20+ Years of Cloud-to-Ground Lightning Observations in the U.S., and Comparison with Climatological Co-variates
No abstract available
Cummins, Kenneth L.↗
Engineering topics
Tippett, Michael K.
Publications and source records attributed to Tippett, Michael K..
Human Influence on Tropical Cyclone Intensity
Recent assessments agree that tropical cyclone intensity should increase as the climate warms. Less agreement exists on the detection of recent historical trends in tropical cyclone intensity.We interpret future and recent historical trends by using the theory of potential intensity, which predicts the maximum intensity achievable by a tropical cyclone in a given local environment. Although greenhouse gas-driven warming increases potential intensity, climate model simulations suggest that aerosol cooling has largely canceled that effect over the historical record. Large natural variability complicates analysis of trends, as do poleward shifts in the latitude of maximum intensity. In the absence of strong reductions in greenhouse gas emissions, future greenhouse gas forcing of potential intensity will increasingly dominate over aerosol forcing, leading to substantially larger increases in tropical cyclone intensities.
Human influence on climate↗
The North American Multi-Model Ensemble (NMME): Phase-1 Seasonal to Interannual Prediction, Phase-2 Toward Developing Intra-Seasonal Prediction
The recent US National Academies report "Assessment of Intraseasonal to Interannual Climate Prediction and Predictability" was unequivocal in recommending the need for the development of a North American Multi-Model Ensemble (NMME) operational predictive capability. Indeed, this effort is required to meet the specific tailored regional prediction and decision support needs of a large community of climate information users. The multi-model ensemble approach has proven extremely effective at quantifying prediction uncertainty due to uncertainty in model formulation, and has proven to produce better prediction quality (on average) then any single model ensemble. This multi-model approach is the basis for several international collaborative prediction research efforts, an operational European system and there are numerous examples of how this multi-model ensemble approach yields superior forecasts compared to any single model. Based on two NOAA Climate Test Bed (CTB) NMME workshops (February 18, and April 8, 2011) a collaborative and coordinated implementation strategy for a NMME prediction system has been developed and is currently delivering real-time seasonal-to-interannual predictions on the NOAA Climate Prediction Center (CPC) operational schedule. The hindcast and real-time prediction data is readily available (e.g., http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/) and in graphical format from CPC (http://origin.cpc.ncep.noaa.gov/products/people/wd51yf/NMME/index.html). Moreover, the NMME forecast are already currently being used as guidance for operational forecasters. This paper describes the new NMME effort, presents an overview of the multi-model forecast quality, and the complementary skill associated with individual models.
NOAA CPC↗
Low-dimensional Representation of Error Covariance
Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.
Tippett, Michael K.↗
Conditioning of the Stable, Discrete-time Lyapunov Operator
The Schatten p-norm condition of the discrete-time Lyapunov operator L(sub A) defined on matrices P is identical with R(sup n X n) by L(sub A) P is identical with P - APA(sup T) is studied for stable matrices A is a member of R(sup n X n). Bounds are obtained for the norm of L(sub A) and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of the the discrete-time algebraic Lyapunov equation (DALE) L(sub A)P = Q can be ill-conditioned only when either L(sub A) or Q is ill-conditioned, these bounds are useful in determining whether P admits a low-rank approximation, which is important in the numerical solution of the DALE for large n.
Tippett, Michael K.↗
Adjoints and Low-rank Covariance Representation
Quantitative measures of the uncertainty of Earth System estimates can be as important as the estimates themselves. Second moments of estimation errors are described by the covariance matrix, whose direct calculation is impractical when the number of degrees of freedom of the system state is large. Ensemble and reduced-state approaches to prediction and data assimilation replace full estimation error covariance matrices by low-rank approximations. The appropriateness of such approximations depends on the spectrum of the full error covariance matrix, whose calculation is also often impractical. Here we examine the situation where the error covariance is a linear transformation of a forcing error covariance. We use operator norms and adjoints to relate the appropriateness of low-rank representations to the conditioning of this transformation. The analysis is used to investigate low-rank representations of the steady-state response to random forcing of an idealized discrete-time dynamical system.
Tippett, Michael K.↗
Model Error Estimation for the CPTEC Eta Model
Statistical data assimilation systems require the specification of forecast and observation error statistics. Forecast error is due to model imperfections and differences between the initial condition and the actual state of the atmosphere. Practical four-dimensional variational (4D-Var) methods try to fit the forecast state to the observations and assume that the model error is negligible. Here with a number of simplifying assumption, a framework is developed for isolating the model error given the forecast error at two lead-times. Two definitions are proposed for the Talagrand ratio tau, the fraction of the forecast error due to model error rather than initial condition error. Data from the CPTEC Eta Model running operationally over South America are used to calculate forecast error statistics and lower bounds for tau.
Tippett, Michael K.↗