Low-altitude Measurements Research Articles

Estimation of Urban Greenhouse Gas Fluxes from Mole Fraction Measurements Using Monin–Obukhov Similarity Theory

Abstract The purpose of this study is to determine whether urban greenhouse gas (GHG) fluxes can be quantified from tower-based mole fraction measurements using Monin–Obukhov similarity theory (MOST). Tower-based GHG mole fraction networks are used in many cities to quantify whole-city GHG emissions. Local-scale, micrometeorological flux estimates would complement whole-city estimates from atmospheric inversions. CO2 mole fraction and eddy-covariance flux data at an urban site in Indianapolis, Indiana, from October 2020 through January 2022 are analyzed. Using MOST flux–variance and flux–gradient relationships, CO2 fluxes were calculated using these mole fraction data and compared to the eddy-covariance fluxes. MOST-based fluxes were calculated using varying measurement heights and methods of estimating stability. The MOST flux–variance relationship method showed good temporal correlation with eddy-covariance fluxes at this site but overestimated flux magnitudes. Fluxes calculated using flux–gradient relationships showed lower temporal correlation with eddy-covariance fluxes but closer magnitudes to eddy-covariance fluxes. Measurement heights closer to ground level produce more precise flux estimates for both MOST-based methods. For flux–gradient methods, flux estimates are more accurate and precise when low-altitude measurements are combined with a large vertical separation between measurement heights. When stability estimates based on eddy-covariance flux measurements are replaced with stability estimates based on the weather station or net radiation data, the MOST-based fluxes still capture the temporal patterns measured via eddy covariance. Based on these results, MOST can be used to estimate the temporal patterns in local GHG fluxes at mole fraction tower sites, complementing the small number of eddy-covariance flux measurements available in urban settings.

A review of N+ observations in the ionosphere-magnetosphere system

Most studies have yet to consider and assess the transport and energization of N+ ions throughout the ionosphere-magnetosphere system, in addition to that of O+ and other heavy ion species. The limited observational record of N+ presence in near-Earth plasma, partly due to instrument limitations to distinguish ion species of similar masses, has obscured its significant contribution to the near-Earth plasma. This letter reviews the most notable observations of N+ ions, starting from the early low altitude measurements from Sputnik III in the ionosphere to the measurements reported by the Enhanced Polar Outflow Probe (e-POP) mission. The available observational data set suggests that nitrogen ions are constant companions of outflowing oxygen ions, and their abundances vary with season, solar cycle, time of day, and geomagnetic activity. This strong record of nitrogen presence in the ionosphere-magnetosphere system raises the question of ionic composition and the need for caution when interpreting O+ measurements from current missions.

Mars Global Distribution of the External Magnetic Field and Its Variability: MAVEN Observation and MHD Prediction

AbstractWe study the average global distribution of the external magnetic field at Mars, and its variability with the upstream solar wind dynamic pressure and interplanetary magnetic field as well as with the ambient crustal magnetic field strength. Our approach involves excluding the intrinsic planetary field from the total magnetic field by applying a crustal field model previously derived using low altitude measurements. The distribution of the average external field that remains is statistically analyzed using nearly 8 years of Mars Atmosphere and Volatile EvolutioN (MAVEN) observations and several global, time‐dependent magnetohydrodynamic simulations. Overall consistent results have been obtained from the data and model, which are complementary to each other and cross validate the findings. It is found that the external field is significantly enhanced from the upstream across the bow shock (BS) and further intensifies closer to the planet in the topside ionosphere. It peaks at ∼170 km altitude near the subsolar point, significantly decreasing with increasing solar zenith angle. There is a strong day‐night asymmetry in the external field, with a typical dayside intensity of ∼15–50 nT and a nightside intensity of ∼5–15 nT. Under high solar wind dynamic pressures and IMFs, the external field may be enhanced by a factor of ∼2 everywhere below the BS, on both the dayside and nightside. In addition, our model results suggest that strong crustal fields, which effectively withstand the penetration of the solar wind, reduce the external field at low altitudes.

Validation of a New UAV Magnetic Prospecting Tool for Volcano Monitoring and Geohazard Assessment

The use of unmanned aircraft vehicles (UAVs) in volcanological contexts is a key challenge in studying volcanoes and improving efficiency in the monitoring of volcanic activity. The coupling of ground and satellite measurements has been reinforced at an intermediate scale thanks to UAV measurements. Along with carrying out visible and infrared measurements, UAVs can conduct geophysical measurements for more in-depth studies. Magnetic field measurements are a powerful tool in volcanic contexts for (i) mapping structural contacts between formations of different ages or type, and (ii) imaging deep thermal anomalies and intrusive systems. Here, we focus on magnetic sensors, which are becoming operational, and in particular on a scalar system recently implemented on a light drone that can be deployed quickly and efficiently in the field. This paper presents several flight test results in order to discuss any artifacts of the UAV or environmental conditions in the magnetic measurements. The results of the comparison between simultaneous UAV and ground surveys are presented. We demonstrate that low altitude measurements are particularly relevant to well-imaged magnetic anomalies and their variation through time in a volcanic context. Some potential uses for this technology and associated applications are also discussed in the fields of exploring and monitoring active volcanoes, for the 4D imaging of volcanoes.

The Lunar Polar Hydrogen Mapper CubeSat Mission

The Lunar Polar Hydrogen Mapper (LunaH-Map) mission will map the distribution of hydrogen around the lunar South Pole using a miniature neutron spectrometer. The mission builds upon a decade of lunar science, which has revealed both regional and more localized enrichments of water ice near the lunar poles. Localized enrichments are primarily within permanently shadowed regions (PSRs) and craters throughout the South Pole. The spatial extent of these regions is often below the resolution of previous neutron instruments that have flown on lunar missions. The neutron leakage spectrum from planetary surfaces is primarily sensitive to hydrogen abundance in the top meter of regolith, however, for neutron spectrometers with omnidirectional sensitivity, the spatial resolution is limited by the spacecraft orbital altitude above the surface. A low altitude measurement from a distance on the same scale of the PSRs could spatially isolate and constrain the hydrogen enrichments both within and around within those regions. A small spacecraft mission is ideally suited to acquire the low-altitude measurements required to localize hydrogen enrichments using neutron spectroscopy at the lunar South Pole. LunaH-Map will use a solid iodine ion propulsion system, X-Band radio communications through the NASA Deep Space Network, star tracker, Command & Data Handling System, and EPS systems from Blue Canyon Technologies, solar arrays from MMA Designs, LLC, mission design and navigation by KinetX. Spacecraft systems design, integration, qualification, test, and mission operations are performed by Arizona State University, AZ Space Technologies and Qwaltec.

First Results From Drone-Based Transient Electromagnetic Survey to Map and Detect Unexploded Ordnance

Unexploded ordnance (UXO), which causes many civilian casualties every year, has become a serious environmental problem. To deal with the problem, we have developed a new drone-based transient electromagnetic (TEM) system, which was designed for the UXO detection through very low altitude measurements. Drone-based TEM system uses the rotorcraft equipped with central loop TEM device to realize the UXO detection. The system was more safe and efficient than a ground-based TEM system in UXO detection. Compared with the airborne magnetic method or helicopter-borne TEM system, it has the advantages of low cost, flight safety, and so on. In this letter, the system characteristics are introduced in detail, providing the theoretical analysis of the system in UXO detection and verification of model data. Finally, through the UXO detection in the former weapon test base, the results show that the system is effective and successful in UXO detection.

Low-altitude geophysical magnetic prospecting based on multirotor UAV as a promising replacement for traditional ground survey

The prospects for expanding the mineral resource base in many countries are linked with the exploration of stranded sites localized at unexplored areas with complex natural and landscape conditions that make any ground survey, including magnetic prospecting, difficult and expensive. The current level of geology requires high-precision and large-scale data at the first stages of geological exploration. Since 2012, technologies of aeromagnetic surveying with unmanned aircraft vehicles (UAV) enter the market, but most of them are based on big fixed-wing UAV and do not allow to substantially increase the level of survey granularity compared with traditional aerial methods. To increase the scale of survey, it is necessary to reduce the altitude and speed of flight, for which the authors develop the methodical and technical solutions described in this article. To obtain data at altitudes of 5 m above the terrain even in a rugged relief, we created heavy multirotor UAVs that are stable in flight and may be used in a wide range of environmental conditions (even a moderate snowfall), and develop a special software to generate flight missions on the basis of digital elevation models. A UAV has special design to reduce magnetic interference of the flight platform; the magnetic sensor is hung below the aircraft. This technology was conducted in a considerable amount of magnetic surveys in the mountainous regions of East Siberia between 2014 and 2016. The results of the comparison between airborne and ground surveys are presented, which show that the sensitivity of the developed system in conjunction with low-altitude measurements can cover any geologically significant anomalies of the magnetic field. An unmanned survey is cheaper and more productive; the multirotor-based technologies may largely replace traditional ground magnetic exploration in scales of 1:10,000−1:1000.

Tethered lunar subsatellites for multipoint and low altitude measurements

The difficulty in making global measurements in orbit close to planetary bodies (and in particular the Moon) seriously constrains our ability to collect crucial, high-resolution data. We describe a unique and groundbreaking approach using tethered subsatellites to make measurements arbitrarily close to planetary surfaces, particularly those with no atmosphere, and to determine altitude profiles of geophysical parameters. The approach is feasible with current technology, and the subsatellite could be as small as a CubeSat. The initial results of a feasibility study and mission design for a tethered lunar CubeSat indicate that it is achievable.

Errors associated with estimating vegetation water content from radar for use in passive microwave brightness temperature algorithms

The Soil Moisture Active Passive Validation Experiment 2012 was conducted as a pre-launch validation campaign for the Soil Moisture Active Passive mission over 6 weeks in June and July 2012. During this campaign, the Passive Active L-Band System (PALS) was flown at a low altitude, providing radar and radiometer measurements that were contained within a single agricultural field. The campaign domain consisted of 55 agricultural fields, where soil moisture was measured coincident to the PALS flight times and measurements of vegetation volumetric water content (VWC) and leaf area index (LAI) were measured weekly. The low-altitude flights allowed for the comparison between measured VWC and LAI for 11 fields to radar parameters derived from the radar backscatter. Only the correlation between the HV backscatter and the soybean VWC was considered strong (|r| > 0.7). All other correlations between the radar parameters and the VWC (or LAI) were moderate (0.3 < |r| < 0.7) or weak (|r|< 0.3). The established relationships between radar parameters and VWC were used in a forward radiation transfer model to estimate H-pol brightness temperature. It was found that the RMSE between the brightness temperatures estimated using the measured VWC was lowest when using the relationship between VWC and LAI (3.9 K for soybeans, 6.8 K for spring wheat, and 9.3 K when all crop data are combined). Despite a lower correlation, the RMSE associated with using the radar vegetation index relationship with VWC was less than when HV was used (7.9 K) for soybeans, which would result in an error in soil moisture estimation of just over 4%. The RMSEs for all other VWC and radar parameter relationships were greater than 10 K.

Rain drop size distribution over the Tibetan Plateau

Over the last decade, interest in measuring and studying rain drop size distribution (DSD) has grown due to applications in cloud physics, in calibration of space-borne and ground-based microwave active precipitation sensors and in soil science and agriculture. Such studies are of particular interest over remote areas, where knowledge of clouds and precipitation processes is lacking while the need for remote sensing based precipitation estimates is growing in global water cycle and climate trend studies.Disdrometric data over the Tibetan Plateau were collected during the 2010 monsoon season using the Pludix disdrometer, a vertically pointing, continuous wave, X-band, low power radar. Three experimental sites were set up at altitudes greater than 3300m a.s.l., and a total number of 37 rain events were measured at two of the three sites.The analysis focuses on 2-min and 5-min DSD data for selected convective and stratiform events and the results are discussed in comparison with previous studies performed at lower altitudes. The time evolution of DSDs shows a regular behavior with respect to rain intensity: they change concavity and show a breakup signature in cases of the highest rain rates. Collisional breakup takes place for relatively lower rain rates, compared to the low-altitude measurements, and the size of the largest drops is also relatively smaller. An overall rainfall characteristic evaluation is also performed on the whole data set, deriving DSD integral parameters in order to compute a relationship between reflectivity and rain rate, resulting in A=214 (A=247) and b=1.25 (b=1.15) for convective (stratiform) precipitation.

Using a Parafoil Kite for Measurement of Variations in Particulate Matter—A Kite-Based Dust Profiling Approach

This paper reports on the use of a kite-based system for measuring low-altitude particulate matter (PM) concentrations over grassland in Inner Mongolia. The motivation came from PM-concentration measurements at heights below 3 m over non-erodible surfaces which showed constant concentrations and made flux calculations relatively uncertain. One aim was the quantification of wind-driven matter fluxes across ecosystem boundaries, where the relevant layer can be assumed at heights below 100 m. Compared to other measurement techniques (e.g. LIDAR, towers and airborne systems) kite-based systems represent an inexpensive, highly flexible research tool which is well-suited for application in remote sites. The basis of the introduced system is a 4 m2 Parafoil kite which has enough lifting capacity to carry equipment of about 6 kg at wind velocities between 3 ms-1 to nearly 20 ms-1. A self-adjusting platform was constructed to balance moves and to carry a portable Environmental Dust Monitor (EDM), anemometer and a GPS receiver. So, all parameters necessary for a vertical profile of dust fluxes could be measured. In the first flights the applied kite-based dust profiling system (KIDS) was examined according to general technical application problems. Firstly, the influence of diverse surface characteristics, the flying condition and height-stability was tested. The result suggests that surface characteristics in general have a higher influence than the optimal wind velocity, which ranged from 9 ms-1 to 17 ms-1. Secondly, uncertainties in the measured data were quantified and assessed. The uncertainties in wind velocity measurements due to motion in horizontal and vertical direction were not higher than 0.45% - 0.65% and 1.8% - 2.2% during the kite ascent. The outcome of the study illustrates the suitable application of KIDS for low-altitude measurements in remote sites.

An inexpensive active optical remote sensing instrument for assessing aerosol distributions

Air quality studies on a broad variety of topics from health impacts to source/sink analyses, require information on the distributions of atmospheric aerosols over both altitude and time. An inexpensive, simple to implement, ground-based optical remote sensing technique has been developed to assess aerosol distributions. The technique, called CLidar (Charge Coupled Device Camera Light Detection and Ranging), provides aerosol altitude profiles over time. In the CLidar technique a relatively low-power laser transmits light vertically into the atmosphere. The transmitted laser light scatters off of air molecules, clouds, and aerosols. The entire beam from ground to zenith is imaged using a CCD camera and wide-angle (100 degree) optics which are a few hundred meters from the laser. The CLidar technique is optimized for low altitude (boundary layer and lower troposphere) measurements where most aerosols are found and where many other profiling techniques face difficulties. Currently the technique is limited to nighttime measurements. Using the CLidar technique aerosols may be mapped over both altitude and time. The instrumentation required is portable and can easily be moved to locations of interest (e.g. downwind from factories or power plants, near highways). This paper describes the CLidar technique, implementation and data analysis and offers specifics for users wishing to apply the technique for aerosol profiles. Implications Air quality studies require information on atmospheric aerosols over both altitude and time. A new inexpensive, simple, ground-based optical remote sensing technique assesses aerosol distributions. In the technique, called CLidar, a laser transmits light vertically into the nighttime atmosphere. The laser light scatters off of air molecules, clouds, and aerosols and the entire beam is imaged using a CCD camera and wide-angle optics. CLidar is optimized for boundary layer measurements where most aerosols are found. The instrumentation is portable and can easily be moved to locations of interest (e.g., downwind from factories or power plants, near highways).

Blood pressure changes in young male subjects exposed to a median altitude

Residence at high altitude has been associated with elevation in systemic blood pressure (BP), but few studies have been done on the time course and the effects of a median altitude. Moreover, there exist population differences in the reactions given to altitude and the mechanism is unknown. This study was therefore designed to determine the effects of a median altitude on resting BP and heart rate (HR) in a group of 15 healthy, young, Turkish male subjects. After basic measurements were carried out in Bursa (155 m), subjects were transported to a mountain hotel (altitude 1,860 m), where the measurements were repeated once every 15 days during a 10-month period. Mean BP and diastolic BP increased on Day 4 and then remained above first values throughout the study. Compared with control measurements, high altitude increased systolic blood pressure (SBP) in all subjects, but in Month 4 and Month 6, SBP returned to control values, and remained elevated thereafter. HR continued to decrease in parallel with time and significant decrease occurred after Month 5. Our findings imply that moderate-altitude living results in a significantly greater BP and lower HR over equivalent low-altitude measurements and we conclude that chronic exposure to hypobaric hypoxia at a median altitude causes increased parasympathetic and sympathetic tone in healthy, young, Turkish males.

Tropospheric methane in northern Finland: seasonal variations, transport patterns and correlations with other trace gases

Methane mixing ratios have been continuously observed at Pallas, Finland since winter 2004. The seasonal variation in monthly means was ca . 40 ppb, showing largest mixing ratios in winter and also high values during late summer. Examination of back-trajectories showed that the air masses with elevated methane mixing ratios arrived from continental Eastern and Central Europe while low methane mixing ratios were connected with Atlantic and Arctic air masses. During summer, air masses with highest mixing ratios arrived from Northwestern Russia indicating wetland sources, while the influence of southern emissions became more significant in winter. Methane was positively correlated with carbon dioxide and negatively correlated with ozone in winter. The average slope of the selected wintertime background hourly mean mixing ratios was 7.0 ± 1.2 ppb(CH 4 )/ppm(CO 2 ). Nocturnal summertime low-altitude measurements above a local wetland source indicated slopes of about 10 ± 1 ppb(CH 4 )/ppm(CO 2 ). The different slopes reflect the differences in emission parameters. DOI: 10.1111/j.1600-0889.2007.00248.x

Tropospheric methane in northern Finland: seasonal variations, transport patterns and correlations with other trace gases

Methane mixing ratios have been continuously observed at Pallas, Finland since winter 2004. The seasonal variation in monthly means was ca. 40 ppb, showing largest mixing ratios in winter and also high values during late summer. Examination of back-trajectories showed that the air masses with elevated methane mixing ratios arrived from continental Eastern and Central Europe while lowmethane mixing ratios were connected with Atlantic and Arctic air masses. During summer, air masses with highest mixing ratios arrived from Northwestern Russia indicating wetland sources, while the influence of southern emissions became more significant in winter. Methane was positively correlated with carbon dioxide and negatively correlated with ozone in winter. The average slope of the selected wintertime background hourly mean mixing ratios was 7.0 ± 1.2 ppb(CH4)/ppm(CO2). Nocturnal summertime low-altitude measurements above a local wetland source indicated slopes of about 10 ± 1 ppb(CH4)/ppm(CO2). The different slopes reflect the differences in emission parameters.

Local inversion of magnetic anomalies: Implication for Mars’ crustal evolution

Martian magnetic anomalies have been revealed by the Mars Global Surveyor (MGS) mission in the south hemisphere of Mars. The present study models anomalies located in the ancient Terra Sirenum area between latitudes 26°S and 40°S and longitudes 185°E and 210°E using forward and inverse approaches. While the high-altitude measurements reveal the presence of two main magnetic anomalies, three are detected by low-altitude data. They are modeled as uncorrelated dipolar sources. Forward models predict large magnetizations between 30 and 60 A/m. A generalized non-linear inversion is used to determine the characteristics of the dipoles, based on different subsets of data. Low-altitude measurements inversion leads to more reliable results than those obtained by the inversion of high-altitude measurements only. Inversion of both low- and high-altitude data together provides with three dipoles that explain more than 57% of the signal, within this 10 6 km 2 area. All dipoles have large magnetizations. Serpentinization of the early martian crust can explain such remanent magnetizations. Two resulting dipoles are 56 km deep, which suggests a locally thick martian crust. The last one is shallower (31 km). This indicates different origins and/or magnetization processes. Paleomagnetic poles are calculated and located around the Tharsis bulge. It suggests that Tharsis formed at high latitudes and moved toward its present location by polar reorientation.

UXO Time-Constant Estimation from Helicopter-Borne TEM Data

We have developed a new helicopter-borne transient electromagnetic system, known as ORAGS-TEM, which was designed for the detection of unexploded ordnance (UXO) through very low altitude measurements. This system has already achieved considerable success in demonstrations over prepared test grids and a bombing site at the former Badlands Bombing Range (BBR) in South Dakota. UXO ranging in size from [Formula: see text] [Formula: see text] bombs to [Formula: see text] illumination shells and [Formula: see text] [Formula: see text] rocket components were detected by both magnetometer and transient electromagnetic technologies during these trials, conducted in September, 2002. The signal∕noise ratio (SNR) observed in TEM measurements during these trials was high, prompting us to ask, “What degree of UXO discrimination can be achieved through detailed analysis of this airborne TEM dataset?” Given the degree of spatial averaging and sampling limitations imposed by the system’s flight height and speed, we felt that a very detailed analysis of the type performed by Pasion and Oldenburg would not be practical. Instead, we developed an improved transient analysis technique based on the Matrix Pencil Method to improve the accuracy of exponential decomposition of the observed transients. Where target SNR values of 10 or higher were present this method yielded repeatable results that reliably distinguished compact, long-time-constant targets such as bombs and artillery shells from short-time-constant targets such as thin-walled scrap from practice bombs. As system sensitivity and resolution continues to improve, we expect that similar target discrimination methods will become standard data analysis tools.

Latitude distribution of vertically precipitating energetic neutral atoms observed at low altitudes

Earlier modeling work of the latitude distribution of earthward traveling energetic neutral atoms (ENA) originating in the ring current have suggested that an isotropic ring current with an empty loss cone will deposit most ENA away from the magnetic equator, while a ring current with an equatorial pitch angle distribution peaked at 90° will deposit most ENA at the magnetic equator. We present the first direct low altitude measurements of energetic particles at low and equatorial latitudes supporting this model. The evolution from an isotropic ring current to a more anisotropic one is manifested in the latitude distribution of the low altitude energetic particles during a geomagnetic storm. In the growth and main phase of the storm the latitude distribution of the energetic particles is wide and often show secondary peaks away from the equator, while in the recovery phase the latitude distribution narrows and peaks at the magnetic equator.

3D modeling of shock-induced trapping of solar energetic particles in the Earth's magnetosphere

The prompt trapping of solar energetic particles (SEPs) in the inner magnetosphere around L = 2 –2.5, including protons and heavier ions, has been observed at both the Cycle 22 and 23 solar maxima, in association with high-speed interplanetary shocks and storm sudden commencements (SSCs). Recent observations include the Bastille Day 2000 CME-driven storm as well as two in November 2001, which produced a long-lived new proton belt, as well as trapping of heavy ions up to Fe in all three cases. A survey of such events around the most recent solar maximum, including high altitude measurements from Polar and HEO satellites along with low altitude measurements from `the Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX)', indicates similarities to the well-studied March 24, 1991 SSC event. In this event, electrons and protons in drift resonance with a magnetosonic impulse were transported radially inward. A requirement for such shock-induced acceleration is a high-speed CME-shock at 1 AU, which launches a perturbation with comparable velocity inside the magnetosphere. Secondly, there must be a source population which is drift-resonant with the impulse. The CME-shock itself is a source of solar energetic particles, both protons and heavy ions, with higher fluxes and harder spectra associated with faster moving CMEs. Arrival of the interplanetary shock compresses and changes the magnetosphere topology, leading to a reduction of the geomagnetic cutoff, initially around L = 4 for SEP protons. This effect is modeled using a 3D Lorentz integration of SEP trajectories in electric and magnetic fields taken from the Lyon–Fedder–Mobarry (LFM) global MHD code, with solar wind input parameters taken from spacecraft measurements upstream from the bow shock, carried out for the November 24, 2001 SEP event. The results indicate that an enhancement in solar wind dynamic pressure for this event plays a role in the observed injection of ions to low L-values, to form a new proton belt which has lasted for more than 2 years.

Predicting the L-position of the storm-injected relativistic electron belt

In the paper we confirm earlier work on the dependence of the L-position (Lmax) of the peak intensity of storm-injected relativistic electrons upon the magnetic storm amplitude | Dst|max. Early results for | Dst|max=30–140 nT were reported by Williams et al. (1968). Later studies gave the following formula: | Dst| max= 2.75·10 4/ L max 4 for | Dst| up to 400 nT (Tverskaya, 1986). This sort of relationship also can be applied to the lowest position of the westward electrojet center during the storm, and the boundaries of both the trapped radiation zone and discrete auroral forms. Data from high-altitude (Polar and 1997-068) satellites, and a low-altitude satellite (SAMPEX) were analyzed and compared to the predictions of the above formula. The congruence between formula and observations is excellent: the discrepancy is not larger than 0.2 Re. There are several reasons why the discrepancies might be expected including: fast radial transport due to sudden impulses; the overlapping in time of multiple storms; and the additional injections onto L>Lmax in the storm recovery phase. There could be difficulty relating high and low altitude measurements due to problems with magnetic field models, but we believe this is not a major factor in our analysis.