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-tion as a basis for rainfall interpolation, it is of interest to determine the estent of correlation between rainfall amounts in a iven month or year and in the correspond-rainfall for the month of April at Albany, N. k., is shown graphically on Figure 3 in comparison with the mean cipitation for the precedin and following months.a given month at Albany and the w a n of the preceding and following months are as follows:Corrt~lution of eot-jicimts baticvm a q i w h irtonth a d the itwan of the pre
-tion as a basis for rainfall interpolation, it is of interest to determine the estent of correlation between rainfall amounts in a iven month or year and in the correspond-rainfall for the month of April at Albany, N. k., is shown graphically on Figure 3 in comparison with the mean cipitation for the precedin and following months.a given month at Albany and the w a n of the preceding and following months are as follows:Corrt~lution of eot-jicimts baticvm a q i w h irtonth a d the itwan of the pre
derived from the five subsets to obtain a single set of clusters. The values of RP are based on spatial correlations between corresponding clusters in the five subsets of the input. As explained in the previous section, each value represents the average of 10 different comparisons. The resulting clusters are shown in Fig. 1 . The first three patterns correspond closely to the regimes G′, A′, and R′ in CW (their Fig. 7). Fig . 1. Composite 500-hPa height anomaly maps of the cluster derived from Ward
derived from the five subsets to obtain a single set of clusters. The values of RP are based on spatial correlations between corresponding clusters in the five subsets of the input. As explained in the previous section, each value represents the average of 10 different comparisons. The resulting clusters are shown in Fig. 1 . The first three patterns correspond closely to the regimes G′, A′, and R′ in CW (their Fig. 7). Fig . 1. Composite 500-hPa height anomaly maps of the cluster derived from Ward
forfurther statistical and synoptic studies to correctcurrent statistics based on erroneous maps, to clarifyremaining differences of viewpoint and to provide afuller description of various circulation features. -1first matter which requires clarification is the distribution of mean surface pressure over the Arctic Sea insummer. An early map of Baur's [11] depicted a regionof flat pressure in July with an average value near1011 mb. A later mean published by the U. S. WeatherBureau [la], based on the 40
forfurther statistical and synoptic studies to correctcurrent statistics based on erroneous maps, to clarifyremaining differences of viewpoint and to provide afuller description of various circulation features. -1first matter which requires clarification is the distribution of mean surface pressure over the Arctic Sea insummer. An early map of Baur's [11] depicted a regionof flat pressure in July with an average value near1011 mb. A later mean published by the U. S. WeatherBureau [la], based on the 40
rainfall fields down to drop scale using data collected by a 2D video disdrometer (2DVD) [see Kruger and Krajewski (2002) for a precise description of the device’s functioning], deployed in the Ardèche region (southeastern France) in the framework of the Hydrological Cycle in Mediterranean Experiment (HyMeX; Ducrocq et al. 2014 ), in an innovative way. Indeed, this device has been extensively used as a reference in comparison with other rainfall-measuring ones ( Krajewski et al. 2006 ; Tokay et al
rainfall fields down to drop scale using data collected by a 2D video disdrometer (2DVD) [see Kruger and Krajewski (2002) for a precise description of the device’s functioning], deployed in the Ardèche region (southeastern France) in the framework of the Hydrological Cycle in Mediterranean Experiment (HyMeX; Ducrocq et al. 2014 ), in an innovative way. Indeed, this device has been extensively used as a reference in comparison with other rainfall-measuring ones ( Krajewski et al. 2006 ; Tokay et al
This appendix derives the expected value and variance of the observational error estimator . All notation is consistent with the main body of the paper. We begin by rewriting the estimator (8) from the main text in vector form, where observed values are in a column vector and the linear matrix operator can be used to map each state-space vector into an observation space column vector. (As in the main text, denotes an ensemble average.) We will derive the moments of using the algebra
This appendix derives the expected value and variance of the observational error estimator . All notation is consistent with the main body of the paper. We begin by rewriting the estimator (8) from the main text in vector form, where observed values are in a column vector and the linear matrix operator can be used to map each state-space vector into an observation space column vector. (As in the main text, denotes an ensemble average.) We will derive the moments of using the algebra
386JOURNAL OF METEOROLOGYVOLUME 6OBJECTIVE WEATHER-MAP ANALYSISBy R. A. PanofskyNew York University'(Manuscript received 7 February 1949)ABSTRACTWind and pressure fields are fitted by third-degree polynomials in areas of the order of 106 square miles.Expressions involving derivatives of wind and pressure are computed and the question of computation ofgeostrophic deviations is re-examined. A method of connecting polynomials in separate areas is investigated.The following conclusions are drawn :1
386JOURNAL OF METEOROLOGYVOLUME 6OBJECTIVE WEATHER-MAP ANALYSISBy R. A. PanofskyNew York University'(Manuscript received 7 February 1949)ABSTRACTWind and pressure fields are fitted by third-degree polynomials in areas of the order of 106 square miles.Expressions involving derivatives of wind and pressure are computed and the question of computation ofgeostrophic deviations is re-examined. A method of connecting polynomials in separate areas is investigated.The following conclusions are drawn :1
population. a. Comparison of bias and variance With a bit of algebra, one can show where, for brevity, the dependence of the ρ quantities on the valid time T has been suppressed. This form of the equations is particularly useful, because the last term on the right-hand side of all three equations involves only ρ M evaluated at different times. The remaining terms on the right-hand side are all perfect squares, and hence nonnegative. For example, consider the first equation in (14) . The first term
population. a. Comparison of bias and variance With a bit of algebra, one can show where, for brevity, the dependence of the ρ quantities on the valid time T has been suppressed. This form of the equations is particularly useful, because the last term on the right-hand side of all three equations involves only ρ M evaluated at different times. The remaining terms on the right-hand side are all perfect squares, and hence nonnegative. For example, consider the first equation in (14) . The first term
1. Introduction Most variables, such as length, age, birth rate, and so on, are continuous and thus can be directly mapped onto the real number line. As a consequence, such variables are called linear variables, and for them the statistical treatment is well established. However, there exist other variables, such as the horizontal wind direction, that cannot be mapped onto a line because they are periodic, restarting from zero at a certain point. Such periodic variables need to be mapped on a
1. Introduction Most variables, such as length, age, birth rate, and so on, are continuous and thus can be directly mapped onto the real number line. As a consequence, such variables are called linear variables, and for them the statistical treatment is well established. However, there exist other variables, such as the horizontal wind direction, that cannot be mapped onto a line because they are periodic, restarting from zero at a certain point. Such periodic variables need to be mapped on a
modest degree of smoothing, the tracer field evolving from a localizedrelease rapidly attains the form of an algebraically spreading cloud. The zonal size ofthe cloud increases linearlywith time (superdilfusively), owing to the systematic shear in the extratropical zonal jets, while the meridionalspread has the square-root-of-time increase characteristic of classical diffusion. It is argued, however, that thesmall-scale tracer structure missing from current general circulation models and from
modest degree of smoothing, the tracer field evolving from a localizedrelease rapidly attains the form of an algebraically spreading cloud. The zonal size ofthe cloud increases linearlywith time (superdilfusively), owing to the systematic shear in the extratropical zonal jets, while the meridionalspread has the square-root-of-time increase characteristic of classical diffusion. It is argued, however, that thesmall-scale tracer structure missing from current general circulation models and from
gives the results of the analysis. These results are compared with those of Wilcoxand Sanders (1976), who evaluated thicknesses derivedfrom the Nimbus 5 NEMS (Nimbus E MicrowaveSpectrometer). Table 3 shows the comparisons. Notethat the layers ~re not strictly comparable because ofthe availability of data. Inspection of Table 3 showsthat the algebraic signs of the discrepancies are oppositein the two studies. We are unable to explain this disagreement. The difference probably is intrinsic
gives the results of the analysis. These results are compared with those of Wilcoxand Sanders (1976), who evaluated thicknesses derivedfrom the Nimbus 5 NEMS (Nimbus E MicrowaveSpectrometer). Table 3 shows the comparisons. Notethat the layers ~re not strictly comparable because ofthe availability of data. Inspection of Table 3 showsthat the algebraic signs of the discrepancies are oppositein the two studies. We are unable to explain this disagreement. The difference probably is intrinsic
