Artillery Meteorology

Estimates of meteorological parameters are generally needed for the employment of extended-range ballistic systems. Such estimates allow operators to increase first round on-target probability by compensating for deviations in wind, density and temperature along a trajectory. The U.S. Army currently uses balloon-borne soundings to calculate ballistic corrections for extended range artillery fire. The accuracy of adjusted fire relies on the close proximity of these soundings in space and time to the trajectories they affect.

Other ways of approximating ballistic conditions have been developed, including the Computer Assisted Artillery Meteorology (CAAM) system (Haines et al., 1997). The CAAM system can operate in concert with the BFM or in conjunction with the Time-Space weighting technique (Blanco, et al., 1993). However, new estimation techniques must be shown to produce improved accuracy before being integrated into current artillery meteorology procedures.

Ballistic errors can be approximated by comparing the ballistic displacement of verification and operational estimators or by evaluating the results of live-fire tests (Blanco, et al., 1996). The first option is the most feasible as it can be performed in a variety of geographic areas and synoptic situations without the expense and manpower requirements of live-fire tests.

The confidence intervals surrounding ballistic error estimates depend in part on the standard error of the verification data set, which can be computed theoretically or empirically, depending on the estimation technique used. These brackets are necessary for making sound decisions concerning implementation of the proposed method (Cohen et al., 1998). If the mean ballistic error of the current method lies within the confidence interval surrounding mean ballistic error of the proposed method, a change in meteorological techniques is not indicated.

Ballistics Background

Artillery rounds fired without adjustment for non-standard atmospheric conditions might impact a significant distance from their intended target (Ballistic adjustments are computed with respect to the U.S. standard Atmosphere). The consequences of this type of miss are manifold in combat situations. First, the target is not destroyed. Second, if friendly troops are stationed near the target, the chance of fratricide increases dramatically. Third, the additional time needed to make aiming corrections and fire again, puts artillery operators at greater risk and may delay action on other targets. Finally, ammunition is wasted, adding to the expense of the operation (Department of the Army, 1997).

Figure 1 illustrates the effect of 20-knot (ballistic) tail wind on the trajectory of a 155-millimeter artillery round. The shell overshoots its intended target by a significant distance. For the sake of clarity, impact errors are exaggerated in all subsequent illustrations.

Figure 1: Impact without adjustment for 20-knot tail wind
(adapted from FM 6-15, 1997)

In practice, firing tables are used to compute adjustments for errors such as the one shown in Figure 1, given an estimated profile, or "met-message", of meteorological variables. This is a two-step process.

Ballistic winds, temperatures and densities are first calculated using density weighting tables (see Department of the Army, 1982); these represent the bulk effects of all wind, density and temperature conditions encountered over an entire trajectory (Department of the Army, 1997). Horizontal displacements are then calculated for each ballistic effect using parameters unique to particular weapon systems. As shown in Equations 1 and 2, total ballistic displacement is computed as a linear combination of meteorological effects.

Equation 1
Equation 2

D is the ballistic displacement in the range, R, (along trajectory) and cross, C, (across trajectory) aspects. Profiles of wind, u, and deviations in density ((() and temperature ((T) at different heights, z, are associated constants a, b, c and k which assign weighted displacements to each variable and layer. Note that ballistic effects are actually nonlinear functions, as shown in McShane et al., 1953; linear approximations are simply easier to use when computation cannot be automated.

The sum of vector displacements for all effects, Equations 1 and 2, is the unadjusted impact displacement vector, the opposite of the adjustment vector. Figure 2 shows unadjusted impacts computed for three met-messages, each derived using a different method such as extrapolation, time-space weighting or numerical prediction. There is also an impact point labeled "truth". This is a hypothetical displacement obtained given real conditions and no adjustments. Of course, the exact state of the atmosphere can only be approximated. Consequently, the "truth" method is only useful in a theoretical sense.

Figure 2: Unadjusted impact displacements
for three arbitrary methods and truth

Adjustment vectors for the impacts in Figure 2 would simply be the opposite of the vectors pointing from the target to the unadjusted impact points. For example, firing table calculations might indicate that shells launched without adjustment under atmospheric conditions indicated by method 2 would fall short by 100 meters. One would expect an improved accuracy by adjusting fire Northward by 100 meters.

Some amount of miss is expected, even after adjustment, due in part to differences between estimated and real meteorological conditions. The imperfect representation of ballistic effects provided by firing tables and irregularities in muzzle velocity add to the miss after adjustment. Nevertheless, the actual vector miss given adjustment for any method can be approximated by subtracting the unadjusted vector miss for that method from that of the true ballistic wind.

Figure 3 shows adjusted impacts for the three arbitrary methods in figure 2. It is evident that corrections made for good estimators, such as method 1, result in impacts very near the target and that methods 2 and 3 produce relatively poor accuracy in comparison to method 1. It should be noted that adjusting for the real ballistic wind results in a direct hit (not shown) and that adjusting fire for method 3 leads to greater inaccuracy than no adjustment at all.

Figure 3: Actual impacts after adjustment
for methods shown in Figure 2

Calculating Ballistic Errors

To calculate the impact errors in Figure 3, a standard or best-estimator for the true ballistic wind is needed, since the exact state of the atmosphere cannot be known. In general, the mean miss for the standard must be much smaller than the mean scalar difference between unadjusted impact displacements of the standard and operational estimate. Figure 4 demonstrates that under these constraints an estimate of ballistic displacement can be used as "truth".

Figure 4: Approximating vector miss

As the ratio of |R1-R2| and |R2-R3| approaches zero, R2-R3 approaches R1-R3, thus R2-R3 can be used as to approximate the miss of an arbitrary estimator. The magnitude of this vector difference only has significance if it is much larger than the magnitude of the mean miss vector for the standard. Thus, it is crucial that the accuracy of the standard is established before it is used as such, otherwise calculations of adjusted miss have little meaning.

Figure 5 shows ellipse probable error for each method. Each ellipse is centered on the mean vector impact error for a particular method; the ellipse itself is a boundary defined to contain a fixed percentage (usually 50%) of all adjusted impacts for the method in question.

Figure 5: Ellipse Probable Error for
three arbitrary methods

In Figure 5, the method 1 ellipse provides a relatively good approximation of the target position. Therefore, following the logic surrounding Figure 4, method 1 could clearly be used as a standard with which to judge the accuracy of methods 2 and 3. Furthermore, one only needs to determine the mean miss for one proposed standard estimator and then demonstrate theoretically that it is much smaller than the mean unadjusted scalar difference between the standard and other estimators. Once this determination is made, the adjusted miss for each method can be approximated by subtracting the unadjusted miss vector of the proposed estimator from that of the standard. The magnitude of this vector difference only has significance if it is much larger than the magnitude of the mean miss vector for the standard. Thus, it is crucial that the accuracy of the standard is established before it is used as such, otherwise calculations of adjusted miss have little meaning.

Two methods have been proposed as standard estimators of real-time conditions. The first is a simple sounding taken at a representative location close to the time of firing, the second is a sounding taken from an objective analysis or other interpolation. Consider the test range setup depicted in Figure 6.

Figure 6: Test range scenario

Time-stale soundings taken a short but significant distance from the gun position (as depicted Northwest of the gun position in Figure 6) have generally competed with model data interpolated to the location of apogee. However, soundings taken at this site at the time of firing cannot also be used as verification. To do so would imply that in practice, there is no significant spatial separation between available persistence soundings and actual trajectories. Another sounding, taken at the time and location of simulated artillery fire could be used as verification. A profile drawn from a composite of all available data, including radiosonde, wind profiler and surface observations could also be used for verification of both the stale sounding and model forecasts. Due to the sparseness of upper air observations, the latter method is likely to be imployed.

The 3-D objective analysis capability offered by the BFM provides a convenient method of compositing data over an entire simulated battlefield and producing met-messages at convenient and representative locations. Interpolated data derived from the objective analysis process can be used to judge estimators which would potentially be available on the battlefield, such as time-stale soundings or numerical forecasts.

The luxury of using data from an entire test range for verification purposes is afforded by the density of observations typical of selected1 areas in the Continental United States; this does not suggest that in-situ data would be available from the opposing side of the forward line of troops in a real battlefield scenario.

A statistical method, such as Ordinary Kriging, could also be used to provide interpolated ballistic conditions at convenient locations. The advantage of this method is the straightforward calculation of error variance. The magnitude of mean miss vectors can be derived from the error variance of impact displacement because of the unbiased nature of the Kriging method.

It should be noted for further clarity that in practice, only raw data available from the friendly side of the battlefield would be used to augment the regional scale gridded model data (such as NOGAPS or MM5) typically used to initialize the BFM. Therefore, for decision-making purposes, the BFM would compete only with time-stale data from the friendly side, however, both BFM and time-stale soundings would be measured against the composite of all available data to determine the absolute accuracy of each.

It should be stressed that before statistically supportable conclusions can be drawn about the usefulness of any artillery meteorological estimator such as the BFM, the standard against which it is judged should be validiated. The accuracy of profiles produced by 3DOBJ or the Ordinary Kriging method should therefore be verified, as these methods have been suggested as "truth" estimators. This can be accomplished by analyzing the standard error of adjusted miss for either method. Alternatively, either method could be used for ballistic adjustment in a series of range trials.

There are advantages and disadvatages to each of these options. While standard error calculations only provide information on inaccuracy due to meteorological uncertainties, they do not require additional personnel. Range tests would be expensive and would require additional personnel. They would, however, yield a composite picture of all factors affecting artillery accuracy, such as meteorological uncertainty, the imperfect treatment of ballistic effects by the firing tables method and abnormalities in the weapon system.