Wind drift of snowfall between the radar volume and ground

This study evaluates how the advection of precipitation, or wind drift, between the radar volume and ground affects radar measurements of precipitation. Normally precipitation is assumed to fall vertically to the ground from the contributing volume, and thus the radar measurement represents the geographical location immediately below. In this study radar measurements are corrected using hydrometeor trajectories calculated from measured and forecasted winds, and the effect of trajectory-correction on the radar measurements is evaluated. Wind drift statistics for Finland are compiled using sounding data from two weather stations spanning two years. For each sounding, the hydrometeor phase at ground level is estimated and drift distance calculated using different originating level heights. This way the drift statistics are constructed as a function of range from radar and elevation angle. On average, wind drift of 1 km was exceeded at approximately 60 km distance, while drift of 10 km was exceeded at 100 km distance. Trajectories were calculated using model winds in order to produce a trajectory-corrected ground field from radar PPI images. It was found that at the upwind side from the radar the effective measuring area was reduced as some trajectories exited the radar volume scan. In the downwind side areas near the edge of the radar measuring area experience improved precipitation detection. The effect of trajectory-correction is most prominent in instant measurements and diminishes when accumulating over longer time periods. Furthermore, measurements of intensive and small scale precipitation patterns benefit most from wind drift correction. The contribution of wind drift on the uncertainty of estimated Ze (S) - relationship was studied by simulating the effect of different error sources to the uncertainty in the relationship coefficients a and b. The overall uncertainty was assumed to consist of systematic errors of both the radar and the gauge, as well as errors by turbulence at the gauge orifice and by wind drift of precipitation. The focus of the analysis is error associated with wind drift, which was determined by describing the spatial structure of the reflectivity field using spatial autocovariance (or variogram). This spatial structure was then used with calculated drift distances to estimate the variance in radar measurement produced by precipitation drift, relative to the other error sources. It was found that error by wind drift was of similar magnitude with error by turbulence at gauge orifice at all ranges from radar, with systematic errors of the instruments being a minor issue. The correction method presented in the study could be used in radar nowcasting products to improve the estimation of visibility and local precipitation intensities. The method however only considers pure snow, and for operational purposes some improvements are desirable, such as melting layer detection, VPR correction and taking solid state hydrometeor type into account, which would improve the estimation of vertical velocities of the hydrometeors.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.