behavior.Comment: 10 pages, 3 figures. Accepted for publication in Physica

Generation of short and long range temporal correlated noises

We present the implementation of an algorithm to generate Gaussian random noises with prescribed time correlations that can be either long or short ranged. Examples of Langevin dynamics with short and long range noises are presented and discussed.Comment: 7 pages, 6 figs, submitted to J. Comp. Phy

Fractal Analysis of River Flow Fluctuations (with Erratum)

We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at $s_{1\times}\sim12$ and $s_{2\times}\sim130$ months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second ones is approximately equal to the well known cycle of sun activity. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The value of Hurst exponent of the runoff water of rivers without the sinusoidal trend shows a long range correlation behavior. For the Daugava river the value of Hurst exponent is $0.52\pm0.01$ and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.Comment: 13 pages, 10 figures, V2: Added comments, references and one more figure, improved numerical calculations with new version of data, accepted for publication in Physica A: Statistical Mechanics and its Applications. The version with Erratum contains some notes concerning Ref. [58

Multifractality of river runoff and precipitation: Comparison of fluctuation analysis and wavelet methods

We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima technique and obtain agreement within the error margins. In contrast to previous studies, we find non-universal behaviour: On long time scales, above a crossover time scale of several months, the runoff records are described by fluctuation exponents varying from river to river in a wide range. Similar variations are observed for the precipitation records which exhibit weaker, but still significant multifractality. For all runoff records the type of multifractality is consistent with a modified version of the binomial multifractal model, while several precipitation records seem to require different models.Comment: 7 pages with 4 eps figure

Long term persistence in the sea surface temperature fluctuations

We study the temporal correlations in the sea surface temperature (SST) fluctuations around the seasonal mean values in the Atlantic and Pacific oceans. We apply a method that systematically overcome possible trends in the data. We find that the SST persistence, characterized by the correlation $C(s)$ of temperature fluctuations separated by a time period $s$, displays two different regimes. In the short-time regime which extends up to roughly 10 months, the temperature fluctuations display a nonstationary behavior for both oceans, while in the asymptotic regime it becomes stationary. The long term correlations decay as $C(s) \sim s^{-\gamma}$ with $\gamma \sim 0.4$ for both oceans which is different from $\gamma \sim 0.7$ found for atmospheric land temperature.Comment: 14 pages, 5 fiure