*2.4. Performance Metrics*

The spatial coverage performance of the various constellation configurations considered is quantified by a Zonal Spatial Coverage (ZSC) metric. The Earth surface is first divided up into a 25 km grid in latitude and longitude. All grid cells in which at least one observation is made within a 24 h period are noted. Then, the percentage of grid cells sampled across all longitudes is computed in each latitude zone and that percentage is reported as a function of latitude.

We quantify the temporal coverage performance of our analyzed constellations using a Zonal Temporal Coverage (ZTC) metric. The analysis uses the same equidistant geo-spatial grid covering the entire surface of the Earth as was used for the ZSC. The simulation calculates a binary decision in every grid cell over a chosen time interval. If there was one or more observations in a given grid cell, the cell is labelled with a one (1). If no observations occurred, it would be labeled with a zero (0). The time interval we use in our analysis is six hours, with four total time intervals in a day. Therefore, the maximum ZTC coverage a location on Earth could achieve per day is 4 (i.e., at least one observation was made in each of the 4 6 h intervals in the day). This 6 h quantization of the 24 h cycle was chosen to support the input data assimilation needs of major weather prediction models with a 6-hourly reporting interval (e.g., the NOAA/NCEP Global Forecast System (GFS) and the ECMWF High Resolution 10-day Forecast (HRES). By matching our ZTC interval to the needs of the models, we address the potential value of GNSS-R observations for use by these major operational models. Naturally, analysis of other intervals with other metrics is possible. Previous studies of the sampling properties of similar satellite constellations have considered the time separation between successive samples in the same grid cell [19]. Our approach expands upon this prior work by considering the ZTC as defined above to provide a more practical and useful quantification of the temporal sampling properties as they relate to the use of the measurements by numerical weather prediction models.

For each of the constellation configurations considered below, sampling performance is derived from a population of sample times and locations generated by an orbit simulation model. The model propagates the orbital locations for each of the science observatories as well as all members of the GPS, Galileo and SBAS constellations of GNSS satellites. At each one-second time step over the course of a 24 h period, the locations of all possible surface reflections are determined for signals propagating from every GNSS satellite transmitter to every science observatory receiver via specular point reflection by the Earth surface. In addition to the time and location of each sample, the value of the receive antenna gain in the direction of the specular point reflection is also noted. This allows the signal-to-noise-ratio quality of the received signal to be determined.
