Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty

One of the ways to quantify uncertainty of deterministic forecasts is to construct a joint distribution between the forecast variable and the observed variable; then, the uncertainty of the forecast can be represented by the conditional distribution of the observed given the forecast. The joint distribution of two continuous hydrometeorological variables can often be modeled by the bivariate meta-Gaussian distribution (BMGD). The BMGD can be obtained by transforming each of the two variables to a standard normal variable and the dependence between the transformed variables is provided by the Pearson correlation coefficient of these two variables. The BMGD modeling is exact provided that the transformed joint distribution is standard normal. In real-world applications, however, this normality assumption is hardly fulfilled. This is often the case for the modeling problem we consider in this paper: establish the joint distribution of a forecast variable and its corresponding observed variable for precipitation amounts accumulated over a duration of 24 h. In this case, the BMGD can only serve as an approximate model and the dependence parameter can be estimated in a variety of ways. In this paper, the effect of tuning this parameter is studied. Numerical simulations conducted suggest that, while the parameter tuning results in limited improvements in goodness-of-fit (GOF) for the BMGD as a bivariate distribution model, better results may be achieved by tuning the parameter for the one-dimensional conditional distribution of the observed given the forecast greater than a certain large value.

The Quanto Theory of Exchange Rates

We present a new identity that relates expected exchange rate appreciation to a risk-neutral covariance term, and use it to motivate a currency forecasting variable based on the prices of quanto index contracts. We show via panel regressions that the quanto forecast variable is an economically and statistically significant predictor of currency appreciation and of excess returns on currency trades. Out of sample, the quanto variable outperforms predictions based on uncovered interest parity, on purchasing power parity, and on a random walk as a forecaster of differential (dollar-neutral) currency appreciation. (JEL C53, E43, F31, F37, G12, G15)

High-Resolution GFS-Based MOS Quantitative Precipitation Forecasts on a 4-km Grid

The Meteorological Development Laboratory (MDL) of the National Weather Service (NWS) has developed high-resolution Global Forecast System (GFS)-based model output statistics (MOS) 6- and 12-h quantitative precipitation forecast (QPF) guidance on a 4-km grid for the contiguous United States. Geographically regionalized multiple linear regression equations are used to produce probabilistic QPFs (PQPFs) for multiple precipitation exceedance thresholds. Also, several supplementary QPF elements are derived from the PQPFs. The QPF elements are produced (presently experimentally) twice per day for forecast projections up to 156 h (6.5 days); probability of (measurable) precipitation (POP) forecasts extend to 192 h (8 days). Because the spatial and intensity resolutions of the QPF elements are higher than that for the currently operational gridded MOS QPF elements, this new application is referred to as high-resolution MOS (HRMOS) QPF. High spatial resolution and enhanced skill are built into the HRMOS PQPFs by incorporating finescale topography and climatology into the predictor database. This is accomplished through the use of specially formulated “topoclimatic” interactive predictors, which are formed as a simple product of a climatology- or terrain-related quantity and a GFS forecast variable. Such a predictor contains interactive effects, whereby finescale detail in the topographic or climatic variable is built into the GFS forecast variable, and dynamics in the large-scale GFS forecast variable are incorporated into the static topoclimatic variable. In essence, such interactive predictors account for the finescale bias error in the GFS forecasts, and thus they enhance the skill of the PQPFs. Underlying the enhanced performance of the HRMOS QPF elements is extensive use of archived fine-grid radar-based quantitative precipitation estimates (QPEs). The fine spatial scale of the QPE data supported development of a detailed precipitation climatology, which is used as a climatic predictive input. Also, the very large number of QPE sample points supported specification of rare-event (i.e., ≥1.50 and ≥2.00 in.) 6-h precipitation exceedance thresholds as predictands. Geographical regionalization of the PQPF regression equations and the derived QPF elements also contributes to enhanced forecast performance. Limited comparative verification of several 6-h model QPFs in categorical form showed the HRMOS QPF with significantly better threat scores and biases than corresponding GFS and operational gridded MOS QPFs. Limited testing of logistic regression versus linear regression to produce the 6-h PQPFs showed the feasibility of applying the logistic method with the very large HRMOS samples. However, objective screening of many candidate predictors with linear regression resulted in slightly better PQPF skill.