2092 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63 Predictability of Precipitation from Continental Radar Images. Part IV: Limits to Prediction URS GERMANN MeteoSwiss, Locarno-Monti, Switzerland ISZTAR ZAWADZKI AND BARRY TURNER Atmospheric and Oceanic Sciences, McGill University, Montréal, and J. S. Marshall Weather Radar Observatory, Sainte Anne de Bellevue, Québec, Canada (Manuscript received 6 June 2005, in final form 9 December 2005) ABSTRACT Predictability of precipitation is examined from storm to synoptic scales through an experimental ap- proach using continent-scale radar composite images. The lifetime of radar reflectivity patterns in Eulerian and Lagrangian coordinates is taken as a measure of predictability. The results are stratified according to scale, location, and time in order to determine how predictability depends on these parameters. Three companion papers give a detailed description of the methodology, and present results are obtained for 143 hours of North American warm season rainfall with emphasis on lifetime, scale dependence, optimum smoothing of forecast fields, and predictability in terms of probabilistic rainfall rates. This paper discusses the sources of forecast uncertainty and extends the analysis to a total of 1424 hours of rainfall. In a Lagrangian persistence framework the predictability problem can be separated into a component associated with growth of precipitation and a component associated with changes in the storm motion field. The role of changes in the motion field turned out to be small but not negligible. A stratifi- cation of lifetime according to location reveals the regions with high predictability and significant nonsta- tionary storm motion. This work is of high practical significance for three reasons: First, Lagrangian persistence of radar patterns was proved to have skill for probabilistic precipitation nowcasting. The discussion of the sources of uncertainty provides a guideline for further improvements. Second, a scale- and location-dependent benchmark is obtained against which the progress of other precipitation forecasting techniques can be evaluated. And, third, the experimental approach to predictability presented in this paper is a valuable contribution to the fundamental question of predictability of precipitation. 1. Introduction dimensional system it can be investigated analytically. But, as soon as the system becomes complicated, as is From a purely dynamic point of view predictability is the case for the atmosphere, or even more pronounced related to the sensitive dependence of the trajectory of for precipitation, it is difficult to study its predictability. the atmospheric state in phase space to small perturba- Then, any approach can only give an estimate of the tions in the initial conditions. No matter how small the true predictability. difference between two initial states is, it will grow and There is a variety of studies that allow inferences of eventually be so large that the two atmospheric states the predictability of the atmosphere: some follow a are no more similar than any randomly chosen pair of purely analytical approach, others are more of experi- possible states. This sensitivity is an intrinsic and fun- mental character. Table 1 gives an overview of predict- damental property of any nonlinear system, and is re- ability studies including some selected references. An ferred to as the initial value problem. For a simple low- example of a purely analytical approach is the evalua- tion of the Liouville equation to examine perturbation Corresponding author address: Dr. Urs Germann, MeteoSwiss, growth of a dynamic system. The Liouville equation, CH-6605 Locarno-Monti, Switzerland. introduced in a meteorological context by Gleeson E-mail: [email protected] (1966) and Epstein (1969), describes the evolution of © 2006 American Meteorological Society Unauthenticated | Downloaded 10/03/21 05:02 AM UTC JAS3735 AUGUST 2006 G E R MANN ET AL. 2093 TABLE 1. Predictability studies. Purely experimental approach Studies with observations: Autocorrelation and spectral analysis (Lorenz 1973; Zawadzki 1973) Analogs and periodicity (Lorenz 1993), interdependence (Zawadzki et al. 1981; Lilly 1986) Hovmöller diagram (Carbone et al. 2002; Ahijevych et al. 2004), composite analysis Precursor and predictor analysis (Bocquet 2002) Studies with statistical models: Forecast skill as evaluated against observations: Eulerian and Lagrangian persistence (Zawadzki et al. 1994; Germann and Zawadzki 2002) Dependence on scale (Lorenz 1969; Germann and Zawadzki 2002; Turner et al. 2004) Dependence on location (this paper) and weather Studies with numerical weather prediction models: Precursor analysis (Massacand et al. 1998) Forecast skill as evaluated against observations Sensitivity to initial conditions: singular vectors (Ehrendorfer et al. 1999), ensembles (Palmer 2002; Buizza et al. 1999; Walser et al. 2004) Studies with idealized systems of dynamic equations: Liouville equation (Gleeson 1966; Epstein 1969; Ehrendorfer 1994a,b) Lyapunov exponent (Hergarten 2002) Lorenz model, attractor (Lorenz 1963, 1993; Palmer 1993; Hergarten 2002) Purely analytical approach probability density of the atmospheric state in phase in the model structure, lack of resolution, errors in space and is the analog to the equation of mass conser- scale interactions, inadequate parameterization, param- vation in physical space. It states that realizations of the eter uncertainty, problems in boundary conditions if state of a system cannot spontaneously appear or dis- running a regional model, and numerical and compu- appear. Principally, it can be solved analytically for any tational errors that result, for instance, from finite dynamic system but, in practice, it is only applicable to difference schemes. In practice it is difficult to sepa- low-dimensional problems, such as a one-dimensional rate the problem of predictability into a component Riccati equation (Ehrendorfer 1994a). associated with initial error and a component associ- On the other end of the spectrum of predictability ated with model error (Palmer 2002). The validity of studies are those purely based on observations, such as the results of predictability studies using numerical autocorrelation analysis of the variable of interest weather prediction models can be very sensitive to (Lorenz 1973; Zawadzki 1973) or studies looking for model errors. precursors in the observation space (Bocquet 2002). Zängl (2004) found sensitivity of simulated oro- Between the purely analytical and purely experimental graphic rainfall to model components other than cloud approach there is a variety of studies employing statis- microphysics. He compared the sensitivity to param- tical and numerical weather prediction models that eterization for cloud microphysics with the sensitivity to combine analytical concepts with observations. In a the implementation of horizontal diffusion, the type of model approach predictability can be measured by the vertical coordinates, and boundary layer parameteriza- skill of the model to predict a certain phenomenon as tions. The experiment was conducted with the fifth- evaluated by statistical comparison with observations, generation Pennsylvania State University–National or by the growth of initially small perturbations in Center for Atmospheric Research (NCAR) Mesoscale model phase space using singular vector analysis or en- Model (MM5) and four nested domains with a horizon- sembles of model runs. tal mesh size being 37.8, 12.6, 4.2, and 1.4 km. Precipi- The analytical approach allows one to understand tation of the 1.4-km run accumulated over 36 h and basic concepts of nonlinearity, perturbation growth, averaged over a domain with a 200-km side length var- and sensitive dependence. But, as studies with idealized ied by a factor of 1.4 when using two different imple- systems of dynamic equations or with state-of-the-art mentations of horizontal diffusion. This and other re- numerical weather prediction models both assume the sults indicate that errors in simulated precipitation model to be representative of the true system, the crux fields are not only the result of weaknesses in the cloud lies in all sorts of model errors. These include errors microphysics scheme but may also arise from model Unauthenticated | Downloaded 10/03/21 05:02 AM UTC 2094 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 63 components that are not directly related to precipita- weather in order to determine the dependence of pre- tion such as the diffusion scheme. dictability on these parameters. Another difficulty comes from the dimension and A similar stratification of predictability is not complexity of the weather system, which makes analyti- straightforward when using a numerical weather pre- cal approaches computationally expensive or impracti- diction model because design and implementation of a cal. To obtain a representative estimate of sensitive model both have a significant influence on the perfor- dependence we may need more than just a handful of mance at different scales, locations, and in different ensemble members calculated for a specific weather weather situations. Of course there are problems in the situation, location, and time. But this is often not pos- experimental approaches as well. First there are mea- sible because of limited computation time. surement errors, and, second, there is some difficulty in linking the results to the nonlinear and chaotic nature a. Predictability of precipitation of the system. There are