2.1 Synthethic TCs and Simulated TC Precipitation
 Synthetic TCs were generated using thermodynamic and kinematic statistics and a random seeding approach. The simulation of TCs started with seeding weak vortices (12 m s−1) randomly distributed over the global oceans at all times. Tropical cyclones were identified only when a vortex developed winds of at least 21 m s−1 (40 kt). The tracks of the vortices are based on the beta and advection model [Holland, 1983], and the intensity of the wind is calculated by the Coupled Hurricane Intensity Prediction System (CHIPS) model [Emanuel et al., 2004]. The simulation is based on atmospheric and ocean conditions obtained from the National Center for Atmospheric Research/National Centers for Environmental Prediction (NCAR/NCEP) reanalysis from 1980 to 2010. The cyclogenesis climatology developed here is independent of the statistics of historical hurricane observations. A detailed description of this technique is provided in Emanuel . The synthetic TC climatology generated using this approach has been validated with observations [Emanuel, 2013], and the results are also generally in good agreement with those from a high-resolution (~14 km) global simulation of TCs [Emanuel et al., 2010]. However, Strazzo et al. show that the intensity of synthetic TCs may be less sensitive to sea surface temperature than is shown in the observations.
 The synthetic TCs used in this study are sampled from a global data set of synthetic TCs [Emanuel, 2006]. All TCs that made landfall in Texas or came within 100 km of the state were included. This distance was selected because the most intense TCP typically occurs within 100 km of the center of circulation [Zhu and Quiring, 2013]. There were 3085 synthetic TCs that met this criterion. The rain rate was simulated for all 3085 TCs at 2 h intervals. The outer radius and the radius of maximum wind of the TCs were estimated according to a nondimensional factor randomly derived from the log-normal distribution and the global mean value of TC size based on observations [Chavas and Emanuel, 2010].
 While the CHIPS model internally produces vertical velocities and convective mass fluxes as functions of time and distance from the storm center, these do not take into account topographic and baroclinic effects, and recording the radial vertical velocity for each storm at each radial computational node increases the output size by a large factor. Thus, we developed an algorithm for estimating the vertical velocity in the lower troposphere from the standard output variables of the model; these vertical velocities were then coupled with estimates of the saturation specific humidity. We emphasize that this algorithm cannot estimate rainfall on the scale of individual convective cells or mesoscale features such as spiral bands and is therefore unsuited to rainfall estimation for single events. But given that we are estimating rainfall risk averaged over a large ensemble of events, we may expect that chaotic convective and mesoscale variability will average out over the ensemble.
 The algorithm estimates contributions to the storm-scale vertical velocity from, respectively, axisymmetric overturning associated with vortex spin-up and spin-down, Ekman pumping, orographic ascent/descent, and interactions with environmental wind shear and baroclinity.
 The first step in the algorithm is to estimate the vertical velocity at the top of the boundary layer from the curl of the wind stress estimated using the gradient wind (including any background flow) and a suitably defined drag coefficient. Because of the background flow and the nonlinearity of surface drag, this Ekman component will not, in general, be axisymmetric.
 To this estimate of the vertical velocity at the top of the boundary layer is added a topographic component, which is estimated as the dot product of the horizontal wind (the sum of the TC-related gradient wind and low-level background horizontal wind) with the gradient of the topographic heights, using a ¼ × ¼ degree topographic data set. While this is a crude approximation, more sophisticated models that account for the effects of stratification and cloud microphysics reduce to it when the effective stratification and microphysical time scales vanish [Barstad and Smith, 2005].
 After fitting a standard radial profile of gradient wind to the recorded radius of maximum winds and outer radius at each 2 h output time, the time evolution of the gradient wind is estimated. The difference between the vertical velocity in the middle troposphere and that at the top of the boundary layer is that required to produce enough stretching to account for the time rate of change of the vorticity of the gradient wind. The vertical velocity in the middle troposphere is simply this difference added to the vertical velocity at the top of the boundary layer.
 Finally, we add a baroclinic component to the vertical velocity field at middle levels. Following the work of Raymond , we recognize four components of the interaction of baroclinic vortices with environmental shear: isentropic ascent/descent owing to the interaction of the vortex flow with the background isentropic slope; isentropic ascent/descent associated with the interaction of the background shear with the vortex-related sloping isentropic surfaces, time dependence of the isentropic surfaces in the vortex coordinate frame, and self interaction of the distorted vortex flow with the associated distorted isentropic field. The time dependence is partially accounted for here in the spin-up, spin-down contribution to the axisymmetric vertical motion. Raymond  found that the first of the four processes contributes roughly as much to the net vertical velocity as the other three combined. For simplicity, we therefore include only this first component here, representing it as the dot product of the gradient wind with the background isentropic slope. This produces a component of ascent downshear of the TC center, as is observed in nature [Chen et al., 2006].
 The total vertical velocity thus calculated is multiplied by a saturation specific humidity at 900 hPa to obtain an estimate of the vapor flux through that level. The specific humidity is based on the recorded ambient temperature at 600 hPa, extrapolated to 900 hPa along a moist adiabat, and the effect of the warm TC core is not accounted for. We assume that a fixed fraction (set equal to 0.9 here) of that vapor flux falls to the surface as precipitation.
 A long-term TCP climatology was generated for Texas based on the 3085 synthetic TC events. In this paper we present results at the daily and TC event scales aggregated from the 2 h intervals.
2.2 Observed TC Precipitation
 The simulated TCP was validated using a TCP climatology extracted from NOAA COOP daily rain gauges from 1950 to 2009 [Zhu and Quiring, 2013]. A total of 54 TCs made landfall in Texas or passed within 100 km of the state. These TCs were used to develop the TCP climatology because they match the filtering criteria used for the synthetic TCs. We used a Moving ROCI (radius of the outermost closed isobar) Buffer Technique (MRBT) which accounts for variations in TC size and translation speed to identify rain gauges that received TCP [Zhu and Quiring, 2013]. A TCP day is defined as a day when any of the rain gauges within the MRBT region received precipitation. There were a total of 128 TCP days associated with the 54 TCs (an average of ~ 2.4 days per event) that influenced Texas between 1950 and 2009. Therefore, we used 2 days as the time period for determining event TCP for the synthetic TCs. Daily TCP was extracted from gauge observations with serially complete 60 year record at four locations in Texas.
2.3 Statistical Analysis
 TCP based on the synthetic and observed TCs were compared at four locations. Houston (29.77°N, 95.38°W) and Corpus Christi (27.75°N, 97.40°W) are more frequently influenced by TCs because they are near the Gulf of Mexico. San Antonio (29.72°N, 98.50°W) is less frequently influenced by TCs because it is ~200 km from the Gulf of Mexico. Dallas (32.77°N, 96.78°W) is the second largest city in Texas, but its inland location means that TCs are relatively infrequent. Another reason for selecting these four cities is the completeness of their daily precipitation data.
 The return periods in this paper are calculated using the approach of Emanuel and Jagger . Emanuel and Jagger  found that the return-period distributions calculated using their approach compare well to those estimated from extreme-value theory with parameter fitting using a peaks-over-threshold model [Jagger and Elsner, 2006; Malmstadt et al., 2010]. An additional advantage of this approach is that the return periods are valid over the whole range of hurricane wind speeds. Kernel smoothing was applied to the probability density estimation for the total sample of the daily and event TCP at each location. The smoothing interval was set to 0.03 of the maximum precipitation value in the sample to ensure a dense sampling rate. The normalized cumulative distribution (u1, u2…un) was then calculated from the probability density of the precipitation sample. The annual frequency (Frn) of each kernel of TCP magnitude was given by ((1))
 Freq is the frequency of the observed storms that passed within 100 km to Texas from 1980 to 2010, which is 0.90, since we used reanalysis data to generate the synthetic TCs. Rz is the number of synthetic TCP amounts > 0 in the sample. Ri is the sample size. The recurrence interval was calculated by taking the reciprocal of Frn for each TCP magnitude. The return periods of different TCP magnitudes from the observation (54 best tracks) were estimated in a similar way to what was done for the synthetic events. The only difference is that we used an annual storm frequency of 0.88 for the observed storms for Texas from 1950 to 2009. Confidence intervals (90%) were calculated using the same approach as Emanuel and Jagger  to quantify the agreement between the return periods calculated based on the observed and synthetic TCs. An assumption is made that the time interval is randomly drawn from a Poisson distribution. We calculated return periods for the hourly rain rate, daily and event precipitation amount for both simulated (3085) and observed (54) storms at all four selected locations. The comparisons of the simulated and observed TCP climatologies are presented in section 3.
 To show the spatial variations in the TCP risk with different return periods, we constructed a grid with a resolution of 0.25° covering Texas. We fitted the discrete recurrence interval curves for the daily and event TCP from the 3085 synthetic TCs and 54 observed TCs and at each grid using the same approach as that at the four cities. Observed daily precipitation was interpolated from 220 gauges that have a 60 year serially complete record of precipitation using an Inverse Distance Weighting approach [Zhu and Quiring, 2013]. The TCP associated with the 50, 100, 500, and 1000 year return periods was estimated by linearly interpolating the recurrence interval curves. Each curve has at least 100 intervals (sampling with intervals equal to 0.01 of the maximum precipitation).