1. Introduction
a. Impacts of temperature on aviation performance
High air temperature and dewpoint temperature combined with high altitude are a dangerous combination for aircraft performance. As temperature, dewpoint temperature, and altitude increase, the air becomes less dense. An air density that is reduced translates to a high density altitude (DA) [Federal Aviation Administration (FAA) 2008]. The density of the air has a pronounced effect on aircraft and engine performance. Regardless of the actual altitude at which the aircraft is operating, it will perform as though it were operating at an altitude equal to the existing DA (FAA 2016).
High DA impacts aircraft performance in the following ways: reduction in power because the engine takes in less air, reduction in thrust because a propeller is less efficient in thin air, and reduction in lift because the thin air exerts less force on the airfoils (FAA 2016; Reynolds 2012). These impacts are not trivial and can be catastrophic (FAA 2008).
1) Aircraft performance impacts—fixed wing
For fixed wing, high DA affects the ability of an aircraft to land and/or take off within a very short distance. This is an important impact to factor into military mission planning for operations in locations with limited resources and harsh flying conditions.
Aircraft performance impacts due to increased DA fall mainly into the following categories: decreased maximum takeoff weight and increased takeoff and landing distance (National Research Council 2008; Brandt et al. 2004). Additionally, high DA negatively affects an aircraft’s ability to carry heavy payloads, to fly at high altitudes at fast speeds, and/or to travel long distances—all essential mission capabilities. Specific aircraft performance impacts are identified through flight test data and recorded in pilot operator’s handbook with performance charts. To keep this research unclassified, we used the following general aviation (GA) rules of thumb to illustrate specific aircraft performance thresholds due to increased DA:
Gross weight: There will be a 3.5% reduction in engine horsepower for every 1000-ft (1 ft = ~0.3 m) increase in DA (Hoover 2010; Collins 2016; Hudson 2015).
Takeoff distance: For every 1000-ft increase in DA, there will be a 10% increase in takeoff distance (Hudson 2015; Cutler 2020).
Landing distance: For every 1000-ft increase in DA, the landing distance will increase by 3.5% (Hurt 1965; FAA 2016).
2) Aircraft performance impacts—rotary wing
Increased DA has two impacts on rotary-wing performance: reduced engine power (horsepower) and reduced rotor efficiency (lift) (FAA 2012; Civil Aviation Authority of New Zealand 2020). These impacts translate into the following performance impacts: reduced power margin, reduced maximum takeoff weight (MTOW), reduced hover ceiling and reduced rate of climb. As with fixed wing, specific aircraft performance impacts are identified through flight test data and recorded in pilot operator’s handbook through performance charts. However, unlike fixed wing, there are no GA rules of thumb to demonstrate DA impact in an unclassified format. Therefore, we developed a power margin methodology to illustrate a DA threshold translated to a rotary-wing performance threshold.
For rotary-wing aircraft, high DA decreases engine power margin. The following examples illustrate the serious consequences that can result from reduced power: 1) A vortex ring state can occur during takeoff when less power is available than expected and the helicopter sinks unexpectedly (Tucker 2015). 2) Overpitching occurs when the power required for takeoff is greater than what the engine can deliver. A reduction in rotor revolutions per minute (rpm) occurs, and sometimes this situation may not be recoverable (Civil Aviation Authority of New Zealand 2020). 3) Loss of tail rotor effectiveness (LTE) is experienced as the increased power required to hover at higher DA produces more torque, which means more antitorque thrust is required, and the tail rotor thrust may not be sufficient to maintain directional control. In some helicopters during high-altitude operations, the maximum antitorque produced by the tail rotor during a hover may not be sufficient to overcome torque even if the gross weight is within limits (FAA 2012; Broderick 2013; FAA 1995).
Power margin is defined as power required minus power available (FAA 2012). Because power margin is often small for rotary wing, DA is extremely important to helicopter pilots because there is far less room for error (Civil Aviation Authority of New Zealand 2020). Of all the U.S. Army helicopter crashes from 2002 through 2011, about 20% could be attributed to enemy fire. The other 80% were attributed to pilot error (Darack 2014). A power margin of zero means that even a slight change in wind direction can flip the power margin into the negative range and cause a helicopter to stall (Darack 2014).
The power available was determined by calculating the engine power due to decreased air density using the GA rule of thumb for engine horsepower: for every 1000-ft increase in DA, the engine horsepower is reduced 3.5% (Hoover 2010; Collins 2016; Hudson 2015). The power required was determined by using Froude’s momentum theory (actuator disk theory) and incorporating the reduced air density in lift calculations (Froude 1889). The power margin was calculated as the difference between power available and power required. This power margin was then compared with power margin under International Standard Atmospheric (ISA) conditions (pressure of 1013.25 hPa, 15°C, and no dewpoint temperature), and the percent decrease in power margin was calculated.
b. DA
DA is formally defined as pressure altitude corrected for nonstandard temperature variations (FAA 2008, 2014). Under standard atmospheric conditions, air at each level in the atmosphere has a specific density and pressure altitude and density altitude identify the same level. DA is the vertical distance above sea level in the standard atmosphere at which a given density is to be found (FAA 2008). There are three important factors that contribute to high DA:
Altitude: The higher the altitude is, the less dense is the air.
Temperature: The warmer the air is, the less dense it is. When the temperature rises above the standard temperature for a particular place, the density of the air in that location is reduced, and the DA increases.
Humidity: An increase in the amount of water vapor in the air leads to a decrease in air density, which in turn leads to an increase in the DA (FAA 2016; Guinn and Barry 2016)
Although the importance of accurate DA calculations is well known among aviators, most introductory pilot training manuals fail to address the impact that atmospheric humidity has on the results (Guinn and Barry 2016). The published performance criteria in the “Pilot’s Operating Handbook” (POH) are generally based on ISA conditions at sea level (59°F/15°C and 29.92 in. Hg/1013.25 hPa) without consideration of dewpoint temperature (FAA 2008). The calculation of DA for aircraft performance charts or manual flight computers only requires knowledge of the pressure altitude and the air temperature (Guinn and Barry 2016). Most introductory pilot training manuals do not address the impact of humidity. In fact, much of aviation literature (FAA 1975, 2014; U.S. Air Force 1997; FAA 2016) does not address the impact of dewpoint temperature on DA calculations at all (Guinn and Barry 2016). However, the importance of accurate calculations of DA is deemed such an integral part of flight planning that moist DA must be considered. Climate change increases this importance of considering dewpoint temperature in DA calculations as described below.
Dry DA and moist DA
Although it does not have as great of an impact on performance as altitude and temperature, humidity does affect the way planes fly. When air is humid, it is actually less dense than dry air. Furthermore, warmer temperatures allow for greater dewpoint temperature values. While there is no rule of thumb or performance chart that is currently used in professional aviation to compute the effects of humidity on DA, it must be taken into consideration as a decrease in overall performance in high humidity conditions can be expected (FAA 2016). Guinn and Barry summarize in their research that the effect of temperature on DA is 10 times the rate of change of density altitude due to humidity (measured by dewpoint temperature). However, they conclude that because of the importance of DA to flight safety, and the criticality of the accurate calculation of DA as an integral part of flight planning, the effect of humidity on DA can be operationally significant especially in high dewpoint temperature environments (Guinn and Barry 2016).
c. Current understanding
Research studying the impact that rising air temperatures due to climate change will have on aviation is scarce. The impact of extreme temperatures on commercial fixed-wing aircraft performance has been analyzed with emphasis on maximum takeoff weight restrictions and resulting airport restrictions (Coffel and Horton 2015; Coffel et al. 2017). While this research does introduce some of the performance impacts of rising temperature to aviation, several gaps remain. This research considered commercial jet airliners, while additional fixed-wing aircraft types and rotary-wing aircraft still need to be examined. Additionally, the impacts of moist DA, which captures the effect of rising dewpoint temperature, that must be considered along with rising maximum air temperatures needs to be addressed and researched. Furthermore, a method needs to be developed for utilizing moist DA and aircraft performance thresholds as indicators that can capture the risk probability of multiple aviation performance impacts. Also, a method that enables the assessment of climate change vulnerabilities of both fixed- and rotary-wing aircraft, for selected geographic sites, time periods, emissions scenarios, and performance impacts for decision-making needs to be developed. Previous work has analyzed the impacts of climate variability on seasonally averaged DA as a function of El Niño–Southern Oscillation and the Arctic Oscillation (Goodman and Small Griswold 2018). However, the impacts of climate change on multiple variables such as air temperature, monthly station pressure, and dewpoint temperature that are key components of DA projections needs further work. Additionally, projected DA trends with specified climate change scenarios needs to be analyzed. Finally, previous work has been done that has looked at the importance of including dewpoint temperature in DA calculations (Guinn and Barry 2016). Combining this finding with the projected increases in both maximum air temperature Tmax and dewpoint temperature, using minimum air temperature Tmin as a surrogate can be utilized further in climate change impact analysis. Additionally, applying projected increases in moist DA due to climate change into a vulnerability assessment of aviation performance needs to be researched.
2. Data description
This research is intended to support decision-making for aircraft acquisition within the U.S. Department of Defense. The geographic site selected for this research effort is Little Rock Air Force Base (AFB), Arkansas (34.9375°N, 92.1875°W). This installation site was chosen because of the moderate nature of both altitude and temperature extremes that allowed a manageable in-depth analysis of all temperature variance. Additionally, Little Rock AFB is home to the largest fleet of C-130 airplanes in the world and therefore has significant operational relevance (Sharp 2018). For Little Rock, Arkansas (34.44°N, 92.13°W), the annual precipitation is 74.9% of the annual potential evapotranspiration; therefore, as described above, Tmin can be used as a surrogate for dewpoint temperature without the need for the evapotranspiration factor formula (Kimball et al. 1997).
The Climate and Hydrology Projections (DCHP) data archive from phase 3 of the downscaled Coupled Model Intercomparison (CMIP3) and phase 5 of CMIP (CMIP5) was chosen for the observed and projected temperature data. This archive content is based on global climate projections from the World Climate Research Programme’s CMIP5 multimodel dataset that informed the Intergovernmental Panel on Climate Change (IPCC) Fifth Assessment (Maurer et al. 2007; Brekke et al. 2013). This data archive contains fine-spatial-resolution translations of climate projections over the contiguous United States. The downscaled climate projections of ⅛° latitude–longitude spatial resolution were selected. One grid cell was selected for this site because it best captured the proximity to the runway and did not introduce any mountains or lakes/rivers in the temperature collection as these both can skew the temperature data (Maurer et al. 2002). Because of the interest in the variability of temperature on a daily occurrence, the downscaling technique selected was the daily bias correction with constructed analogs (BCCA) (Maurer et al. 2010).
The general circulation models (GCMs) selected for this research are shown in Table 1. As in the IPCC Fifth Assessment Report (AR5; IPCC 2013), the model selection was purely democratic, in that all models were given the same weight. This democratic selection is one of the most often used strategies in quantifying uncertainty based on multimodel ensembles (Zubler et al. 2016).
GCMs used for this research effort; ID is the identifier. Expansions for model names can be found online (https://www.ametsoc.org/PubsAcronymList).
3. Method and results
a. Calculation of Tmax and Tmin
1) Method
The selected time periods for initial analysis and comparison of Tmax and Tmin variables are as follows: observed (historical) time period of 1970–99; near-term projected time period of 2020–39, as because this time period captures aircraft already in operational use; midterm projected time period of 2040–69, because this time period captures aircraft currently in the design phase; and far-term projected time period of 2060–89, because this time period captures next-generation aircraft that would currently be in the research and development phase.
Representative concentration pathways (RCPs) are four greenhouse gas concentration trajectories adopted by the IPCC for its AR5 in 2014 (Moss et al. 2008). The four RCPs—RCP2.6, RCP4.5, RCP6.0, and RCP8.5—are named after a possible range of radiative forcing values in the year 2100 relative to preindustrial values (+2.6, +4.5, +6.0, and +8.5 W m−2, respectively) (Weyant et al. 2009). The RCP selected for this research effort was RCP8.5 and was chosen to show the maximum potential climate stress to the selected installation site.
2) Results
Tmax and Tmin have a direct impact on DA as discussed in section 2a. To gain essential insight into the characteristics of these variables from both a historical and projected perspective, the monthly means for both Tmax and Tmin were analyzed for each time period (including the observed time period) using each of the 20 GCMs. To ensure the downscaled bias correction used in the DCHP archive was accurate and that no further bias correction was needed, the modeled temperature data from the 20 GCMs for the observed period of 1970–99 was compared with the observed data for this same time period (1970–99). Figure 1a captures the 20 GCMs combined monthly mean Tmax for observed with a 95% confidence interval (standard deviation of ±0.26). Figures 1b–d illustrate individual GCM projections for Tmax for each time period 2020–49 (standard deviation of ±0.68), 2040–69 (standard deviation of ±0.88), and 2060–89 (standard deviation of ±1.14). Figure 2 captures this same information for Tmin. Figure 2a illustrates the 20 GCMs combined monthly mean Tmin for observed with a 95% confidence interval (standard deviation of ±0.21). Figures 2b–d illustrate individual GCM projections for Tmin for each time period 2020–49 (standard deviation of ±0.0.53), 2040–69 (standard deviation of ±0.66), and 2060–89 (standard deviation of ±0.89).
(a) Mean monthly Tmax for Little Rock AFB using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval. Mean monthly Tmax for (b) 2020–49, (c) 2040–69, and (d) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Mean monthly Tmax for Little Rock AFB using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval. Mean monthly Tmax for (b) 2020–49, (c) 2040–69, and (d) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Mean monthly Tmax for Little Rock AFB using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval. Mean monthly Tmax for (b) 2020–49, (c) 2040–69, and (d) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Mean monthly Tmin for Little Rock AFB using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval. Mean monthly Tmin for (b) 2020–49, (c) 2040–69, and (d) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Mean monthly Tmin for Little Rock AFB using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval. Mean monthly Tmin for (b) 2020–49, (c) 2040–69, and (d) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Mean monthly Tmin for Little Rock AFB using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval. Mean monthly Tmin for (b) 2020–49, (c) 2040–69, and (d) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
b. Calculation of DA—Frequency of occurrence
1) Method
As mentioned earlier, moisture content, or Tmin in this case, must be included in DA calculations (Guinn and Barry 2016). Therefore, it is important to understand the dynamics of Tmin projections, that are the surrogate for dewpoint temperature in the DA calculations. To illustrate the scope of effects that the rising Tmin and Tmax temperature projections shown in section 2c will have on aircraft performance, the frequency of occurrence of both Tmax and Tmin and the combination of these two variables was analyzed. To keep the quantity of days in the time periods consistent between observed and modeled, the observed time period used for this next analysis was 1970–99. This enables the quantity of climate data (10 957 data points) to remain constant when comparing observed to projected time periods.
As noted in Eq. (2), in addition to temperature and humidity, DA is also affected by station pressure. Station pressure is defined as the pressure that is observed at a specific elevation and is the true barometric pressure of a location. It is the pressure exerted by the atmosphere at a point as a result of gravity acting upon the “column” of air that lies directly above the point (NOAA 2020). The DCHP site used in this research for projected Tmax and Tmin values does not project hourly downscaled, bias-corrected sea level pressure or station pressure. Therefore, for this case study, a monthly mean station pressure for Little Rock Arkansas was used to approximate this variable (NCEI 2017). Using a monthly mean station pressure does introduce uncertainty in the calculation of DA. To examine the significance of this uncertainly, we compared DA calculations using two methods: observed Tmax, dewpoint temperature, and station pressure (method 1) and observed Tmax, Tmin, and mean monthly station pressure (method 2) for the months of June, July, and August 2010 at a set time of day: 1500 local solar time (LST).
2) Results
DA calculation resulted in the following monthly mean DA (ft) showing method 1 and method 2, respectively; June: 2871, 2929 (standard deviation of ±41); July: 2796, 2837 (standard deviation of ±29); and August: 3012, 3057 (standard deviation of ±32). The complete observed period of 1970–99 could not be examined as NCEI does not have recorded station pressure data for Little Rock Arkansas from 1971 to 2005. However, although these data represent only a subset, these results do show a statistical similarity and warrant justification to examine a complete 30-yr time period. Furthermore, these results support that Tmax is the strongest contributor to DA and using Tmin as a surrogate for dewpoint temperature and monthly station pressure does add a measurable but acceptable amount of uncertainty.
Figure 3 illustrates the mean frequency of occurrence (in number of days) for daily Tmax and daily Tmin, respectively, for observed (1970–99), 2020–49, 2040–69, and 2060–89 time periods using the 20 GCMs shown in Table 1 with a 95% confidence interval. Figure 3a shows the composition of Tmax changes dramatically as early as 2020–49 with the Tmax occurring with most frequency rising 5°C above observed (from 29° to 34°C). This figure clearly demonstrates a shift to a higher Tmax occurring with increasing frequency. For example, in 2060–89, the most frequent projected Tmax of 36°C illustrates a 160% increase relative to the observed time period (from 191 to 496 days). Similarly, Fig. 3b illustrates an even more dramatic shift to a higher Tmin occurring with increasing frequency. For example, in 2060–89, the most frequent Tmin of 25°C illustrates an 1194% increase relative to the observed time period (from 50 to 647 days). Figure 3 illustrates how both Tmax and Tmin are shifting with climate change projections and because both variables affect DA in combination, these projections need to be understood and analyzed.
(a) The Tmin frequency of occurrence in mean number of days, Little Rock AFB, and RCP8.5 with 95% confidence interval. The graph starts at 25°C to see more clearly the temperatures at which the highest frequency occurs. (b) The Tmax frequency of occurrence in mean number of days, Little Rock AFB, and RCP8.5 with 95% confidence interval. Graph starts with 13°C to see more clearly the temperatures at which the highest frequency occurs.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) The Tmin frequency of occurrence in mean number of days, Little Rock AFB, and RCP8.5 with 95% confidence interval. The graph starts at 25°C to see more clearly the temperatures at which the highest frequency occurs. (b) The Tmax frequency of occurrence in mean number of days, Little Rock AFB, and RCP8.5 with 95% confidence interval. Graph starts with 13°C to see more clearly the temperatures at which the highest frequency occurs.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) The Tmin frequency of occurrence in mean number of days, Little Rock AFB, and RCP8.5 with 95% confidence interval. The graph starts at 25°C to see more clearly the temperatures at which the highest frequency occurs. (b) The Tmax frequency of occurrence in mean number of days, Little Rock AFB, and RCP8.5 with 95% confidence interval. Graph starts with 13°C to see more clearly the temperatures at which the highest frequency occurs.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Because DA is affected by the combination of Tmax and Tmin, the relationship of these climate variables and how this relationship is projected to change needs to be clearly understood. For example, for the historical period of 1970–99, the Tmax/Tmin combination that occurred most frequently was 29° and 19°C, respectively. For the time period of 2020–49, the Tmax/Tmin combination projected to occur most frequently rises to 34° and 22°C; for 2040–69, this combination rises further to 35° and 23°C; and finally, for the 2060–89 period, the Tmax/Tmin combination that is projected to occur most frequently is 36° and 24°C, respectively. This illustrates how both Tmax and Tmin are projected to rise simultaneously. An awareness of the combinations of Tmax and Tmin is key when understanding how higher DA and therefore greater impact to aircraft performance is projected to occur.
c. DA thresholds
1) Method
A useful way to illustrate the probability of DA impacts is to establish thresholds. In this manner, a defined DA (in ft) can be used as a “bar” or “gate” to determine when this parameter will be surpassed. A DA threshold can be defined simply as a numerical value (e.g., DA > 1000 ft, DA > 2000 ft, DA > 3000 ft). Or a DA threshold can be defined as a specific aircraft performance [e.g., DA = 5000 lb (1 lb = ~0.45 kg) weight reduction]. The concept of using a specific aircraft performance threshold is discussed further in section 5. The annual average station pressure for Little Rock AFB for the time period of 1983–2012 was 1004.65 ± 1.92 hPa. This time period is used by NCEI as their 30-yr station pressure data for Little Rock AFB and the only time period available for these data. The monthly mean station pressure was used for the corresponding monthly DA calculations (NCEI 2017).
2) Results
The Tmax required to reach a specific DA threshold is lowered when dewpoint temperature is considered. Table 2 illustrates this point and shows the Tmax that is necessary to attain a specified DA threshold when 1) dewpoint temperature is not considered (Tmax alone) and when 2) dewpoint temperature is considered (Tmax and Tmin combination). Every increase in DA impact aircraft performance in a negative way as discussed in section 1a. The performance impact of a certain increase in DA is specific to each type of aircraft yet impacts all aircraft. This example is for Little Rock Air Force Base, with an estimated annual station pressure of 1003 mb. Identifying all the combinations of Tmax and Tmin for a specific DA threshold is certainly more labor intensive than just using Tmax alone; however, it is key that dewpoint temperature (Tmin) be considered in DA projections to ensure the full spectrum of projected performance impacts is captured.
Comparison of Tmax alone and Tmax/Tmin combination required to reach specific DA thresholds (ft) for Little Rock AFB using an estimated annual mean station pressure of 1003 hPa.
Including dewpoint temperature in DA calculations enables a more accurate projection of the frequency of occurrence of surpassing specific DA thresholds. This concept can be illustrated by comparing frequency of occurrence of dry DA to moist DA for various DA thresholds. To keep the quantity of days in the time periods consistent between observed and modeled, the observed time period used for this analysis was 1970–99. This enables the number of climate data points to remain constant when comparing observed to projected time periods. It should be noted that the correlation of GCMs modeled observed temperature data to observed temperature data is lower when translating these data to a frequency of occurrence measurement. This uncertainty is acknowledged; however, this variation in correlation does not negate the overall proposed method and can be incorporated into the framework to improve and refine accuracy.
Observed and modeled Tmax, observed and modeled Tmin as a surrogate for dewpoint temperature and mean monthly station pressure for Little Rock AFB are used to show a summary in Table 3 of the mean number of days surpassing a DA threshold for observed (1970–99), and also the increase in frequency when comparing projected time periods to observed. The italicized cells show the greatest increase in frequency of surpassing the DA threshold when compared with observed. It is interesting to note that this increase in frequency occurs in various different months and includes some of the “cooler” months like October and November. This is of interest because a decision-maker or mission planner might not consider the cooler months to have any significance regarding DA impact to aircraft performance, yet these months still warrant monitoring. This increase in frequency can be attributed to the significant rise of projected Tmin in the cooler months as discussed in section 2c and by taking dewpoint temperature into consideration. As mentioned, each DA threshold represents a negative impact to aircraft performance and the operational significance of the impact of each DA increase is specific to the exact type of aircraft.
Summary of months and mean number of days surpassing DA threshold for observed data (1970–99), and increase in frequency when compared with observed data. The italics are explained in the text.
Table 4 illustrates how the difference in frequency of occurrence compared between dry and moist DA. These calculations use Tmax, Tmin, and mean monthly station pressure for Little Rock AFB. Here again, it shows that nonsummer months show an increase in frequency in occurrence of surpassing each DA threshold. Aviation planners may only focus on the summer months to analyze increased DA; however, incorporating dewpoint temperature into DA demonstrates how even moderate months like October, November, and March do show increases when comparing dry to moist DA. Therefore, moist DA should be the default calculation for any and all aircraft performance assessment as it shows the complete spectrum of impact and gives important insight into the changing landscape of DA increases due to climate change.
Frequency of occurrence in mean number of days of dry and moist DA thresholds, with 95% confidence interval.
DA thresholds combined with frequency of occurrence as introduced is especially useful when translating the projection of rising DA into a meaningful metric for assessing risk. Figure 4 illustrates this application and shows the mean frequency (in percent of time period) that surpass specific DA thresholds for observed and projected time periods for Little Rock AFB, with RCP8.5 with a 95% confidence interval. To further help translate the projected rise in DA into a more meaningful format to assist with risk assessment in decision-making, the frequency of occurrence can be translated from mean number of days to a percent of a time period. This method of data representation allows the decision-maker to more easily correlate the probability of occurrence to a time frame of potential mission impact.
Percent of time period that defined moist DA thresholds are surpassed for Little Rock AFB using monthly average station pressures, the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Percent of time period that defined moist DA thresholds are surpassed for Little Rock AFB using monthly average station pressures, the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Percent of time period that defined moist DA thresholds are surpassed for Little Rock AFB using monthly average station pressures, the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
This frequency of occurrence data can now be plotted as a cumulative distribution function that enables a decision-maker to visualize how a specific percentage of time period will (or will not) be impacted in future scenarios. For example, a decision-maker might consider an event that occurs 80% of a time period as a high risk. Figure 5 shows how the number of days can be directly translated to a percent of occurrence (e.g., 80% of 30-yr time period = 8766 days). Figure 5 shows a specified 80% of time period superimposed over data results for mean frequency of occurrence (number of days) for a specified performance impact, in this case a DA threshold of ≥ 500 ft. This illustrates the first step in translating a projected increase in frequency of occurrence (future time periods) of a performance impact (DA ≥ 500 ft) to a decision-maker’s defined risk threshold (80% of time period).
Cumulative distribution function plot of frequency of occurrence (in number of days) for a DA threshold of 500 ft with a specified 80% of time period superimposed for Little Rock AFB using the 20 GCMs identified in Table 1, with RCP8.5 (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Cumulative distribution function plot of frequency of occurrence (in number of days) for a DA threshold of 500 ft with a specified 80% of time period superimposed for Little Rock AFB using the 20 GCMs identified in Table 1, with RCP8.5 (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Cumulative distribution function plot of frequency of occurrence (in number of days) for a DA threshold of 500 ft with a specified 80% of time period superimposed for Little Rock AFB using the 20 GCMs identified in Table 1, with RCP8.5 (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
d. Risk assessment matrices
1) Method
This same information can be displayed in a risk probability matrix. The horizontal axis represents specific DA thresholds, and the vertical axis represents a selected percentage of time period (numbers of days). The colors represent the percent of GCMs that project this specific DA threshold will be surpassed. surpass the specified threshold. For example, a red-colored cell represents that 100% of the 20 GCMs agree this DA threshold will be surpassed. Similarly, a green-colored cell represents that none (0%) of the GCMs project this DA threshold will be surpassed.
2) Results
Figure 6a shows the risk probability matrix chart for the mean annual DA for Little Rock AFB with RCP8.5, using average monthly station pressures, with the x axis representing DA thresholds of ≥ 500 ft through ≥ 4000 ft in 500 ft increments periods, and the y axis representing a percentage of 30-yr annual time period of observed (1970–99). Figures 6b–d show the results for the time periods of 2020–49, 2040–69, and 2060–89, respectively.
Risk probability matrix for DA thresholds at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and monthly average station pressures for (a) observed (1970–99), (b) 2020–49, (c) 2040–69, and (d) 2060–89 (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Risk probability matrix for DA thresholds at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and monthly average station pressures for (a) observed (1970–99), (b) 2020–49, (c) 2040–69, and (d) 2060–89 (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Risk probability matrix for DA thresholds at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and monthly average station pressures for (a) observed (1970–99), (b) 2020–49, (c) 2040–69, and (d) 2060–89 (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Similarly, a monthly risk probability matrix can also be established. The capturing of these data in a monthly perspective can give a decision-maker insight into how each month is projected to change and more importantly it highlights the months that show a significant increase in a DA threshold being surpassed. Figure 7 shows risk probability matrices for Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5 and using mean monthly station pressure. It is interesting to note that Fig. 7a shows that for a DA ≥ 1000 ft threshold, the month of November and the frequency of occurrence (represented by the y axis) rises from an occurrence of 20% of the time period (180 days) for the observed time period to a projected occurrence of 70% (630 days) in 2060–89. Similarly, for a DA ≥ 2000 ft threshold, Fig. 7b shows that for the month of May the frequency of occurrence (y axis) rises from an occurrence of 40% for the observed time period (372 days) to a projected occurrence of 90% (837 days) in 2060–89. These examples illustrate how monthly insight is key because a decision-maker might not think that a month in the winter season (November) or spring (May) would need to be addressed in terms of aircraft performance and increased DA. A decision-maker could also combine the months to display seasonal summaries or semiannual summaries or to compare a specific DA threshold in multiple months. This is illustrated in Figs. 8a–c, which show a DA ≥ 3000 ft threshold for the summer months June, July, August, respectively. These results clearly illustrate the versatility of this method and the increased insight gained from assessing monthly risk probability versus an annual assessment of risk probability. The significant increase in probability of surpassing a DA threshold within specific months and time periods is essential to good decision-making and critical to mission planning.
Risk probability matrix for DA threshold of (a) 1000 ft for November and (b) 2000 ft for May at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and mean monthly station pressure.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Risk probability matrix for DA threshold of (a) 1000 ft for November and (b) 2000 ft for May at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and mean monthly station pressure.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Risk probability matrix for DA threshold of (a) 1000 ft for November and (b) 2000 ft for May at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and mean monthly station pressure.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Risk probability matrix for DA threshold of 3000 ft for (a) June, (b) July, and (c) August at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and mean monthly station pressure.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Risk probability matrix for DA threshold of 3000 ft for (a) June, (b) July, and (c) August at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and mean monthly station pressure.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Risk probability matrix for DA threshold of 3000 ft for (a) June, (b) July, and (c) August at Little Rock AFB, using the 20 GCMs identified in Table 1, RCP8.5, and mean monthly station pressure.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
e. Performance impacts and risk assessment examples
1) Fixed wing
(i) Method
The C-130J was used to illustrate specific fixed-wing aircraft performance impacts. The C-130 J is a military transport aircraft with four turboprops (Rolls-Royce AE2100D3, 4591 shaft horsepower turboprop engine), has a maximum takeoff weight of 164 000 lbs and maximum payload of 42 000 lbs (Lockheed Martin 2015). Little Rock AFB has an assault strip runway with a distance of 3499 ft that C-130’s use to practice short landing and takeoffs. Note: the rules of thumb for general aviation were applied to the C-130J for example purposes only. This enables all results to remain unclassified and serves solely to show an application of the method.
(ii) Results
Using the GA rules of thumb, the following aircraft performance DA thresholds were estimated: DA threshold 1 = 5000-lb payload reduction; DA threshold 2 = takeoff distance > assault strip; DA threshold 3 = 10 000-lb payload reduction; DA threshold 4 = 15 000-lb payload reduction; DA threshold 5 = 20 000-lb payload reduction. Note that these DA thresholds and corresponding performance thresholds were chosen as they are feasible to occur at Little Rock AFB airport (using GA rules of thumb). This example illustrates that not every airport will experience the full spectrum of potential performance impacts. This method helps determine which performance thresholds will not occur at specific airport infrastructures (i.e., runways are long enough to accommodate all DA threshold possibilities). The DA threshold for a C-130J to overshoot landing on the main runways was extremely high and would never be surpassed at Little Rock AFB. Therefore, landing performance impact was not captured in this specific example. Figure 9 shows the mean frequency as a percentage of time period and uses these aircraft specific performance thresholds.
Percent of time period that defined aircraft performance thresholds are surpassed for a C-130J at Little Rock AFB using an annual station pressure of 1003 hPa, using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Percent of time period that defined aircraft performance thresholds are surpassed for a C-130J at Little Rock AFB using an annual station pressure of 1003 hPa, using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Percent of time period that defined aircraft performance thresholds are surpassed for a C-130J at Little Rock AFB using an annual station pressure of 1003 hPa, using the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval (McRae 2018).
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Furthermore, these DA thresholds that correlate to a specific aircraft performance impact can also be used to develop a risk probability matrix. Figures 10 and 10b illustrates risk probability matrices using the aircraft performance thresholds for the C-130J for the time periods 2020–49 and 2060–89, respectively.
(a) Risk probability matrix for estimated C-130J aircraft performance thresholds at Little Rock AFB using mean station pressure of 1003 hPa, the 20 GCMs identified in Table 1, and RCP8.5 for 2020–49 and (b) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Risk probability matrix for estimated C-130J aircraft performance thresholds at Little Rock AFB using mean station pressure of 1003 hPa, the 20 GCMs identified in Table 1, and RCP8.5 for 2020–49 and (b) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
(a) Risk probability matrix for estimated C-130J aircraft performance thresholds at Little Rock AFB using mean station pressure of 1003 hPa, the 20 GCMs identified in Table 1, and RCP8.5 for 2020–49 and (b) 2060–89.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Correlating a DA threshold to a specific aircraft performance impact can enable a decision-maker to make a direct translation of a projected warming climate to a potential mission impact. Identifying operational impacts through the use of DA thresholds further assists the decision-maker in identifying and assessing potential performance vulnerabilities of specific aircraft, both fixed and rotary wing, in specific geographic locations. Interpreting a risk probability matrix by illustrating the specific aircraft performance impacts gives a decision-maker another tool to identify mission vulnerabilities and assess aircraft capabilities to best meet the mission needs and challenges.
2) Rotary wing
(i) Method
To illustrate this method on a rotary-wing aircraft, a UH-60L Black Hawk helicopter with two T700-GE-701D engines, with an assumed 100% (maximum) revolutions per minute (rpm) and a maximum gross weight = 22 000 lbs was used (Lockheed Martin 2016; General Electric 2014). As with the fixed wing, specific impacts due to increase DA for every type of rotary aircraft are known and documented; however, to keep information unclassified and for general use only, GA rules of thumb were applied to the UH-60L in this research for illustration purposes only.
(ii) Results
Table 5 shows the results of moist DA thresholds and corresponding power margin percent decrease from power margin under ISA conditions.
Moist DA thresholds and corresponding percent decrease in power margin relative to power margin at ISA conditions for UH-60L at 100% rpm with a maximum gross weight of 22 000 lbs at Little Rock AFB with RCP8.5.
Figure 11 shows the frequency of occurrence (percent of time period) surpassing each of these aircraft specific performance thresholds for the UH-60L for Little Rock AFB, RCP8.5. As discussed earlier, correlating a DA threshold to a specific aircraft performance impact can enable a decision-maker to make a direct translation of a projected warming climate to a potential mission impact.
Mean frequency in percent of time period that aircraft performance thresholds are surpassed for a UH-60L with a maximum gross weight of 22 000 lbs at Little Rock AFB, using average monthly station pressure, the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Mean frequency in percent of time period that aircraft performance thresholds are surpassed for a UH-60L with a maximum gross weight of 22 000 lbs at Little Rock AFB, using average monthly station pressure, the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
Mean frequency in percent of time period that aircraft performance thresholds are surpassed for a UH-60L with a maximum gross weight of 22 000 lbs at Little Rock AFB, using average monthly station pressure, the 20 GCMs identified in Table 1, RCP8.5, and a 95% confidence interval.
Citation: Weather, Climate, and Society 13, 1; 10.1175/WCAS-D-20-0098.1
4. Conclusions and discussions
Maximum air temperature Tmax and minimum air temperature Tmin, used as a proxy for dewpoint temperature, are projected to rise due to anthropogenic climate change. Both of these climate variables and their relationship are critical factors when assessing the potential for increases in DA in both magnitude and frequency of occurrence. High DA impacts aircraft performance in the following ways: reduction in power because the engine takes in less air, reduction in thrust because a propeller is less efficient in thin air, and reduction in lift because the thin air exerts less force on the airfoils (FAA 2016; Reynolds 2012). For fixed-wing aircraft, the performance impacts include decreased maximum takeoff weight and increased true airspeed (TAS), which results in longer takeoff and landing distance (U.S. Air Force 1954; FAA 2008, 2016). For rotary wing, the performance impacts include reduced power margin, reduced maximum gross weight, reduced hover ceiling, and reduced rate of climb (FAA 2012; Civil Aviation Authority of New Zealand 2020).
While GCMs do not specifically project dewpoint temperature, Tmin can be used as a surrogate directly if annual precipitation is less than 30% of the annual potential evapotranspiration or modified for arid and semiarid locations as shown in Eq. (5). The incorporation of dewpoint temperature into DA calculations is shown to be increasingly important as the rate of increase is projected to rise significantly in a warming climate. Even at lower DA thresholds (e.g., 1000 ft), there is an increase in both magnitude and frequency of occurrence when dewpoint temperature is considered (moist DA) for projected time periods in cooler months (e.g., February, March, November). Furthermore, this frequency of occurrence of moist DA for the summer months (June, July, August) increases significantly at higher DA thresholds (e.g., 3000 ft) when compared with dry DA (dewpoint temperature not considered). It is recommended that dewpoint temperature, using Tmin as a surrogate where needed, be considered in all DA calculations because it shows the complete spectrum and magnitude of impact of the changing landscape of increased DA due to climate change. As the rate of increase in Tmin rises, its inclusion in all DA assessments will become more critical.
Translating GCM projected increases in Tmax and Tmin into DA thresholds provides a useful method to illustrate the probability of DA impacts. A defined DA can be used as an indicator to determine when this parameter will be surpassed. A DA threshold can be defined as a numerical value (e.g., DA > 1000 ft, DA > 2000 ft, DA > 3000 ft) or defined as a specific aircraft performance (e.g., power margin decrease). Establishing DA thresholds combined with frequency of occurrence is especially useful when translating the projection of rising DA into a meaningful metric for assessing risk probability. As previously mentioned, the correlation of GCMs modeled observed temperature data to observed temperature data is lower when translating these data to a frequency of occurrence measurement. This uncertainty is acknowledged; however, this variation in correlation does not negate the overall proposed methodology and can be incorporated into the framework to improve and refine accuracy.
Displaying these results in the form of a risk probability matrix further enables a quantifiable and easily understood metric to be developed for impact assessment. Furthermore, risk probability matrices based on specific months of the year provide critical insight into time periods where the greatest aircraft performance impact may occur. This insight would not otherwise be identified if viewed only as an annual assessment.
In agreement with reviewer’s insightful comments, further research is planned to expand this dataset to a 30-yr time period. Additionally, to build upon the reviewer’s perspective for suggested improvements, the following research is planned to continue to reduce this uncertainty: 1) utilize mean daily observed station pressure and 2) incorporate the variable of sea level pressure and include an imbedded conversion calculation of sea level pressure to station pressure (which requires site elevation and temperature). This will then allow the incorporation of climate modeling projections into the third variable of station pressure. This additional research will build on the proposed framework and add more accuracy to this method. Furthermore, as the capability to project sea level pressure due to climate change matures and is increasingly incorporated into modeling data sites, it could be readily implemented into this proposed methodology framework.
By assessing potential future aircraft performance impacts now, decision-makers can take proactive steps in mission planning and aircraft acquisition. These steps include identifying changing mission requirements and defining aircraft performance criteria. While mission planning can be considered a near-term effort, changing mission requirements may require modifications to acquisition planning, which is a strategic long-range effort. Furthermore, assessing and planning for aircraft performance impacts from increased DA now will encourage these challenges to be addressed by industry early and result in a more efficient and economical solution. The potentially devastating consequences of inadequately assessing the spectrum of projected increases in DA and subsequent impacts to aircraft performance due to a warming climate warrant the most comprehensive and timely analysis possible.
Acknowledgments
We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Table 1 of this paper) for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led the development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The authors thank Drs. Dave Titley, C. Nataraj, Gabrielle Gaustad, Amy Hoover, and Ethan Coffel for their insights and support during this research.
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