Resolving Tropical Storm Inner Core Temperatures with a

Geostationary (GEO) weather satellites have differed from low-Earth orbiting (LEO) weather satellites in that they have not carried microwave radiometers. The reason is that to get LEO resolution from GEO, one needs an antenna forty times as large. Even scaling the small AMSU antenna requires a 6-meter dish. As discussed elsewhere, a 3-meter antenna still provides adequate spatial resolution for measuring precipitation and an initial guess for infrared soundings in cloudy conditions. The higher temporal sampling possible from GEO also permits improved monitoring of severe storms, but an objection to developing a GEO microwave sounder has been that tropical storm inner core temperature profiles would not be adequately resolved with such an antenna. This paper demonstrates how inner core temperatures may be measured from GEO using a 3-meter antenna and post-processing. Because this trades sensitivity for resolution, radiometer system noise must be as low as possible. Other sources of error sources imperfect boundary temperature knowledge and antenna pattern uncertainty. Simulations and covariance analyses suggest that the required system noise temperatures, although not yet commercially available, are not beyond the state-of-the-art. Although one might have to choose between inner core temperature soundings and hourly full-disk soundings, it would eliminate one more objection to flying a modest size microwave radiometer at geostationary altitude. Problem A microwave sounder has been proposed as a Pre-Planned Product Improvement (PI) for the GOES-R series of geostationary environmental satellites. The first GOES-R satellite is to be ready for launch in 2012, but the microwave sounder would probably not be ready until 2015. It is to provide temperature and humidity soundings, precipitation, sea surface winds and tropical storm inner core temperature profile. Its performance requirements are summarized in Table 1. While the temperature, humidity and precipitation requirements are relatively easy to meet, the sea surface wind and inner core temperature requirements are more difficult. Possible solutions to the inner core problem are discussed here. The term “warm core anomaly” refers to the increased temperature around the eye of a tropical storm. At the 250 mb pressure level, the temperature can be as much as 20 K higher than its surroundings. This temperature elevation indicates storm strength and can only be measured remotely using microwave radiometers. Although soundings are typically done at 60 GHz to get surface temperatures, inner core temperatures are also observable at 118 GHz because of their altitude. Table 1. GOES-R Microwave Sounder Requirements Temperature Sounding Humidity Sounding Precipitation Sea Surface Winds Warm Core Profile Resolution (km) 100 30 30 25 20 Sensitivity (K) 1 1 1 1 1 Frequency (GHz) 54-60 183 118-183 20 54-60 Bandwidth (MHz) 200 500 500 200 200 Even with large antennas, resolving inner core profiles is difficult. This can be seen from simulations where horizontal temperature distribution is modeled using a Gaussian function whose peak value decreases by 1/e at a radial distance of 20 km ( ) 2 2 1 ) ( r rc e T T r T − ∞ − ⋅ Δ + = (1) This formula is based on a paper by Greg Holland. Here is the background temperature, ∞ T T Δ is the warm core temperature anomaly, is the core radius, and c r r is the radial distance from the core center ) , ( 0 0 y x 2 0 2 0 2 ) ( ) ( y y x x r − + − = (2) Figure 1 shows that a 6-meter antenna operating at 60 GHz from GEO captures less than 40% of the warm core temperature anomaly from GEO altitude. Even a 24-meter antenna recovers only 55% of the peak temperature. Launch vehicle size and the need to control antenna dimensions to a fraction of a wavelength, however, make 3 meters about the largest practical diameter for an antenna operating at up to 183 GHz. Hypothesis If we had a 3-meter antenna at GEO and could oversample the inner core region, we might be able to estimate its temperature profile. On the surface, that might appear to violate the diffraction limit, but diffraction applies to a fixed view and does not consider signal strength. Because of numerical error, post-processing trades signal strength for spatial resolution. Rather than give up on a GEO microwave sounder due to the difficulty of flying a large, tightly-controlled antenna, we would try to improve sensitivity and then trade surplus sensitivity for spatial resolution. Figure 1. Warm Core Temperature Profiles Resolved from GEO -100 -50 0 50 100 0 2 4 6 8 10 12 14 16 18 20 distance (km) te m pe ra tu re ( K) true 3 m 6 m 12 m 18 m 24 m Sensitivity T σ depends on system temperature , integration time s T τ and bandwidth B