Introduction

Offshore producers of crude oil and natural gas in the Gulf of Mexico (GOM) are literally on the front line of hurricane hazards. The impacts of hurricanes on oil and gas producers can be considerable. For example, Hurricane Andrew in 1992 destroyed 13 offshore oil and gas production platforms, 4 of which disappeared without a trace. Another 40 platforms were damaged, and 5% of the natural gas supply in the United States was temporarily lost (McDonald 1992).

The Gulf of Mexico is one of the most promising oil and gas prospects in North America, producing about 5.1 trillion cubic feet of natural gas per year and more than 1.2 million barrels of crude oil per day, representing nearly 27% and 21% of total U.S. production, respectively. The oil and gas infrastructure in the Gulf of Mexico is substantial, with 6400 producing wells, 4000 active platforms, and 29 000 miles of pipelines. The Minerals Management Service (1999) predicts significant increases in production, almost entirely from deep-water tracts that are particularly vulnerable to storm events. Hence, the value of hurricane forecast information will likely rise in the future with this increased production activity.

Offshore energy producers must make two decisions when confronting the threat of a hurricane: one involves the temporary cessation of the current flow of hydrocarbons from producing fields, and the other involves the evacuation of drilling rigs supporting exploration and development. Firms often shut in wells and cease production during hurricanes. In this case, if the platform is destroyed, no hydrocarbons escape from the well. For staffed production platforms, evacuation would prevent any loss of life. Under these circumstances, production is not lost but simply delayed. The economic value of these disruptions is the lost revenue of deferred production discounted for the time value of money. Temporary reductions in energy production during hurricanes are illustrated for crude oil in Fig. 1, indicating sharp reductions in production during hurricanes.

In addition to current production, oil companies explore and develop new fields, leasing exploration, and production rights from the Minerals Management Service (MMS) of the U.S. federal government. A typical offshore lease block in the Gulf of Mexico is 9 mi². Once a lease is acquired, the oil company may elect to drill exploration wells. Between 1995 and 1998, an average of 233 drilling rigs operated in the Gulf of Mexico per year.

Oil companies engage the services of a drilling contractor who owns the drilling rig and employs and manages the drilling crew. These companies also coordinate other subcontractors who perform specialty services. When a hurricane threat looms, both the drilling contractor and the oil company jointly decide whether to evacuate the drilling rig. Most drilling rigs are rated to withstand approximately 100-kt (1 kt = 0.5144 m s⁻¹) winds. If winds exceed this rating, severe damage is possible. Any personnel remaining on board during a hurricane would be subject to this catastrophic risk. The oil company controls all modes of transportation to and from the rig and is, therefore, responsible for personnel safety and would likely incur a large financial loss if the entire crew were lost from failure to evacuate. Even if the oil company or drilling contractor carried general liability insurance, deductibles are often large, often in the tens of millions of dollars. Also, failure to evacuate could be construed by the insurer as negligence and grounds for refusal to pay for any losses. Beyond such direct economic considerations, the ethical and operating guidelines of oil companies mandate that protection of workers is paramount. These considerations imply that the burden is clearly put on decision makers to avert personal injuries and deaths.

The oil and gas lease areas in the Gulf of Mexico, and some selected hurricane tracks, are displayed in Fig. 2. The producing areas extend from the western panhandle of Florida, around the coast of Alabama and Louisiana, and to the barrier islands in southern Texas. Drilling is now occurring 200 miles offshore.

The economic value of forecasts

Because the value of weather forecast information is often difficult to determine, an indirect approach to valuation is necessary, involving calculation of the user's satisfaction or utility with and without the forecast information. For hurricane rig managers baseline utility is the net cost from using no forecast information.¹ In this simple case, the rig managers could use historical probabilities of hurricane strikes at the rig location or could ignore probabilities altogether. The utility from using a government or private-sector forecast would presumably provide them with more information, which, if reasonably more accurate than the baseline information, would allow them to make more timely and efficient decisions.²

Previous forecast valuation studies include harvest timing (Lave 1963; Wilks et al. 1993), prevention of rain damage (Kolb and Rapp 1962), orchard heating during frost conditions (Baquet et al. 1976; Katz et al. 1982), and irrigation decisions (Rogers and Elliot 1988). Although there have been descriptive studies of hurricane evacuations, there are no studies that measure forecast accuracy and the costs and losses associated with hurricane evacuation decisions with and without forecast information.

A model of the hurricane hazard decision process can be developed from the cost–loss framework developed by Nelson and Winter (1964) and Katz and Murphy (1997). Decisions to shut in production and to evacuate drilling rigs are conceptually the same—only the costs and potential losses differ. Thus, the following discussion focuses on the evacuation decision for a drilling rig manager at any arbitrary point in time.

Consider that the manager receives a public probabilistic forecast of a hurricane π in which the rig is projected to be somewhere within a strike area identified by the National Hurricane Center (NHC) forecast. Many companies purchase private weather services that translate this public information into a forecast of weather conditions important to the rig operator at the drilling location, such as wind speed and wave height, designated by z. Assume that private forecasts are based in part upon information provided by government forecasters. Hence, the expectation of z is conditional upon the probabilistic forecast of a hurricane strike made by the government and private information ϕ. Denote this private forecast as E{z|π, ϕ}, or the expected value of z given π and ϕ.

The decision rule for the manager is to evacuate if the expected weather conditions exceed some critical threshold z_c. The use of a critical threshold is similar to the adaptation of this framework by Howe and Cochrane (1976) in their study of snowstorm hazards. This threshold would be a function of the design parameters of the rigs, such as its tolerance for wind speed and wave height. The decision to evacuate (a = 1) is discrete, dependent upon whether E{z|π, ϕ} exceeds z_c:

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In other words, if the forecast implies destructive or bad conditions, then, under certainty, the decision should be to evacuate the rig. In a similar way the second condition in (1) implies no evacuation because the forecast implies that conditions are expected to be “good” or not destructive.

Equations (1) and (2) represent a set of simple decision rules in which the optimal action â is equal to 1 (evacuate) if C < π⁽¹⁾L, or the optimal action is to remain if the cost of evacuation is greater than the expected loss, or â = 0 when C > π⁽¹⁾L.

This discussion clearly illustrates that estimation of the value of hurricane forecasts requires three key pieces of information: historical and conditional probabilities, costs of acting to evacuate drilling rigs and shut in production, and the potential losses from inaction.

Hurricane forecast accuracy

Estimating the value of hurricane forecasts and improvements in forecast accuracy requires the elucidation of the relationships between hurricane forecasts and actual storm events, which permits measurement of forecast accuracy. Many studies of forecasting accuracy focus on hurricane landfalls. Our area of interest, however, is at sea, specifically for thousands of oil and gas leasing locations at 6-h intervals during the progression of many individual storm events. This level of spatial and temporal detail complicates our analysis considerably but provides a large and unique dataset to measure and to evaluate hurricane forecasts. This study requires three principal inputs: data concerning the location, size, and intensity of hurricanes and tropical storms in the GOM; the records of all forecasts of storm location, extent, and intensity; and geographical data about the location of oil and gas lease blocks in the GOM producing region.

A history of all North Atlantic tropical storms for the period of 1980–2000 was obtained from the archives of the NHC. The variables included in this dataset are as follows:

1. Storm location—the postevent best estimate of the center of the eye of the storm, in degrees of longitude and latitude;

2. Peak wind speed—the top sustained wind speed at the wall of the eye of the storm, as observed by measurement from National Oceanic and Atmospheric Administration (NOAA) and Air Force Reserve flights, satellite radar, and ground and airborne sensor observations, measured in knots; and

3. Size parameters—used by the NHC to describe the size of a storm (a storm is viewed from above as being composed of four 90° circular segments, or “pie slices”) and defined as the distance, in nautical miles, from the center of the storm to a line of constant wind velocity, in each of the four different pie-slice directions (northeast, northwest, southeast, and southwest).

The predicted position and intensity of the storm are compared with actual conditions at each location for every 6-h interval during a storm event. For example, a 12-h forecast for a particular lease location at 0900 UTC is evaluated by comparing the predicted position and intensity of the storm at the site made at 2100 UTC on the previous day.

The relative value of 12-, 24-, 48-, and 72-h forecasts will vary from user to user. Facilities in deep, far-offshore waters generally need more time to shut down operations and/or to evacuate than do facilities nearer to shore. As a consequence, the 72-h forecast is generally more important to far-offshore facilities than the 24-h forecast is to near-shore facilities and vice versa. Evacuating rigs in deep water far from shore is more costly. The value of forecasts for these rigs is thus relatively higher. Nevertheless, our analysis does not distinguish between track and timing errors. A forecast that correctly predicted the hurricane route but nevertheless misforecast the position of a hurricane by 600 km because the simulated hurricane moved too quickly is not valued more highly than a forecast with a 600-km position error that was due to route error rather than speed error.

There were typically three sets of observations: the distances from the center to the line of 34-kt winds, signifying the extent of tropical-storm-force winds; the distances to the line of 50-kt winds, specifying gale-force winds; and the distances to the arcs of 64-kt winds, signifying category-1-hurricane-force winds. The extent of a typical storm is shown in Fig. 3. Each of the four arcs describes a line of constant wind velocity, or a wind speed contour. Assuming that the storm in Fig. 3 is a 50-kt (gale force) storm, then the four arcs each describe the line of 50-kt winds. At every location between one of the arcs and the storm center, the wind speed is greater than 50 kt. At all locations outside the arcs, the wind velocity is below 50 kt. On the four arcs the speed is assumed to be 50 kt. The storm illustrated in Fig. 3 extends mostly to the northwest. This figure is obviously a simplification of the actual shape and size of a typical tropical storm, but it is an abstraction that is necessary to enable computation of storm extent.

Forecast data for a similar period were obtained from archives located at the NHC FTP Web site. The forecast data contained data similar to those described in the storm data section, as well as one other piece of information: the span of the forecast, that is, the time into the future for which the forecast is made. This study examines the five common forecast spans issued by the NHC: 12, 24, 36, 48, and 72 h. These forecasts are typically issued as parts of Marine Forecast/Advisory (MFA). MFAs are typically issued 4 times per day (at 0300, 0900, 1500, and 2100 UTC) during a tropical storm in the North Atlantic basin and contain descriptive warnings about coming storm conditions, as well as numerical forecasts.⁴

The GOM oil and gas production region is mapped into a set of blocks by the MMS. This mapping has been done for the purpose of leasing oil and gas drilling and production rights to companies. Most of these blocks are approximately 3 mi × 3 mi squares. Boundaries and centerpoints of each of these lease blocks were downloaded from the MMS Web site.

The blocks extend from the Gulf Coast of Florida in the east to the Texas barrier islands in the west. The southern boundary is delineated in the west by the extension of the U.S.–Mexico border (26° latitude) and extends southward to below 24° latitude in the eastern gulf. The blocks extend northward to the Gulf Coasts of Texas, Louisiana, Alabama, and the Florida Panhandle. There are currently 29 544 defined blocks.

A significant amount of data manipulation is required before commencing calculations. All of the storm events and forecasts had to be matched into pairs; that is, each forecast had to be matched up with the observed storm events at the times for which the forecasts were made.⁵ Eight sets of storm–forecast pairs were compiled: 50-kt size parameter forecasts were compiled for 12-, 24‐, 36-, 48-, and 72-h forecasts; 64-kt size parameter forecasts were compiled for 12-, 24-, and 36-h forecasts.⁶ To facilitate the computation of distance errors, we converted the position data to three-dimensional Cartesian coordinates at location i (x_i, y_i, z_i), where

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The distance between two points i and j, d_i,j, in nautical miles, is calculated using the following formula:

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The definitions and conventions used in these calculations are summarized in Considine et al. (2003). An initial filtering of storm and forecast data was performed to include only data that were pertinent to the region under study. The eastern boundary defined for this study is 75° longitude. All event–forecast pairs that were completely to the east of this line, which is approximately 300 miles east of Miami, Florida, were excluded from the analysis. In a similar way, pairs completely south of the 15° and completely north of the 35° latitude lines were also excluded. These lines correspond approximately to the extreme southern tip of Mexico, about 600 miles south of the Florida Keys, and the Tennessee– Georgia border, about 300 miles north of the Gulf Coast near New Orleans.

Not all forecasts are included in this study for several reasons. First, some forecasts were made for storms that no longer existed when the forecast time passed, that is, the storm had dissipated between the issuing of the forecast and its effective date/time.⁷ If the storm had dissipated, the NHC did not issue an MFA and did not track the storm position or intensity. Second, not all forecasts (and in some cases, not all verified storm event reports) contained size parameters. Some forecasts only contained peak speed and storm position estimates, and as such they were not considered in this analysis. After compiling all available event–forecast pairs, it was necessary to exclude those that lacked size parameter specifications. Table 1 summarizes the completeness of storm event and forecast data. The term “E–F pairs” refers to event–forecast pairs.⁸

The second column from the right in Table 1 contains the final, workable number of pairs used for analysis. After the event–forecast pairs were fully prepared and filtered, they were divided into separate spreadsheets— one for each year of each available forecast type. A total of 105 storm data input files were compiled.

The number of blocks associated with these definitions created an insurmountable computational burden; attempting to model whether each storm was present at each of nearly 30 000 blocks overloaded the available software. This constraint required the aggregation of the GOM region, using a grid with a spacing of 0.25°. This grid spacing equates to a 15 n mi north–south spacing, and an east–west spacing that varies from 13.7 n mi in the south of the region in question to 13.0 n mi in the north of the region. The resultant grid contains 1060 nodes.⁹

A program was written in Time Series Processor 4.4 (Hall and Cummins 1999) code to calculate the accuracy of the forecasts for each fully specified event–forecast pair, at each of the 1060 nodes on the grid. For each node, the program examined the actual storm event and forecast storm and reported whether the node was under actual and/or forecast storm conditions at each given point in time. The program computed the distance and direction from the node to the storm center and reported whether the node is inside or outside the appropriate directional size parameter, for both the actual and forecast storms. The result was binary variables (m, n), where m pertains to the criticality of the atmospheric state that actually occurred and n pertains to the criticality of the corresponding forecast state. To be specific, m = 1 (n = 1) if the node of interest is under actual (forecast) storm conditions at time t; m = 0 (n = 0) otherwise. Thus, each pair corresponded to one of the quadrants of an event–forecast matrix in Table 2.

For purposes of data compilation, it was inconvenient to store data in these two-by-two matrices, and so the data are stored in tabular form, with each quadrant in the event–forecast matrix assigned a sector code. These sector codes and their descriptions are defined in Table 3. The sector codes are graphically depicted in Fig. 4, in which the actual and forecast storms are modeled illustratively as circular storms.

In addition, if a node was some large distance from the location of the forecast storm center, then the lease was assumed to be unaffected by the storm in question, and the result is assumed to be in quadrant “e,” which is simply a proxy for “nonevents.” A criterion had to be established for deciding on the critical cutoff distance. For each of the forecast spans, the distance between the center of the actual storm event and the forecast location for each event–forecast pair was calculated. This is referred to as the track error. The track errors for the previous 5 yr were tabulated, from which the 95th percentile of these data was established. The 95th percentile was assumed to be the maximum margin of error. This margin was added to the largest of the available storm size parameters, to define a critical distance cutoff. If the distance between node i and the forecast location was greater than this cutoff distance, the node was taken to be outside of the range of influence of the forecast, and thus the event–forecast couple was assigned to quadrant e and classified as a nonevent.

There are several different ways to measure hurricane forecast accuracy for the 105 output files that were generated. Each file contains six columns: the reference number of the node and the five sector codes of the event–forecast matrix. A cumulative summary of these output files for the entire period in question is contained in Table 4. An annual breakdown of the distribution of sector codes can be found in Considine et al. (2003). These data were used to generate event–forecast matrices for each lease location in the Gulf of Mexico. These matrices measure errors both in terms of location, that is, whether the storm was outside the designated vicinity of the lease, and in terms of timing, that is, whether the storm existed within the area at a specific time.

To provide an overview of forecast accuracy for the entire offshore oil and gas leasing area in the Gulf of Mexico, the study by Considine et al. (2003) computes several different summary measures of forecast accuracy that convey essentially the same story. For this article, the false-alarm rate (FAR) is presented because it is a critical piece of information in the valuation of forecasts. This is the proportion of forecast events that fail to occur, that is, the rate of “false positives,” or the probability that a hurricane did not occur given that one was forecast to occur. It is calculated as c/(a + c). It takes values from 0 to 1, with a lower value accompanying a more accurate forecast. The detailed values are displayed in Table 5. As can be seen, FAR increases as the span of the forecast increases and is smaller for 64-kt size parameters than for 50-kt size parameters. This result is consistent, because the 64-kt contour will be smaller than that of the 50-kt one. The FARs increase as forecast range increases and are lower in active hurricane years.

Another method of assessing the accuracy of forecasts is to examine the errors contained in them. Two types of error exist for the forecasts in this study. The first is track error, defined as simply the distance between the actual storm location and the forecast storm location, reported in nautical miles. The other error is in the prediction of peak wind speeds. Some storms that are forecast to be below tropical-storm force may be of hurricane force, or vice versa. This measure is reported as the forecast peak speed minus the observed peak speed. Therefore, a positive value means that the speed was overforecast, and a negative value means too low of a speed was forecast. The reporting unit for this error is knots.

Some summary statistics for the errors of the aggregate storm–forecast dataset are contained in Table 6. The track errors for each year and each forecast type are displayed in Fig. 5. As can be seen from these figures, the track accuracy is increasing, except for a marked increase in errors between 1997 and 2000. The fact that the mean error of the wind speed forecast is near zero merely indicates that forecasts of hurricane wind strength from 1980 to 2000 were, on average, unbiased.

To approximate the Bayesian subjective probabilities, a moving average of probabilities is made to capture decision makers' accumulated knowledge of and changes to forecast accuracy. These probabilities are computed using a cumulative approach. For example, the Bayesian probabilities in 1990 use the counts of observations from 1980 to 1989. For 1991, the counts of observations for 1990 are included. Subsequent years are computed in a similar fashion. These cumulative probabilities appear in Table 7 for the 24- and 48-h forecasts. First of all, notice that the 24-h forecasts have a 63%–65% probability of a strike occurring when one is forecast (Table 7) but the 48-h forecast has only a 25%–28% strike probability when a strike is forecast (see Table 7). There is a gradual improvement in accuracy of no-hit 48-h forecasts (π₂₂) and a steady decline in accuracy of strike forecasts (π₁₁), with the exception of an increase in 1999.

Estimates of forecast value

Evacuation costs for drilling rigs contain a fixed transportation component and the opportunity cost of foregone drilling time, which is the daily cost for the drilling rig services because the oil company is responsible for paying for these services even while on standby. The cost of evacuating production platforms and shutting in production includes the cost of removing personnel from the platforms and the present value of the deferred production of the oil and gas that is not produced during evacuation and shutdown. Procedures for estimating these costs are described by Considine et al. (2003).

While many rigs are built to withstand 100-kt winds, riding out a hurricane on these facilities places workers at considerable peril. Depending upon the location of the storm in relation to the rig, wave and wind interactions can topple a rig even if winds are below this critical threshold. If a facility is toppled with workers on board, considerable loss of life is likely. Nevertheless, these facilities often withstand hurricane strikes, escaping destruction and/or major damage. This durability has not escaped the attention of rig managers. Indeed, there are some managers who decide to remain on rigs during some hurricanes. This behavior suggests that they consider the possibility of complete loss during a hurricane not as a certainty but as a probabilistic event, which is essentially the conditional probability of complete loss given the probability of a hurricane strike.

This probability can be computed by counting the number of rigs lost and dividing by the number of rigs exposed to hurricane-force winds. Estimating this probability is not possible because not all rigs operating during a hurricane will be exposed to hurricane-force winds, given the geographic extent of the drilling area. Instead, our proxy is the probability of rig loss given that a hurricane exists. To estimate this probability, rig losses from strong hurricanes (category 2 or stronger) in the Gulf of Mexico were compiled from 1980 to 2000. Of the 76 strong storms, 10 hurricanes resulted in rig loss, which implies a 0.13 probability for catastrophic loss.

To compute an expected monetary loss, the value of a statistical life (VSL), or the willingness to pay for a given reduction in mortality risk divided by that risk reduction (Krupnick 2002), is needed. In a metaanalysis, Mrozek and Taylor (2002) examine how VSL estimates vary with the level of risk (measured as lives lost per worker population). This effect is particularly relevant for this study because individuals with low risk aversion may require less compensation for higher-risk jobs. Given the likelihood that offshore oil and gas workers come from such a population, the VSL used in this study is $2.275 million, which is the average of two estimates for high-risk occupations.¹⁰ Given this estimate, the probability of rig destruction given a strong hurricane, and the average number of workers on a drilling rig, our potential loss estimate is $16.5 million per drilling rig. The estimated loss for production platforms is computed in a similar fashion, implying a potential loss of $1.5 million per facility.

The estimates of forecast value for drilling rigs varies by rig type, storm, and production location (grid block) and over time. Note that the source of this variation comes from the spatial and temporal variation in the conditional and unconditional probabilities, as well as variation in evacuation costs across rig types over time. The aggregate value of information for drilling rig evacuations in any year is simply the sum over storms, grids, and drilling rigs.

The data supporting estimates of forecast values for production decisions are less detailed, varying by location based upon the number of staffed platforms operating in each MMS region. Although the NHC produces a range of different forecasts, the results presented in Table 8 focus on the 24- and 48-h forecasts, which are commonly employed by rig and production platform managers.

The evaluations use the 50-kt forecast because this is the maximum wind speed for helicopter departure from the rig. For each forecast type, the value of historical information and the value of perfect information are both computed, with the latter calculated by setting π₁₁ = π₂₂ = 1, π₁₂ = π₂₁ = 0, π₁ = π⁽¹⁾, and π₂ = π⁽²⁾.

Estimated values of historical and perfect forecasts, using a VSL of $2.275 million under a range of different costs, appear in Table 8. The standard deviations in Table 8 are computed plus and minus one standard deviation for evacuation durations, which is the primary driver for evacuation costs. The study by Considine et al. (2003) also estimates forecast value assuming a VSL of $6 million and values assuming complete loss, rather than expected losses. The forecast values reported in Table 8 are substantially higher than those using the $6 million VSL. For example, forecast value rises from $0.60 million under the $6 million VSL to $10.5 million under the $2.275 million VSL for the 24-h forecast and from $0.65 million to $7.0 million, respectively, for the 48-h forecast. The cost–loss ratio increases considerably with a lower VSL, and so more observations meet the criterion π₁₂ < C/L < π₁₁ and are included in the calculations. With a higher VSL, evacuation is more likely, and so the value of forecasts is diminished because managers will vacate the rigs under most conditions. As the VSL declines, then the cost of evacuation increases relative to the losses of not evacuating. Under these conditions, forecast value increases because it is now relatively more costly to evacuate.

The value of historical forecasts under the expected loss assumption and $2.275 million VSL ranges from $0.2 million to $28.4 million per year for the 24-h forecast, with a central estimate of $10.5 million per year, and from $0.3 million to $11.1 million per year for the 48-h forecast, with a mean of $7.0 million. Even though these estimates may seem sizeable, they are small in comparison with overall spending in the industry, where one well of medium complexity may cost over $5 million.

The value of perfect forecasts for drilling decisions under the expected loss assumption ranges from $57 million to $199 million per year for the 24-h forecast, with a central estimate of $141 million per year, and from $57 million to $151 million per year for the 48-h forecast, with a mean of $120 million per year. Most meteorologists assume that an accurate long-term forecast is worth more than an accurate short-term forecast. Forecast valuation in this study, however, depends upon the incremental value, in our case in terms of net cost, of decisions based upon the forecast from those based upon historical information. As (7) indicates, this increment is a function of probabilities, costs, and losses. Because the costs and losses are relatively constant across forecasts, the incremental forecast value varies primarily with the historical and forecast probabilities, which differ between forecasts. Hence, the higher value of the 24-h forecast simply reflects relatively greater accuracy. These estimates suggest that perfect hurricane forecast information would be valuable to the oil and gas industry.¹¹

The value of historical forecasts for production decisions under the expected loss assumption and $2.275 million VSL ranges from $0 to $23.8 million per year for the 24-h forecast, with a central estimate of no value, and from $0.6 million to $7.1 million per year for the 48-h forecast, with a mean of $1.1 million. The value of perfect forecasts under the expected loss assumption ranges from $17 million to $270 million per year for the 24-h forecast, with a central estimate of $98 million per year, and from $20 million to $129 million per year for the 48-h forecast, with a mean of $87 million per year.

These values are considerably lower than the value of forecast information for drilling-rig evacuation decisions. The reason again revolves around the relative value of the cost–loss ratio in relation to the critical conditional probabilities. Production decisions have a much lower cost–loss ratio. Even though drilling rigs have more lives at risk, their evacuation costs are relatively larger than production shut-in costs primarily because of the rather substantial opportunity costs from lost drilling time. This situation means that there are relatively fewer instances in which the perceived quality of the hurricane forecast in production shut-in decisions justifies a reversal of decisions based upon historical information alone.

The average combined value of the 24-h forecasts based upon the historical performance is $10.5 million. The average annual values of 48-h forecasts for drilling rigs and production platforms are $7.0 million and $1.1 million, respectively. Because some facilities will rely more heavily on the 24-h forecast than on the 48-h forecast, the combined value to the oil and gas industry of these forecasts would be some kind of weighted sum of $10.5 million and $8.1 million. For simplicity, we did not perform this breakdown.

As expected, the value of forecasts decreases significantly with a decrease in evacuation costs. The value of historical forecast information under the low cost assumption is 2%–4% of the value in the expected cost case (see Table 8). The value of perfect information also declined to 40%–47% of expected loss values. Under higher evacuation costs, the value of historical forecasts increases by 57%–70% and the value of perfect information increases by 26%–40% (see Table 8).

These estimates should be viewed as conservative forecast valuations. In our selection of drilling rigs from the MMS database, only those rigs that are in a drilling mode could be observed. All rigs that are performing completions, are performing work-over operations, are abandoned, or are in transit are not included. For these excluded rigs, location or any of the other necessary criteria to perform a similar value of forecast calculation is unavailable. It is also true that the persons-on-board (POB) figure when rigs are in a nondrilling mode is less than it would be in a drilling mode. Our estimates indicate that approximately 60% of the rigs in the GOM are in a drilling mode at a given moment. Rigs performing these nondrilling operations are more likely to be platform work-over rigs (lower day rates and POB), but this still leaves a considerable number of rigs whose location, description (rig type), and POB at the time of the hurricane are unknown. Given these gaps in the available data, a quantitative estimate for the value of forecasts for these rigs was not attempted.

The results illustrate the nonordinal, discontinuous nature of the decision model. For example, unlike the drilling case, the value of the 24-h mean historical forecast for production shut-in decisions is lower than the value of the 48-h forecast (see Table 8). Forecasts only have value if the following condition is satisfied: π₁₂ < C/L < π₁₁. In almost every case in our set of production decisions, the C/L ratio is below π₁₂. For every instance in the 24-h case, this condition is violated. For almost every instance in the 48-h case this is also true, except for MMS region 6. In this case, the inequality conditions are met, but only for one reason. For this MMS district, there were no false negatives from 1985 to 1998. That is, under no instance did a hurricane strike a block when no hurricane was forecast. This fact is largely due to the small number of hurricanes that made it into the western gulf in that period. Hence, π₁₂ is zero for MMS region 6, and this condition is what causes the inequality conditions to be met.

In this rare case, 48-h forecasts were more valuable because they were more accurate than 24-h forecasts. In 1988, in the 48-h forecast for all grid blocks in MMS, there were 6 true positives and 16 false positives, but no false negatives. For the 24-h forecasts for the same storm and same region, there were 4 true positives, 18 false positives, and (critical) 2 false negatives.

The final forecast scenario is a 50% improvement in 48-h forecast accuracy. In this case, our assumption is that the strike probability given a strike forecast, π₁₁, roughly doubles to 0.60. To maintain consistency with the other probabilities, π⁽¹⁾, π₁₂, and π₂₂ are set to their historical means and π₁ is solved using π⁽¹⁾ = π₁π₁₁ + π₂π₁₂. The values for this forecast scenario appear in the middle of Table 9. In this case, a 50% improvement in the accuracy of the 48-h forecast, assuming a VSL of $2.275 million, would increase value from $8.2 million to $23.7 million for an incremental value of more than $15 million. The incremental value is only $2.2 million with a VSL of $6 million. This diminishing marginal value of forecast information suggests that perceived losses, in this case approximated by VSL, or risk aversion may be an important factor in the value of hurricane forecast information. In other words, if losses are perceived to be very substantial, producers will always take preventive action regardless of evacuation costs. Last, the nonlinear nature of the forecast value is illustrated by the perfect forecast scenarios, which suggest that potential marginal benefits from perfect information would be $200 million per year with a VSL of $2.275 million and roughly $240 million with a VSL of $6 million.

Conclusions

The Gulf of Mexico is becoming an increasingly important component of America's energy production portfolio and is on the front line of hurricane hazards. This study adapts a classic cost–loss decision model to estimate the value of hurricane forecasts to these producers. This application is unique because it is focused on a specific industry with direct estimates of the cost of evacuation and the potential losses from not evacuating. This model also requires historical and conditional probabilities of events and forecasts, which we compute for every oil and gas lease area in the gulf since 1980. Our analysis provides estimates of probabilities of hurricane strikes (misses) given strike and no-strike forecasts.

Our analysis indicates that the value of pre-2000 hurricane forecast information to the oil and gas industry is $10.5 million and $8.1 million for 24- and 48-h forecasts, respectively, both of which are substantially more than the $4.4 million annual operating budget of the National Hurricane Center. This information clearly generates benefits to many other sectors of the economy, which, when combined with the results of this study, suggests that the social net rate of return from hurricane forecasts is likely to be substantial. Current techniques for remote sensing, observational network design, data assimilation, and dynamical/statistical modeling of the atmosphere are crude. Well-focused investments in endeavors to increase the accuracy of these techniques and/ or the core meteorological observing and remote sensing network could significantly improve hurricane forecasts. This study provides evidence from one industry on the potential benefits of such investments. The incremental annual value of benefits to the oil and gas industry from a doubling of the accuracy of hurricane forecasts is approximately $15 million. Such an improvement in hurricane forecasts would no doubt generate value to other industries. In summary, the economy clearly would be well served by improved hurricane forecasts.