Real-time radar-rainfall bias adjustment procedures for weather surveillance Doppler radar (WSR-88D) are investigated. Statistical analysis of the mean-field bias is performed on a 2-year record of WSR-88D observations from Tulsa, Okla., and rain gauge measurements from a dense network under the radar umbrella. The analysis shows strong seasonal effect. A data-based Monte Carlo simulation experiment is performed on the same data to quantify the sampling error of estimated bias for varying rain gauge network densities. Simulation results show (1) that the sampling error decreases proportionally to the square of the rain gauge network density; and (2) that the sampling error is higher in the warm season. The performance of three mean-field radar-rainfall bias estimation and prediction algorithms is investigated. The algorithms include the WSR-88D precipitation adjustment procedure, the adaptive error parameter technique, and the maximum likelihood autoregressive model. A Monte Carlo simulation experiment is used to assess the algorithms' error statistics for the two seasons, three accumulation timescales, and two modes of operation (prediction and update). Results show significant seasonal and time-scale effects.

We describe an experimental study of the forces acting on a square cylinder (of width $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}b$ ) which occupies 10–40 % of a channel (of width $w$ ), fixed in a free-surface channel flow. The force experienced by the obstacle depends critically on the Froude number upstream of the obstacle, ${\mathit{Fr}}_1$ (depth $h_1$ ), which sets the downstream Froude number, ${\mathit{Fr}}_2$ (depth $h_2$ ). When ${\mathit{Fr}}_1<{\mathit{Fr}}_{1c}$ , where ${\mathit{Fr}}_{1c}$ is a critical Froude number, the flow is subcritical upstream and downstream of the obstacle. The drag effect tends to decrease or increase the water depth downstream or upstream of the obstacle, respectively. The force is form drag caused by an attached wake and scales as $\overline{F_{D}}\simeq C_D \rho b u_1^2 h_1/2$ , where $C_D$ is a drag coefficient and $u_1$ is the upstream flow speed. The empirically determined drag coefficient is strongly influenced by blocking, and its variation follows the trend $C_D=C_{D0}(1+C_{D0}b/2w)^2$ , where $C_{D0}=1.9$ corresponds to the drag coefficient of a square cylinder in an unblocked turbulent flow. The r.m.s. lift force is approximately 10–40 % of the mean drag force and is generated by vortex shedding from the obstacle. When ${\mathit{Fr}}_1={\mathit{Fr}}_{1c}\, (<1)$ , the flow is choked and adjusts by generating a hydraulic jump downstream of the obstacle. The drag force scales as $\overline{F}_D\simeq C_K \rho b g (h_1^2-h_2^2)/2$ , where experimentally we find $C_K\simeq 1$ . The r.m.s. lift force is significantly smaller than the mean drag force. A consistent model is developed to explain the transitional behaviour by using a semi-empirical form of the drag force that combines form and hydrostatic components. The mean drag force scales as $\overline{F_{D}}\simeq \lambda \rho b g^{1/3} u_1^{4/3} h_1^{4/3}$ , where $\lambda $ is a function of $b/w$ and ${\mathit{Fr}}_1$ . For a choked flow, $\lambda =\lambda _c$ is a function of blocking ( $b/w$ ). For small blocking fractions, $\lambda _c= C_{D0}/2$ . In the choked flow regime, the largest contribution to the total drag force comes from the form-drag component.

The motion of a vortex near two circular cylinders of arbitrary radiia problem of geophysical significanceis studied. The fluid motion is governed by the two-dimensional Euler equations and the flo...

Nonlinear internal waves are commonly observed in the coastal ocean. In the weakly nonlinear long wave régime, they are often modeled by the Korteweg-de Vries equation, which predicts that the long-time outcome of generic localised initial conditions is a train of internal solitary waves. However, when the effect of background rotation is taken into account, it is known from several theoretical and numerical studies that the formation of solitary waves is inhibited, and instead nonlinear wave packets form. In this paper, we report the results from a laboratory experiment at the LEGI-Coriolis Laboratory which describes this process.

Nonlinear advective adjustment of a discontinuity in free-surface height under gravity and rotation is considered, using the method of contour dynamics. After linear wave-adjustment has set up an interior jet and boundary currents in a wide ([Gt ] one Rossby radius) channel, fluid surges down-channel on both walls, rather than only that wall supporting a down-channel Kelvin wave. A wedgelike intrusion of low potential vorticity fluid on this wall, and a noselike intrusion of such fluid on the opposite wall, serve to reverse the sign of relative vorticity in the pre-existing currents. For narrower channels, a coherent boundary-trapped structure of low potential vorticity fluid is ejected at one wall, and shoots ahead of its parent fluid. The initial tendency for the current to concentrate on the ‘right-hand’ wall (the one supporting a down-channel Kelvin wave in the northern hemisphere) is defeated as vorticity advection shifts the maximum to the left-hand side. Ultimately fluid washes downstream everywhere across even wide channels, leaving the linearly adjusted upstream condition as the final state. The time necessary for this to occur grows exponentially with channel width. The width of small-amplitude boundary currents in linear theory is equal to Rossby's deformation radius, yet here we find that the width of the variation in velocity and potential vorticity fields deviates from this scale across a large region of space and time. Comparisons of the contour dynamics solutions, valid for small amplitude, and integration of the shallow-water equations at large amplitude, show great similarity. Boundary friction strongly modifies these results, producing fields more closely resembling the linear wave-adjusted state. Observed features include those suggestive of coastally trapped gravity currents. Analytical results for the evolution of vorticity fronts near boundaries are given in support of the numerical experiments.