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Monitoring with Trackers Based on Semi-Quantitative Models

In three years of NASA-sponsored research preceding this project, we successfully developed a technology for: (1) building qualitative and semi-quantitative models from libraries of model-fragments, (2) simulating these models to predict future behaviors with the guarantee that all possible behaviors are covered, (3) assimilating observations into behaviors, shrinking uncertainty so that incorrect models are eventually refuted and correct models make stronger predictions for the future. In our object-oriented framework, a tracker is an object which embodies the hypothesis that the available observation stream is consistent with a particular behavior of a particular model. The tracker maintains its own status (consistent, superceded, or refuted), and answers questions about its explanation for past observations and its predictions for the future. In the MIMIC approach to monitoring of continuous systems, a number of trackers are active in parallel, representing alternate hypotheses about the behavior of a system. This approach is motivated by the need to avoid 'system accidents' [Perrow, 1985] due to operator fixation on a single hypothesis, as for example at Three Mile Island. As we began to address these issues, we focused on three major research directions that we planned to pursue over a three-year project: (1) tractable qualitative simulation, (2) semiquantitative inference, and (3) tracking set management. Unfortunately, funding limitations made it impossible to continue past year one. Nonetheless, we made major progress in the first two of these areas. Progress in the third area as slower because the graduate student working on that aspect of the project decided to leave school and take a job in industry. I enclosed a set of abstract of selected papers on the work describe below. Several papers that draw on the research supported during this period appeared in print after the grant period ended.

Kuipers, Benjamin↗

Influence of Nucleation Mechanisms on the Radiative Properties of Deep Convective Clouds and Subvisible Cirrus in CRYSTAL/FACE

During the past few years we have conducted work on several different topics, as reflected by our publications. As one of the Co-Project scientists for The Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida Area Cirrus Experiment (CRYSTAL FACE) we worked to help design the mission and then conduct it in the field. Another major activity during the past two years has been to pull together various groups to formulate plans for follow on missions to CRYSTAL FACE. We organized a workshop at the University of Colorado during the summer of 2003 to assess the best locations for future missions. Working with a group of about 10 scientists from around the country we prepared a science-planning document (Tropical Composition, Cloud and Climate Coupling Experiment (TC(sup 4)) that outlined the rationale, locations, strategy to accomplish the goals, and possible payloads for a set of three tropical missions. We also prepared background materials for various NRAs being prepared at NASA Headquarters for missions in Costa Rica, Darwin and Guam. In conjunction with the group at NASA Ames we have helped build a new numerical model for deep convection and have applied that model to simulate the CRYSTAL data. Our goal in particular has been to better understand how convection distributes water vapor isotopes. CRYSTAL observations of water isotopes are very different from those suggested by previous workers who assumed the isotopes would obey Rayleigh fractionation. The water isotope study has several implications. First it is a check on the realism of the deep convection model. Second, the isotopes are a measure of the precipitation removal in the atmosphere. Hence they provide a constraint on a parameter that is difficult to otherwise measure. Finally it has been suggested that isotopes may be the key to unraveling the water transport into the stratosphere and upper troposphere. Such transport is critical both for the radiation balance and for stratospheric chemistry. Ours is the first model that is able to treat this transport. Our initial results have just been submitted to Geophys. Res. Lett (Smith et al., 2005). Essentially we are able to explain the vertical profiles of isotopes in the tropical tropopause transition layer. We are also able to account for stratospheric humidity and isotope abundances with this model. We have also been heavily involved in trying to improve our understanding of nitric acid condensation on ice. Gao et al (2004) have shown that water supersaturations above ice occur when the atmosphere is supersaturated with respect to nitric acid trihydrate. As one of the co-authors of that work, we suggested the mechanism that may explain why this is occurring. Essentially, ice does not like to grow near unit supersaturation, but does so because the water molecules can find sites on the ice surface to attach themselves to before they fly off the ice surface. This phenomena was well known in the 1960s when it was a source of debate about whether condensation and evaporation coefficients for ice would be the same. Evaporation does not require any molecular orientation, while condensation does, so it was possible that the coefficients would differ. They don't differ because the water molecules rapidly move across the surface and find places to attach. Nitric acid may be occupying these preferred sites and therefore the water molecules can't find a desirable place to attach. We anticipate that this research will be the subject of laboratory work during the coming few years. Another possibility that has been suggested is that cubic ice is forming in clouds. We have measured the vapor pressure of cubic ice, and plan to publish that result in the next few months. We have also been working on additional aspects of the condensation of nitric acid on ice. With Y. Kondo we studied the condensation of NOy on ice using the SOLVE data. Gamblin et al. have continued this work. The CRYSTAL NOy and HNO, groups have shown th their data can be fit using standard Langmuir isotherms as suggested in some, but not all, laboratory studies. We have found in the SOLVE data set that this is not the case. Moreover some laboratory studies show there are important kinetic effects that may be occurring in the atmosphere limiting the transfer of nitric acid to the ice. The SOLVE data seem consistent with these studies. We are currently re-analyzing the CRYSTAL data to look for these kinetic effects. There are a number of implications of these studies. One of the more interesting is that the nitric acid coating on ice can be used as a cloud clock to determine how long the cloud parcel has been in existence. We have also been involved with several laboratory studies. We have worked to improve the database on ice optical constants, which are critical for remote sensing. We have also studied the ways in which ice nucleates on clays. We suspect now that the standard theories used for depositional ice nucleation are completely incorrect. Further work will be needed to develop a new theory.

Toon, Owen B.↗

Aerodynamic and Aeroacoustic Wind Tunnel Testing of the Orion Spacecraft

The Orion aerodynamic testing team has completed more than 40 tests as part of developing the aerodynamic and loads databases for the vehicle. These databases are key to achieving good mechanical design for the vehicle and to ensure controllable flight during all potential atmospheric phases of a mission, including launch aborts. A wide variety of wind tunnels have been used by the team to document not only the aerodynamics but the aeroacoustic environment that the Orion might experience both during nominal ascents and launch aborts. During potential abort scenarios the effects of the various rocket motor plumes on the vehicle must be accurately understood. The Abort Motor (AM) is a high-thrust, short duration motor that rapidly separates Orion from its launch vehicle. The Attitude Control Motor (ACM), located in the nose of the Orion Launch Abort Vehicle, is used for control during a potential abort. The 8 plumes from the ACM interact in a nonlinear manner with the four AM plumes which required a carefully controlled test to define the interactions and their effect on the control authority provided by the ACM. Techniques for measuring dynamic stability and for simulating rocket plume aerodynamics and acoustics were improved or developed in the course of building the aerodynamic and loads databases for Orion.

Ross, James C.↗

Command Process Modeling & Risk Analysis

Commanding Errors may be caused by a variety of root causes. It's important to understand the relative significance of each of these causes for making institutional investment decisions. One of these causes is the lack of standardized processes and procedures for command and control. We mitigate this problem by building periodic tables and models corresponding to key functions within it. These models include simulation analysis and probabilistic risk assessment models.

functional analysis↗

Integrated Test and Evaluation Flight Test 3 Flight Test Plan

The desire and ability to fly Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) is of increasing urgency. The application of unmanned aircraft to perform national security, defense, scientific, and emergency management are driving the critical need for less restrictive access by UAS to the NAS. UAS represent a new capability that will provide a variety of services in the government (public) and commercial (civil) aviation sectors. The growth of this potential industry has not yet been realized due to the lack of a common understanding of what is required to safely operate UAS in the NAS. NASA's UAS Integration into the NAS Project is conducting research in the areas of Separation Assurance/Sense and Avoid Interoperability, Human Systems Integration (HSI), and Communication to support reducing the barriers of UAS access to the NAS. This research is broken into two research themes namely, UAS Integration and Test Infrastructure. UAS Integration focuses on airspace integration procedures and performance standards to enable UAS integration in the air transportation system, covering Sense and Avoid (SAA) performance standards, command and control performance standards, and human systems integration. The focus of Test Infrastructure is to enable development and validation of airspace integration procedures and performance standards, including the integrated test and evaluation. In support of the integrated test and evaluation efforts, the Project will develop an adaptable, scalable, and schedulable relevant test environment capable of evaluating concepts and technologies for unmanned aircraft systems to safely operate in the NAS. To accomplish this task, the Project will conduct a series of Human-in-the-Loop and Flight Test activities that integrate key concepts, technologies and/or procedures in a relevant air traffic environment. Each of the integrated events will build on the technical achievements, fidelity and complexity of the previous tests and technical simulations, resulting in research findings that support the development of regulations governing the access of UAS into the NAS.

Unmanned↗

UAS Integration in the NAS Project: Integrated Test and Evaluation (IT&E) Flight Test 3

The desire and ability to fly Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) is of increasing urgency. The application of unmanned aircraft to perform national security, defense, scientific, and emergency management are driving the critical need for less restrictive access by UAS to the NAS. UAS represent a new capability that will provide a variety of services in the government (public) and commercial (civil) aviation sectors. The growth of this potential industry has not yet been realized due to the lack of a common understanding of what is required to safely operate UAS in the NAS. NASA's UAS Integration into the NAS Project is conducting research in the areas of Separation Assurance/Sense and Avoid Interoperability, Human Systems Integration (HSI), and Communication to support reducing the barriers of UAS access to the NAS. This research is broken into two research themes namely, UAS Integration and Test Infrastructure. UAS Integration focuses on airspace integration procedures and performance standards to enable UAS integration in the air transportation system, covering Sense and Avoid (SAA) performance standards, command and control performance standards, and human systems integration. The focus of Test Infrastructure is to enable development and validation of airspace integration procedures and performance standards, including the integrated test and evaluation. In support of the integrated test and evaluation efforts, the Project will develop an adaptable, scalable, and schedulable relevant test environment capable of evaluating concepts and technologies for unmanned aircraft systems to safely operate in the NAS. To accomplish this task, the Project will conduct a series of Human-in-the-Loop and Flight Test activities that integrate key concepts, technologies and/or procedures in a relevant air traffic environment. Each of the integrated events will build on the technical achievements, fidelity and complexity of the previous tests and technical simulations, resulting in research findings that support the development of regulations governing the access of UAS into the NAS.

interoperability↗

UAS-NAS Flight Test Series 3: Test Environment Report

The desire and ability to fly Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) is of increasing urgency. The application of unmanned aircraft to perform national security, defense, scientific, and emergency management are driving the critical need for less restrictive access by UAS to the NAS. UAS represent a new capability that will provide a variety of services in the government (public) and commercial (civil) aviation sectors. The growth of this potential industry has not yet been realized due to the lack of a common understanding of what is required to safely operate UAS in the NAS. NASA's UAS Integration in the NAS Project is conducting research in the areas of Separation Assurance/Sense and Avoid Interoperability (SSI), Human Systems Integration (HSI), and Communications (Comm), and Certification to support reducing the barriers of UAS access to the NAS. This research is broken into two research themes namely, UAS Integration and Test Infrastructure. UAS Integration focuses on airspace integration procedures and performance standards to enable UAS integration in the air transportation system, covering Detect and Avoid (DAA) performance standards, command and control performance standards, and human systems integration. The focus of Test Infrastructure is to enable development and validation of airspace integration procedures and performance standards, including integrated test and evaluation. In support of the integrated test and evaluation efforts, the Project will develop an adaptable, scalable, and schedulable relevant test environment capable of evaluating concepts and technologies for unmanned aircraft systems to safely operate in the NAS. To accomplish this task, the Project is conducting a series of human-in-the-loop (HITL) and flight test activities that integrate key concepts, technologies and/or procedures in a relevant air traffic environment. Each of the integrated events will build on the technical achievements, fidelity, and complexity of the previous tests and technical simulations, resulting in research findings that support the development of regulations governing the access of UAS into the NAS. The integrated events started with two initial flight test used to develop and test early integrations and components of the test environment. Test subjects and a relevant test environment were brought in for the integrated HITL (or IHITL) conducted in 2014. The IHITL collected data to evaluate the effectiveness of DAA Well Clear (DWC) algorithms and the acceptability of UAS concepts integrated into the NAS. The first integrated flight test (and the subject of this report) followed the IHITL by replacing the simulation components with live aircraft. The project finishes the integrated events with a final flight test to be conducted in 2016 that provides the researchers with an opportunity to collect DWC and Collision Avoidance (CA) interoperability data during flight encounters.

flight test↗

NASA Observations and Modeling During ICE-POP

Recap: NASA-Specific Objectives for ICE-POP: Provide real-time observational and NWP data in support of ICE-POP, participate in significant international science effort; GPM (Global Precipitation Measurement) Ground Validation and NASA Weather Program -Direct/physical validation of active/passive satellite-based snowfall retrieval algorithms over coastline and mountains; melting layer interaction with terrain -Physics of snow, coupling to snow water equivalent rate and satellite remote sensor retrieval algorithm assumptions - -Size distributions, types/habit, water equivalent, profiles -NU-WRF (NASA-Unified Weather Research and Forecasting) Model plus Observational analyses: Movement toward “level IV products” leverage intensive and multi-faceted NWP (Numerical Weather Prediction) component -Model precipitation processes (liquid, mixed phase and frozen); Build model testing database for further active/passive remote sensing algorithm development (e.g., satellite data simulators) -"Integrated" validation of products in operational context.

Precipitation Science↗

Simulations of the NASA Langley 14- by 22-Foot Subsonic Tunnel for the Juncture Flow Experiment

NASA’s Transformational Tools and Technologies Program’s Juncture Flow experiment aims to provide data to improve Computational Fluid Dynamics (CFD) modeling in the juncture flow region. The experiment is planned to provide validation-quality data for CFD that focuses on the separation bubble near the wing-body juncture trailing edge region. Because wind tunnel tests associated with the Juncture Flow project have been designed for the purpose of CFD validation, considerable effort is going into modeling and simulating the wind tunnel. This is not only important because wind tunnel wall effects can play a role in integrated testing uncertainties, but also because the better the boundary conditions are known, the better CFD can accurately represent the experiment. This paper builds on the recent CFD efforts to model the NASA Langley 14- by 22-Foot Subsonic Tunnel. Current best practices in simulating wind tunnels are evaluated. The features of each method, as well as some of their pros and cons, are highlighted. Boundary conditions and modeling techniques currently used by CFD for empty-tunnel simulations are also described. Preliminary CFD studies associated with modeling the Juncture Flow model are summarized, with the intention to determine sensitivities of the flow near the wing-body juncture region of the model to a variety of modeling decisions.

Subsonic↗

Aircraft Engine Run-to-Failure Dataset Under Real Flight Conditions for Prognostics and Diagnostics

A key enabler of intelligent maintenance systems is the ability to predict the remaining useful lifetime (RUL) of its components, i.e., prognostics. The development of data-driven prognostics models requires datasets with run-to-failure trajectories. However, large representative run-to-failure datasets are often unavailable in real applications because failures are rare in many safety-critical systems. To foster the development of prognostics methods, we develop a new realistic dataset of run-to-failure trajectories for a fleet of aircraft engines under real flight conditions. The dataset was generated with the Commercial Modular Aero-Propulsion System Simulation (CMAPSS) model developed at NASA. The damage propagation modelling used in this dataset builds on the modelling strategy from previous work and incorporates two new levels of fidelity. First, it considers real flight conditions as recorded on board of a commercial jet. Second, it extends the degradation modelling by relating the degradation process to its operation history. This dataset also provides the health respectively fault class. Therefore, besides its applicability to prognostics problems, the dataset can be used for fault diagnostics.

CMAPPS↗

Enter the AHU (36th Chamber of ASHRAE): A Multi-site Field Study of ASHRAE G36

Despite being recognized as the best practice for advanced building controls, ASHRAE Guideline 36 (G36) has seen slow adoption in retrofit cases. Decisionmakers lack credible field evidence to justify the time and person-power investment. Most prior analyses have relied on software simulations, which overlook implementation challenges and fail to persuade owners to move from models to real-world deployment. This paper presents a multi-site field study of G36 performance, drawing on measured results from 17 projects across diverse building types and climate zones. The analysis disaggregates outcomes by the most widely adopted air handling unit (AHU) based G36 strategies, including trim-and-respond approaches to supply air temperature (SAT) and duct static pressure (DSP) reset, and economizer controls. Results for controls re programming implementations are encouraging, with HVAC savings ranging from 2% - 49%, with a median of 18%. The range aligns with simulation study findings showing 1% - 46% savings through these three strategies. These findings show that even without capital investment in control infrastructure upgrades, existing building owners are reaping significant benefits from updating HVAC sequences of operation to industry best-practice solutions. The results give practitioners and decisionmakers a reference point on what to expect, which strategies deliver, and how field performance may compare to simulation.

Deshpande, Reva↗

Pathway for decarbonizing residential building operations in the US and China beyond the mid-century

With global carbon budget targets looming, residential buildings in top economies must become carbon neutral as soon as possible to reserve more emission space for emerging carbon-emitting economies. This study is the first to compare the operational decarbonization process of China’s and the United States (US) residential buildings from 2000 to 2060 by combining the end-use emission model with the decomposing structural decomposition (DSD) method and Monte Carlo simulation. The results show that from 2001 to 2020 China decarbonized 1544 mega-tons of carbon dioxide (MtCO 2 ) and the US decarbonized 1848 MtCO 2 . In the business-as-usual scenario, China will hit its emission peak in 2031 (±3) with 934 (±61) MtCO 2 , while the US will maintain a lock-in level of 736 (±133) MtCO 2 since the 2030s. In the decarbonization scenario, operational carbon neutrality for residential buildings in 2060 is promoted by an increase in clean power generation proportion, building-integrated power generation level, building electrification level, and a reduction in end-use energy intensity, which will contribute 34.4 %, 21.4 %, 14.3 %, and 29.9 % in China and 32.9 %, 33.1 %, 8.2 %, and 25.8 % in the US, respectively. Especially, building-integrated power generation in China only costs about 40 % of what it costs in the US. Besides, high-decarbonization strategies for residential building operations are proposed as references for governments to formulate targeted climate policies. Overall, this study offers data benchmarks for buildings’ carbon neutrality of top economies to further promote synergistic carbon neutrality with the buildings of emerging economies in the age of Post COP27.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A subcellular biochemical model for T6SS dynamics reveals winning competitive strategies

Abstract The type VI secretion system (T6SS) is a broadly distributed interbacterial weapon that can be used to eliminate competing bacterial populations. Although unarmed target populations are typically used to study T6SS function in vitro, bacteria most likely encounter other T6SS-armed competitors in nature. However, the connection between subcellular details of the T6SS and the outcomes of such mutually lethal battles is not well understood. Here, we incorporate biological data derived from natural competitors of Vibrio fischeri light organ symbionts to build a biochemical model for T6SS at the single-cell level, which we then integrate into an agent-based model (ABM). Using the ABM, we isolate and experiment with strain-specific physiological differences between competitors in ways not possible with biological samples to identify winning strategies for T6SS-armed populations. Through in vitro experiments, we discover that strain-specific differences exist in T6SS activation speed. ABM simulations corroborate that faster activation is dominant in determining survival during competition. Once competitors are fully activated, the energy required for T6SS creates a tipping point where increased weapon building and firing becomes too costly to be advantageous. Through ABM simulations, we identify the threshold where this transition occurs in the T6SS parameter space. We also find that competitive outcomes depend on the geometry of the battlefield: unarmed target cells survive at the edges of a range expansion where unlimited territory can be claimed. Alternatively, competitions within a confined space, much like the light organ crypts where natural V. fischeri compete, result in the rapid elimination of the unarmed population.

59 BASIC BIOLOGICAL SCIENCES↗

Spatio-Temporal Surrogates for Interaction of a Jet with High Explosives: Part I - Analysis with a Small Sample Size

Computer simulations, especially of complex phenomena, can be expensive, requiring high-performance computing resources. Often, to understand a phenomenon, multiple simulations are run, each with a different set of simulation input parameters. These data are then used to create an interpolant, or surrogate, relating the simulation outputs to the corresponding inputs. When the inputs and outputs are scalars, a simple machine learning model can suffice. However, when the simulation outputs are vector valued, available at locations in two or three spatial dimensions, often with a temporal component, creating a surrogate is more challenging. In this report, we use a two-dimensional problem of a jet interacting with high explosives to understand how we can build high-quality surrogates. The characteristics of our data set are unique - the vector-valued outputs from each simulation are available at over two million spatial locations; each simulation is run for a relatively small number of time steps; the size of the computational domain varies with each simulation; and resource constraints limit the number of simulations we can run. We show how we analyze these extremely large data-sets, set the parameters for the algorithms used in the analysis, and use simple ways to improve the accuracy of the spatio-temporal surrogates without substantially increasing the number of simulations required.

97 MATHEMATICS AND COMPUTING↗

Magnetotail structures in a simulated Earth's magnetosphere

The structure of the magnetotail is investigated in a laboratory simulated magnetosphere. Particular emphasis is placed on the region of distant magnetotail where the closed field line region of the plasma sheet terminates and the process of reconnection takes place. Our study builds upon the previous investigation of the magnetotail where the main results were based on the magnetic field measurements in the tail region of the simulated magnetosphere. In this paper, more elaborate measurements of plasma flow and electric field are presented. Besides these measurements, this region of distant magnetotail is also explored by high resolution imaging with a gated optical imager (GOI) and by digital image analysis. These images clearly reveal a Y-type magnetic neutral line for the northward 'interplanetary' field (IMF) and a usual X-type for the southward IMF that confirms our previous results deduced from the magnetic field measurements. In the neighborhood of these neutral points a strong component of dawn to dusk electric field (E(sub y)) and a counterstreaming plasma flow is also observed. Plasma flow is measured by using a double sided Faraday cup which is also used to measure the y-component of tail current (J(sub y)) at different locations. These measurements reveal that the tail current is not carried by ions as previously thought, rather it is carried by electrons alone.

Yur, G.↗

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗

Permutation matrix representation quantum Monte Carlo

We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its off-diagonal terms and is both parameter-free and Trotter error-free. In our approach, the quantum dimension consists of products of elements of a permutation group. As such, it allows for the study of a very wide variety of models on an equal footing. To demonstrate the utility of our technique, we use it to clarify the emergence of the sign problem in the simulations of non-stoquastic physical models. We showcase the flexibility of our algorithm and the advantages it offers over existing state-of-the-art by simulating transverse- field Ising model Hamiltonians and comparing the performance of our technique against that of the stochastic series expansion algorithm. Furthermore, we also study a transverse-field Ising model augmented with randomly chosen two-body transverse-field interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Transformative Building Envelope Retrofit Using Insulation-Inflatable Walls Assisted by Automation

This work highlights the effort to develop a low-cost envelope retrofit for homes built prior to the implementation of energy conservation measures established by the Department of Energy. Inflatable structures were constructed to conform to the exterior envelope (a corner wall construction with a fenestration was used as a prototype). The structures were then filled with spray polyurethane foam insulation. The flexibility in construction and the ability to fill with spray polyurethane foam insulation were demonstrated. In addition, hygrothermal simulations showed that the installation of these systems does not compromise the moisture durability of uninsulated and insulated building envelopes across eight climate zones from hot humid to subarctic. Preliminary cost estimates, based on retail pricing, of the inflatable retrofit including 3 inches of spray foam insulation (insulation value of approximately R 20) is $\$ 4.25$ per square foot uninstalled. The installed cost was calculated using two labor rates, the labor rate for the installation of a weather resistive barrier and the installation of spray foam insulation. Aggregating those values into one labor rate results in an installed cost between $\$ 11$ and $\$ 28$ per square foot. The low end includes the installation of vinyl siding as the exterior cladding. The higher value includes an exterior stucco finish.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗