Search Results

You are looking at 1 - 10 of 15 items for :

  • Author or Editor: Keith F. Brill x
  • Refine by Access: All Content x
Clear All Modify Search
Keith F. Brill

Abstract

Performance measures computed from the 2 × 2 contingency table of outcomes for dichotomous forecasts are sensitive to bias. The method presented here evaluates how the probability of detection (POD) must change as bias changes so that a performance measure improves at a given value of bias. A critical performance ratio (CPR) of the change of POD to the change in bias is derived for a number of performance measures. If a change in POD associated with a bias change satisfies the CPR condition, the performance measure will indicate an improved forecast. If a perfect measure of performance existed, it would always exhibit its optimal value at bias equal to one. Actual measures of performance are susceptible to bias, indicating a better forecast for bias values not equal to one. The CPR is specifically applied to assess the conditions for an improvement toward a more favorable value of several commonly used performance measures as bias increases or decreases through the value one. All performance measures evaluated are found to have quantifiable bias sensitivity. The CPR is applied to analyzing a performance requirement and bias sensitivity in a geometric model.

Full access
Keith F. Brill

Abstract

The gradient wind is defined as a horizontal wind having the same direction as the geostrophic wind but with a magnitude consistent with a balance of three forces: the pressure gradient force, the Coriolis force, and the centrifugal force arising from the curvature of a parcel trajectory. This definition is not sufficient to establish a single way of computing the gradient wind. Different results arise depending upon what is taken to be the parcel trajectory and its curvature. To clarify these distinctions, contour and natural gradient winds are defined and subdivided into steady and nonsteady cases. Contour gradient winds are based only on the geostrophic streamfunction. Natural gradient winds are obtained using the actual wind. Even in cases for which the wind field is available along with the geostrophic streamfunction, it may be useful to obtain the gradient wind for comparison to the existing analyzed or forecast wind or as a force-balanced reference state. It is shown that the nonanomalous (normal) solution in the case of nonsteady natural gradient wind serves as an upper bound for the actual wind speed. Otherwise, supergradient wind speeds are possible, meaning that a contour gradient wind or the steady natural gradient wind used as an approximation for an actual wind may not be capable of representing the full range of actual wind magnitude.

Full access
Matthew E. Pyle
and
Keith F. Brill

Abstract

A fair comparison of quantitative precipitation forecast (QPF) products from multiple forecast sources using performance metrics based on a 2 × 2 contingency table with assessment of statistical significance of differences requires accounting for differing frequency biases to which the performance metrics are sensitive. A simple approach to address differing frequency biases modifies the 2 × 2 contingency table values using a mathematical assumption that determines the change in hit rate when the frequency bias is adjusted to unity. Another approach uses quantile mapping to remove the frequency bias of the QPFs by matching the frequency distribution of each QPF to the frequency distribution of the verifying analysis or points. If these two methods consistently yield the same result for assessing the statistical significance of differences between two QPF forecast sources when accounting for bias differences, then verification software can apply the simpler approach and existing 2 × 2 contingency tables can be used for statistical significance computations without recovering the original QPF and verifying data required for the bias removal approach. However, this study provides evidence for continued application and wider adoption of the bias removal approach.

Full access
Bruce A. Veenhuis
and
Keith F. Brill

Abstract

Quantitative precipitation forecast (QPF) applications often demand accumulations of precipitation for both long- and short-duration time intervals. It is desired that the shorter-duration forecasts sum to the longer-duration accumulations spanning the same time period. In the context of calibration, it is further desired that both the subinterval and longer interval accumulations be similarly corrected to have near unit frequency bias on a spatial domain. This study examines two methods of achieving these goals for 6- and 24-h accumulation intervals: 1) the accumulation method bias corrects the 6-h forecasts and accumulates them to create the 24-h accumulations; and 2) the disaggregation method bias corrects the 24-h accumulation and then proportionately disaggregates the 24-h accumulation back into 6-h accumulations. The experiments for the study are done retrospectively so that a “perfect” bias correction is possible for each method. The results of the study show that neither method accomplishes the stated goal for the calibration because QPF placement and/or timing errors contribute to frequency bias in the course of accumulation or disaggregation. However, both methods can improve the frequency bias for both the subinterval and longer interval accumulations. The choice of method may hinge most strongly on the relative tolerance of bias for the subinterval accumulations versus the longer interval accumulation.

Restricted access
Jeffrey S. Whitaker
,
Louis W. Uccellini
, and
Keith F. Brill

Abstract

A model simulation of the rapid development phase of the Presidents' Day cyclone of 19 February 1979 is analyzed in an effort to complement and extend a diagnostic analysis based only on 12-h radiosonde data over the contiguous United States, with a large data-void area over the Atlantic Ocean (Uccellini et al. 1985). As indicated by the SLP and 850 mb absolute vorticity tendencies, rapid cyclogenesis commences between 0300 and 0600 UTC 19 February and proceeds through the remaining 18 h of the simulation. This rapid development phase occurs as stratospheric air [marked by high values of potential vorticity (PV) approaches and subsequently overlies a separate, lower-tropospheric PV maximum confined to the Fast Coast, or during the period when the advection of PV increases in the middle to upper troposphere over the East Coast. The onset of rapid deepening is marked by 1) the transition in the mass divergence profiles over the surface low from a diffuse pattern with two or three divergence maxima to a two-layer structure, with maximum divergence located near 500 mb and the level of nondivergence located new 700 mb., 2) the intensification of precipitation just north of the surface low pressure system., and 3) an abrupt increase in the low-level vorticity.

Model trajectories and Eulerian analyses indicate that three airstreams converge into the cyclogenetic region during the rapid development phase. One of these airstreams descends within a tropopause fold on the west side of an upper-level trough over the north-central United States on 18 February and approaches the cyclone from the west-southwest as the rapid development commences. A second airstream originates in a region of lower-tropospheric subsidence within the cold anticyclone north of the storm, follows an anticyclonically curved path at low levels over the ocean, and then ascends as it enters the storm from the east. A third airstream approaches the storm from the south at low levels and also ascends as it enters the storm circulation. All of the airstreams pan through the low-level PV maximum as they approach the storm system, with the PV increase following a parcel related to the vertical distribution of θ due to the release of latent heat near the coastal region.

A vorticity analysis shows that absolute vorticity associated with the simulated storm is realized primarily through vortex stretching associated with the convergence of the airstreams below the 700 mb level. Although the maximum vorticity is initially confined below the 700 mb level, the convergence of the various airstreams is shown to be directly related to dynamic and physical processes that extend throughout the entire troposphere. Finally, the divergence of these airstreams within the 700 to 500 mb layer increases the magnitude of the mass divergence just north and cast of the storm center and thus enhances the rapid deepening of the surface low as measured by the decreasing sea level pressure.

Full access
Keith F. Brill
,
Anthony R. Fracasso
, and
Christopher M. Bailey

Abstract

This article explores the potential advantages of using a clustering approach to distill information contained within a large ensemble of forecasts in the medium-range time frame. A divisive clustering algorithm based on the one-dimensional discrete Fourier transformation is described and applied to the 70-member combination of the 20-member National Centers for Environmental Prediction (NCEP) Global Ensemble Forecast System (GEFS) and the 50-member European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble. Cumulative statistical verification indicates that clusters selected objectively based on having the largest number of members do not perform better than the ECMWF ensemble mean. However, including a cluster in a blended forecast to maintain continuity or to nudge toward a preferred solution may be a reasonable strategy in some cases. In such cases, a cluster may be used to sharpen a forecast weakly depicted by the ensemble mean but favored in consideration of continuity, consistency, collaborative thinking, and/or the trend in the guidance. Clusters are often useful for depicting forecast solutions not apparent via the ensemble mean but supported by a subset of ensemble members. A specific case is presented to demonstrate the possible utility of a clustering approach in the forecasting process.

Full access
Mukut B. Mathur
,
Keith F. Brill
, and
Charles J. Seman

Abstract

Numerical forecasts from the National Centers for Environmental Prediction’s mesoscale version of the η coordinate–based model, hereafter referred to as MESO, have been analyzed to study the roles of conditional symmetric instability (CSI) and frontogenesis in copious precipitation events. A grid spacing of 29 km and 50 layers are used in the MESO model. Parameterized convective and resolvable-scale condensation, radiation physics, and many other physical processes are included. Results focus on a 24-h forecast from 1500 UTC 1 February 1996 in the region of a low-level front and associated deep baroclinic zone over the southeastern United States. Predicted precipitation amounts were close to the observed, and the rainfall in the model was mainly associated with the resolvable-scale condensation.

During the forecast deep upward motion amplifies in a band oriented west-southwest to east-northeast, nearly parallel to the mean tropospheric thermal wind. This band develops from a sloping updraft in the low-level nearly saturated frontal zone, which is absolutely stable to upright convection, but susceptible to CSI. The updraft is then nearly vertical in the middle troposphere where there is very weak conditional instability. We regard this occurrence as an example of model-produced deep slantwise convection (SWC). Negative values of moist potential vorticity (MPV) occur over the entire low-level SWC area initially. The vertical extent of SWC increases with the lifting upward of the negative MPV area. Characteristic features of CSI and SWC simulated in some high-resolution nonhydrostatic cloud models also develop within the MESO. As in the nonhydrostatic SWC, the vertical momentum transport in the MESO updraft generates a subgeostrophic momentum anomaly aloft, with negative absolute vorticity on the baroclinically cool side of the momentum anomaly where outflow winds are accelerated to the north.

Contribution of various processes to frontogenesis in the SWC area is investigated. The development of indirect circulation leads to low-level frontogenesis through the tilting term. The axis of frontogenesis nearly coincides with the axis of maximum vertical motion when the SWC is fully developed. Results suggest that strong vertical motions in the case investigated develop due to release of symmetric instability in a moist atmosphere (CSI), and resultant circulations lead to weak frontogenesis in the SWC area.

Full access
Louis W. Uccellini
,
Paul J. Kocin
,
Ralph A. Petersen
,
Carlyle H. Wash
, and
Keith F. Brill

Abstract

The Presidents' Day cyclone of 18–19 February 1979 was an intense and rapidly developing storm which produced heavy snowfall along the East Coast of the United States. An analysis of the cyclone is presented which isolates three jet streaks that appear to have played important roles in the development of two separate areas of heavy snow. One area of heavy snow developed prior to cyclogenesis and is linked, in part, to an increasingly unbalanced subtropical jet streak (STJ) and a noticeably ageostrophic low-level jet. The second area of heavy snow developed in conjunction with the explosive cyclogenesis off the East Coast as a polar jet streak and midtropospheric trough propagated toward the coastal region from the north-central United States.

This paper examines the STJ in detail. The maximum wind speeds associated with the STJ increased by 15 to 20 m s-1 between 1200 GMT 17 and 1200 GMT 18 February 1979 as the jet propagated from the south-central toward the eastern United States. During the 24 h period, the flow in the STJ became increasingly supergeostrophic and apparently unbalanced. Ageostrophic wind speeds increased to greater than 30 m s-1, with a significant cross-contour component directed toward lower values of the Montgomery streamfunction, as the flow along the STJ became increasingly divergent with time. The increased wind speed, ageostrophic flow, and divergence along the axis of the STJ are linked to the increasing confluence in the entrance region of the jet streak and the decreasing wavelength of the trough-ridge system in which the jet streak was embedded. The upper level divergence and upward vertical motion near the axis of the STJ along with the moisture transport associated with the LLJ are found to be important factors in the development of the first area of heavy snow.

Full access
Louis W. Uccellini
,
Ralph A. Petersen
,
Paul J. Kocin
,
Keith F. Brill
, and
James J. Tuccillo

Abstract

A series of numerical simulations is presented for the February 1979 Presidents' Day cyclone in order to understand more fully the roles played by upper-level jet streaks the oceanic planetary boundary layer (PBL), and latent heat release in the development of a low-level jet (LU) and secondary cyclogenesis along the East Coast of the United States. Mesoscale model simulations with and without sensible and latent heating show that the diabatic processes, along with the jet streak circulation patterns, contribute to the enhancement of the low-level winds and the initial development of the coastal cyclone. However. none of the mechanisms acting alone is sufficient to yield a satisfactory simulation of the LIJ and secondary cyclogenesis. Furthermore, the model-based diagnostic analyses indicate that a synergistic interaction must exist among these processes to account for the substantial increase in the magnitude of the low-level winds and the decrease in the sea level pressure that mark the secondary cyclogenesis for this case.

The following sequence is derived from the model diagnostic study: 1) Temporally increasing divergence along the axis of an upper-tropospheric jet streak located near the crest of an upper-level ridge is associated with the development of an indirect circulation that spans the entire depth of the troposphere and is displaced to the anticyclonic side of the jet. The lower branch of the indirect circulation appears to extend northwestward from the oceanic PBL up sloping isentropic surfaces toward 700 mb over the Appalachian Mountains. 2) Sensible heating and associated moisture flux within the oceanic PBL warm and moisten the lower branch of the indirect circulation, enhancing precipitation rates and latent heat release west of the coastline. 3) The combination of a shallow direct circulation associated with a developing coastal front, sloping lower-tropospheric isentropic surfaces just to the west of the coastline, and latent heat release contributes to a vertical displacement of parcels within the lower branch of the indirect circulation as they cross the coastline. 4) The vertical displacement of the parcels in a baroclinic environment (in which the pressure gradient force changes with height) results in the rapid increase in the magnitude of the ageostrophic wind and associated unbalanced flow. This imbalance contributes to parcel acceleration resulting in the formation of a LLJ in the lower branch of the indirect circulation over a 2 to 4 h period. 5) The increasing wind speed associated with the developing LLJ is, in turn, responsible for an increase in the horizontal mass flux divergence in the entrance region of the LLJ. The increase in the mass flux divergence in the lower troposphere just above the boundary layer makes a significant contribution to the decreasing sea-level pressure that constitutes the initial development phase of the secondary cyclone along the coast.

Full access
Keith F. Brill
,
Louis W. Uccellini
,
Richard P. Burkhart
,
Thomas T. Warner
, and
Richard A. Anthes

Abstract

Uccellini and Johnson present a case study of a severe weather event in Ohio on 10–11 May 1973 to show evidence for coupling between an upper-tropospheric jet streak and a low-level jet within an indirect transverse circulation found in the exit region of the upper-level jet. The differential advection of moisture and temperature created by the shear between the upper- and low-level jets reduced convective stability, thereby enhancing the potential for severe convection.

Two 12 h numerical simulations of the 10–11 May 1973 case are studied to determine 1) if a transverse indirect circulation with a low-level jet imbedded in its lower branch can be diagnosed in the exit region of the upper-level jet and studied using the model output at 3 h intervals and 2) if the initial magnitude and structure of the upper-level jet have a significant effect on the subsequent development of the low-level jet and the decrease in convectivc stability due to differential advection. In an adiabatic model simulation, an indirect transverse circulation having a low-level jet within its lower branch occurs in the exit region of the upper-level jet. The simulated vertical distribution of mass divergence and ageostrophic flow in the exit region agree with the diagnoses of Uccellini and Johnson. At upper levels, mass divergence (convergence) occurs on the cyclonic (anticyclonic) side of the exit region, while the opposite occurs at low levels. The, upper branch of the indirect circulation is dominated by the inertial–advective contribution to the ageostrophic wind which is related to the alongstream isotach gradient in the exit region. The lower branch is dominated by the wind tendency contribution to the ageostrophic wind. Ageostrophic shear associated with this circulation contributes to the development of differential moisture and temperature advection, which act to destabilize the preconvective environment.

A second simulation using a smoothed, nondivergent initialization with a weaker upper-level jet streak and weaker alongside isotach gradient in the exit region of the upper-level jet produces a weaker indirect transverse circulation even though diabatic heating effects are present. The indirect circulation for this simulation is marked by smaller vertical motions, a weaker low-level return branch, and weaker low-level thermal and moisture advection associated with the low-level flow. Comparison of the two simulations suggests that the indirect circulation in the exit region of the upper-level jet is strongly responsive to dynamical processes associated with the initial structure of the jet streak.

Full access