Uncertainty in Estimates of Effects
The previous chapters describe earth-penetrator and surface-burst nuclear weapons and summarize the effects of their use. Evaluation of these effects is based on a series of coupled physical and chemical models that describe nuclear earth-penetrator weapons (EPWs), surface-burst weapons, and conventional weapons, the performance of the weapons, the extent of target destruction, related prompt effects and effects of fallout, and the resultant health and environmental effects. For the model calculations, a range of boundary conditions has been assumed. Inevitably, there is uncertainty in such calculations, and the scale of these uncertainties is essential to understanding the results of the calculations. The uncertainties are of three types:
Scenario uncertainty. This type of uncertainty encompasses the range of parameters calculated for a variety of conditions. In the committee’s analysis, the principal factors in scenario uncertainty are the weather at the time of detonation, the distribution of the population, and, for the EPW, heterogeneities of the geologic formations surrounding the target.
Data uncertainty. For most of the data inputs into the models there is some level of uncertainty. For fundamental physical constants and materials properties, these uncertainties are generally low. Other parameters may be more uncertain, such as the types and volumes of activation products in the fallout. Data uncertainty arises both from random and systematic sources of error, which degrade precision and accuracy, respectively.
Conceptual model uncertainty. Underpinning all of the calculations are simplified models of the physics, chemistry, and biology of the relevant processes. These include the models of transport and dispersion of the radioactivity, and exposure pathways that lead to a calculated dose and consequent number of fatalities. The conceptual model uncertainty can be large and is the most difficult to quantify, as it is analogous to a systematic source of error in observations.
In any series of calculations, the uncertainty from each of these sources propagates, and grows, through the analysis. To evaluate the sources and magnitude of these uncertainties, the present chapter uses a parametric analysis in which important parameters have been varied across a reasonable range.
The committee has not, however, discussed one of the more important sources of uncertainty in planning the successful defeat of hard and deeply buried targets or their contents (e.g., chemical or biological agents), that is, the need for precise intelligence about the type and configuration of a target.
To assess uncertainties, it is essential to identify the factors to which the model calculations (e.g., estimates of casualties for a given scenario) are more sensitive, as these factors offer the greatest potential contributions to uncertainties. Such factors include wind direction relative to the spatial distribution of a population and the degree to which populations are sheltered. Weather can be accounted for immediately prior to an attack, and sheltering can be accounted for by the timing of an attack (day or night) or perhaps by the issuing of a warning prior to an attack.
For example, based on the Hazard Prediction and Assessment Capability (HPAC) code calculations summarized in Chapter 6, the use of a nuclear EPW instead of an above-surface burst of equivalent military effectiveness (i.e., 25-fold larger yield) is expected to reduce casualties by factors of 2 to 7, 10 to 30, and 15 to 60 for Targets A (urban), B (rural), and C (rural), respectively (the values are for annual estimates of fatalities plus serious injuries). The equivalent military effectiveness coupling factor ranges between 15 and 25. In some of its calculations, the committee compares weapons differing in yield by a factor of 19 because these calculations had already been done and demonstrate the major features of importance. For a given weapon, however, the calculated casualties vary by factors of up to 4 to 8, depending on how well sheltered the population is assumed to be. In addition, Figures 6.9 and 6.11 show that estimates of total casualties can vary by factors as large as 101 to 102, depending on wind direction.1
The general conclusion derived from such comparisons is that the estimated reductions in casualties from a nuclear EPW as opposed to a surface burst of 25-times-higher yield are about 2 to 50 times larger for rural than for urban targets, but the casualty estimates are also more variable by factors of 1 to 2 orders of magnitude in absolute values for the rural than the urban targets. To be sure, all else being equal, use of a weapon with a lower yield is always expected to result in fewer casualties than use of a weapon with a higher yield, for a given set of weather conditions.
SOURCES OF UNCERTAINTY
As discussed in each of the previous chapters, estimates of the effectiveness of as well as the casualties from the attack of a target take into account various sources of uncertainty, which can be summarized as follows.
Positive identification and reliable determination of the three-dimensional coordinates of relevant targets are the main sources of uncertainty considered in Chapter 2 (and again in Chapter 4). Adequate intelligence is required not only to identify those facilities that pose significant threats but also to determine the best modes of attack—which depend on the physical characteristics of the bunker (depth, size, distribution of chambers, hardness, and so on). Uncertainty about these variables affects estimates of target destruction rather than assessment of casualties.
Chapter 3 discusses the heterogeneous nature of low- to medium-strength natural rock formations and the challenge of designing an EPW capable of surviving the lateral and axial forces encountered during impact and penetration of such targets. During the development phase of a given EPW weapon, axial and lateral loading limits of the EPW are determined through extensive component-level shock tests and full-scale EPW system penetration tests. Analytical models are then used to estimate EPW axial and lateral loading for comparison with the EPW survivability limits to assess EPW functionality after the penetration event. The probability of successful penetration is the probability that the EPW will function after it penetrates the target. To determine the probability of successful penetration for a given EPW in a given target, a series of Monte Carlo calculations are run in which each impact parameter and
target property variable is given a distribution based on the best information available. The results of the calculations are compared with the loading limitations of the EPW, and a probability of EPW functionality after penetration is determined statistically.
For completeness, it should be noted that in some instances impact parameters and target properties can be severe enough to cause the structural failure of the EPW’s casing. Safety-related tests conducted on various EPW development projects where EPWs have been tested beyond loading limits indicate that it is extremely unlikely that a second-order detonation of the high explosives will occur, even if the EPW case is ruptured at impact or during penetration. It is possible, of course, that a small number of pieces of nuclear material could be dispersed in the immediate area if the EPW case ruptured on the surface.
Given the impact parameters of the EPW system, the range of forces to which the EPW could be subjected are calculated for a wide range of target properties and impact conditions in order to assess the utility of the weapon. To estimate the uncertainty in EPW functionality, one can then evaluate the range of forces to which an EPW would be subjected, for a wide range of target properties and impact conditions, associated with the known (or estimated) heterogeneity of a given target.
As extrapolated from research done in support of previous design work (e.g., for the Pershing-II EPW, the W61, and the strategic earth-penetrator weapon (SEPW) described in Chapter 3), estimates of the B61-11’s functionality are high for attacks on its design targets, but very low for its attacks on a variety of other complex and harder targets. The robust nuclear earth penetrator (RNEP) weapon concepts currently under consideration could conceivably achieve a probability of functionality of perhaps 40 to 70 percent relative to axial and lateral loads, while an advanced penetrator design could achieve a probability of functionality greater than 90-plus percent.2 The committee emphasizes that these are little more than initial judgments, however. Although informed by a sizeable amount of experimental data, they are supported by only a limited amount of fundamental analysis. The dearth of realistic assessments of subsurface heterogeneity is a notable gap in current analysis.
Chapters 4 and 6 list several sources of uncertainty influencing the calculated effects of nuclear weapons. The source term depends on accurately knowing weapon yield and height or depth of burst, as well as the target environment and consequent effects of secondary (neutron) activation. The reliable prediction of transport, both for nuclear fallout and for released chemical or biological agents, depends on accurate forecasts of wind direction, wind speed, and rain, including the effects of terrain (natural topography and, for urban environments, buildings). Health and environmental consequences are currently evaluated only for military casualties, not for the population at large (e.g., including the young, old, and infirm), and even then are considered reliable to only a factor of two. Also, the population databases are necessarily static, and, even if reliable in an average sense, do not reflect actual locations and movements of individuals. Chapter 5 does note that the integrated dose contours reproduce to within a factor of two the nuclear test results from which the empirical models were derived; however, it is important to acknowledge that the nuclear tests were conducted in good weather and under relatively stable atmospheric conditions.3
Additional sources of uncertainty listed in Chapter 4 include the hardness of the target, the effects of the accuracy of weapons delivery (circular error probable, CEP), and details of fallout assessment (e.g., the relationship between amount of radioactivity and size for particles in the fallout). Chapter 6 documents the importance of target location (urban versus rural, as noted above) and also discusses uncertainties in estimates of casualties resulting from the attack of facilities containing chemical or biological agents. It is noteworthy that a nuclear weapon offers an advantage for defeating biological or chemical weapons agents within the facility only if the warhead can be detonated within the chamber containing these agents; otherwise, the special effects by which the nuclear detonation can neutralize the agents are likely lost.
In summary, estimates of casualties are based on combined modeling of the source, transport, and health consequences of nuclear weapons effects. Uncertainties in the casualty estimates are difficult to evaluate because the underlying processes are poorly understood. In particular, the fidelity with which the transport of aerosols (mimicked by way of advection diffusion) is modeled remains unclear, and the prediction of health effects—based on empirical measurements, but limited by the relative lack of data and unsupported by chemistry- and biology-based theory—is modeled with a reliability that is hard to assess.
MEASURES OF UNCERTAINTY: SENSITIVITY, PRECISION, AND ACCURACY
A part of the overall uncertainty regarding estimates of the effects of weapon use can be inferred from the calculated sensitivity of the results to varying conditions and assumptions. As noted in Chapter 6, expected casualties can be expected to vary by up to a factor of 10 for urban targets, and by a factor of nearly 100 for rural targets, depending on assumptions that are difficult to validate a priori. In terms of absolute numbers of fatalities and injuries, however, attacks on urban targets dominate overwhelmingly. That is, estimated casualties from the use of a nuclear weapon in an urban area are typically in the 105 to 106 range, whereas casualties from the rural targets considered in this study can be as low as in the 101 to 102 range (albeit potentially extending to the 105 range, depending on circumstances and assumptions). For this reason, it is important to consider absolute as well as relative variations in evaluating calculated fatalities and severe injuries.
In addition to sensitivity, both the precision and the accuracy of the modeling are considered. To determine precision, the committee evaluated reproducibility by comparing results using primarily two simulation tools, the Defense Threat Reduction Agency’s (DTRA’s) HPAC code and Lawrence Livermore National Laboratory’s (LLNL’s) K-Division Defense Nuclear Agency Fallout Code (KDOFC). As discussed in Chapters 5 and 6, the numbers of casualties obtained with the two codes generally agree to within 10 to 30 percent for a wide range of scenarios. Given that variations of orders of magnitude in estimated casualties are being considered, the committee considers the codes to yield reproducible and therefore mutually consistent results. This level of agreement no doubt reflects the fact that the codes have been calibrated against the same set of available field measurements (primarily from 10 aboveground nuclear tests).
Absolute accuracy is much harder to quantify, and so the study breaks the problem down into estimating accuracy for key components of the model calculation. For example, the sensitivity of calculated casualties to wind direction, as described in Chapter 6, can be convolved with uncertainties in the forecast winds for a particular location and time in order to deduce one component of the ultimate accuracy of the final results. A full evaluation of meteorological uncertainty is intrinsically difficult because length scales for fluctuations in wind velocity are in the 101 to 102 meter range (e.g., “outer scale” of atmospheric turbulence),4 whereas the smallest grid spacing considered in the models is 103 meters, and this typically represents interpolations across even greater distances.
How good are the predicted wind directions from which to estimate casualties using such tools as HPAC or KDFOC? A qualitative answer is given by recent reports that highlight the role of wind-vector fields in determining the uncertainties in modeling atmospheric plumes.5 Anecdotally, it is also known that the primary wind direction changed by 180° within 18 hours of the Chernobyl incident, thus spreading nuclear contaminants in more directions than might have otherwise been expected, and that the smoke plume from the World Trade Center site was directed opposite to the normal wind direction shortly after the September 11, 2001, attack.6
A more quantitative answer comes from comparing the results of modern numerical weather predic-
tions against field observations. Experience in the Pacific Northwest, for example, shows systematic biases (mean errors) of ±10 to 20 degrees and mean absolute-value errors of ±40 to 50 degrees for near-surface (10 meters) winds at 12 to 24 hours into forecasts, depending on spatial resolution and forecast hour (the near-surface winds are expected to be less subject to directional shear under unstable or neutral conditions than winds at higher elevation).7,8 Similarly, mean absolute-value errors of ±30 to 40 degrees are documented for a model applied to the Savannah River Site in South Carolina, though with excursions reaching 60 to 70 degrees at 12 to 24 hours into the forecast.9 Not surprisingly, the statistics can be somewhat worse for topographically complex areas, such as the region around Salt Lake City, Utah, although mean absolute errors of ±40 to 50 degrees remain possible in many specific locations when extensive modeling and updating are pursued.10,11 In general, wind directions are more poorly forecast at lower than at higher wind speeds, and at lower (near-surface) than higher levels of the atmosphere.
Such discrepancies between forecast and observed wind-vector fields (wind directions, in particular) are widely recognized in the community that models atmospheric dispersion and photochemistry.12 For instance, one document mentions average root-mean-square errors of ±36 to 57 degrees in wind direction (largest values near Earth’s surface, smallest values at pressure levels below 100 millibars), but with directional excursions in estimated surface-wind mean errors (bias) as large as 106 degrees (the analysis pertains to the March 10, 1991, meteorological event of Khamisiyah, Iraq). Similar modeling applied to northern Europe reveals systematic biases (mean errors) and root-mean-square errors of up to ±13 to 15 degrees and ±35 to 41 degrees, respectively, at the lowest levels and beyond 24 hours of forecast.13
Studies of ensemble forecasts do not alter the substance of these findings, but instead reinforce the conclusion that reliable forecasts of dispersion are a challenge: Straume reports root-mean-square deviations in wind direction between 15 and 48 degrees, for example.14 This is not surprising, given the errors to which models are subject and the difficulty—and therefore diminished reliability—with which wind-field directions are measured.15
Overall, it appears that systematic biases (mean errors) of ±10 to 20 degrees and root-mean-square (or mean absolute-value) errors of 30 to 50 degrees should be expected for wind direction forecasts relevant to the present study. Referring to Figures 6.9 (a) and (b), an uncertainty of ±20 degrees encompasses the difference between maximum and minimum estimates of total casualties for Target A (urban), and corresponds to more than a 20-fold difference in casualties for Target B (rural). In both cases, these uncertainties amount to differences on the order of 106 in calculated values of fatalities and serious injuries. In light of the present results, Figures 6.11 (a) and (b) make the point that although a low-yield nuclear EPW is expected to cause fewer fatalities than a higher-yield above-surface nuclear burst, the differences in forecasted deaths for surface versus EPW detonations are comparable to the variability associated with a ±15 to 40 degree uncertainty in forecast wind directions. The general conclusion is that uncertainties in wind direction can result in casualty estimates varying by one order of magnitude or more.
For comparison, the degree to which the population is—and remains—sheltered, or not, affects the results by a smaller amount. Other factors being equal, sheltering is assumed always to lead to a reduction of casualties because of the diminished influence of fallout.16 HPAC analyses show that the ratio of calculated unsheltered/sheltered casualties (fatalities plus serious injuries) varies between 2 and 8 for virtually all cases of a nuclear EPW as considered here. Again, the smallest ratios apply to the urban target (A) but correspond to the largest differences in actual values (a reduction in casualties of between 100,000 and 600,000 if the population stays indoors rather than being outside). The magnitude of these differences in casualty reduction numbers is because of the fact that the absolute number of expected casualties is always high, ranging from 200,000 to 2 million for the urban nuclear EPW
scenarios evaluated for this study. The largest ratios apply to use of a low-yield weapon on a rural target (B or C) but involve relatively few casualties in the first place (e.g., a reduction from 200 to 30 and from 20 to 6 calculated fatalities plus serious injuries for two of the scenarios). Absolute values of fatalities and serious injuries are systematically higher for the above-surface nuclear explosion attacks considered in the study, but the ratios of calculated unsheltered/sheltered casualties are in the same range as for the nuclear EPW attacks of equivalent military effectiveness (i.e., yield reduced by a factor of 25).
As it seems a priori impossible to predict convincingly the degree to which a population will, or will be able to, stay indoors after a nuclear attack, the casualty estimates from such tools as HPAC and KDFOC must be considered globally unreliable to a factor of 2 to 8 as a result of this uncertainty alone. Additional sources of uncertainty were not evaluated in as great detail, but based on the discussions in Chapters 2 to 6, these may again amount to an overall factor of about 2 to 5 (e.g., estimates of the health effects of a given fallout dose for the actual population, rather than for the static, military-age population assumed in the calculations, are by themselves likely to be unreliable by a factor of 2).
Thus, potential errors aside from those associated with weather forecasts can reach an order of magnitude in calculated casualties. Given that uncertainties in wind direction additionally cause variations of one order of magnitude or more, the aggregate uncertainty for calculations of casualties caused by the range of nuclear attack scenarios considered here must be squarely placed in the range of 101 to 102 (factors of 10 to 100), with the lower range applying to urban targets for which casualties will with little doubt be very high.
Current analytical tools have an overall propagated uncertainty no smaller than one order of magnitude (factor of 10), and likely in the range of 101 to 102, for estimates of casualties resulting from a nuclear attack. This conclusion is based both on evaluation of the underlying calculations (source terms, transport models, grid resolution, and so on) and their experimental validation, and on a review of the variability in results that can be obtained for different scenarios when considering plausible ranges in parameters.
At least three key sensitivities affect estimates of military effectiveness and casualties associated with the use of a nuclear EPW or a nuclear burst weapon:
Target location, especially urban versus rural, as illustrated above;
Accuracy of weapons delivery (CEP) and precise knowledge of target location and structure, as military effectiveness depends closely on a combination of accurate delivery and yield; and
Estimates of the source, transport, and influence on populations of the effects of a nuclear explosion, as these can be highly variable (by factors of up to ~101 to 103, depending on assumptions).
One additional sensitivity affects the nuclear EPW:
EPW functionality after penetration, especially as influenced by target heterogeneity and the associated uncertainty (e.g., local geology, or complex structures in urban areas).
Some conclusions involve relatively little uncertainty. All other factors being equal, the use of a lower-yield weapon causes fewer casualties than use of a higher-yield weapon, for example, and a nuclear attack on an urban target must be expected to result in large numbers of fatalities and serious injuries (hundreds of thousands to millions, for the scenarios considered in this study). Relative varia-
tions in calculated casualties are therefore smaller for urban than rural targets, though the absolute numbers of predicted deaths can differ by large amounts (hundreds of thousands) for urban areas depending on factors that are not readily controlled (e.g., degree of sheltering).
For urban and rural targets, respectively, the use of a nuclear EPW is calculated to reduce casualties by a factor of ~2 to 7 and 10 to 60 relative to an aboveground nuclear burst with a yield increased by a factor of 25. This calculated 101 to 102 reduction in fatalities and serious injuries is comparable to the effect of the aggregate uncertainties that the committee has derived for the modeling tools.