Adjoint-Based Analysis of Observation Impact on Tropical Cyclone Intensity Forecasts

An accurate estimate of the relative contributions of various observational datasets to the accuracy of a numerical weather prediction (NWP) forecast is of value to both the research and operational communities, especially when the forecast includes a high-risk event such as a tropical cyclone (TC). It has been observed that while TC track prediction has improved steadily for over the last ten years, improvement of TC intensity prediction has lagged (e.g. DeMaria and Gross 2003). Therefore the question may be asked: “What features of the analysis is the TC intensity forecast most sensitive to, and which assimilated observations impose the largest impact on the TC intensity forecast?” An examination posed in this way attempts to further our understanding of the environmental features and dynamical processes most important to the intensity of the modeled TC, as well as connecting those important features to the observational network in a way that evaluates the relative strengths and weaknesses of various observing platforms.

For a given NWP forecast, one can define the total observation-impact as the difference in forecast TC intensity between a simulation initialized from the analysis state (including all assimilated observations) and a simulation initialized from the background state (the analysis first-guess including no assimilated observations), typically defined as a 6-12 hour longer simulation verifying at the same time, thereby producing the analysis first-guess 6-12 hour forecast at analysis time while integrating forward to the verification time from that state. The difference in forecast TC intensity is by definition the result of the assimilation of the entire observing network. The adjoint of the data assimilation and forecast systems can be employed to estimate the individual contribution of each assimilated observation to the difference between these two forecasts (Langland and Baker 2004). Due to constraints related to the linearity assumption, this observation-impact estimate is only quantitatively valuable for short-range forecasts.

While typically used to monitor the observing system with respect to a global energy-based error-norm of the short-range forecast (Cardinali 2009, Gelaro et al. 2010), any function of the model state over any subset verifying area (i.e. the response function) can be evaluated using this technique. Here, the response function is defined as the integrated lower-tropospheric vorticity in a box surrounding the forecast position of the modeled TC, representing a metric of TC intensity. The adjoint-derived observation-impact therefore measures the contribution of any observation to increasing or decreasing the intensity of the TC, relative to a forecast where no observations are assimilated and the forecast is initialized with the analysis first-guess.

The Navy Global Environmental Model (NAVGEM) and Naval Research Laboratory Variational Data Assimilation System – Accelerated Representer (NAVDAS-AR) are used to evaluate the sensitivity of TC intensity forecasts in both model and observation space. Adjoint-derived sensitivity gradients are used to investigate the sensitivity of the TC intensity forecast to any arbitrary (but small) perturbation to the initial state, providing information about the environmental features and dynamical processes most important to the intensity forecast. Adjoint-derived observation-impact is used to determine which observations are most important to the TC intensity forecast, with comparisons made between observations based on any desired metric a priori (e.g. observing platform, pressure level, observed variable, distance from TC, etc.). Analysis-sensitivity and observation-impact are computed for both 24-hr and 48-hr forecasts for several case-study events.

Features of interest in the analysis-sensitivity and observation-impact are discussed, particularly where the impact deviates strongly from the traditional application of these tools to the global energy-norm. It is found, for example, that observation-impact on TC intensity forecasts conforms closely to a power-law distribution, typical of a system whereby large amounts of the impact are contributed by a very small number of high-impact members. By contrast, the global energy-based error-norm is typically reduced through small contributions by observations throughout the entire observing system. The relative value of various observing platforms to the TC intensity forecast is also context-sensitive in a way that is not observed when applying these tools to the global error-norm; the importance of in-situ, land-based observations to the TC intensity forecast quickly overtakes many satellite-based observation platforms as the TC nears landfall.