Differential absorption lidar (DIAL) is a unique technique for profiling water vapor from the ground up to the lower stratosphere. For accurate measurements, the DIAL laser transmitter has to meet stringent requirements. These include high average power (up to 10 W) and high single-shot pulse energy, a spectral purity >99.9%, a frequency instability <60 MHz rms, and narrow spectral bandwidth (single-mode, <160 MHz). We describe extensive modeling efforts to optimize the resonator design of a Ti:sapphire ring laser in these respects. The simulations were made for the wavelength range of 820 nm, which is optimum for ground-based observations, and for both stable and unstable resonator configurations. The simulator consists of four modules: (1) a thermal module for determining the thermal lensing of the Brewster-cut Ti:sapphire crystal collinear pumped from both ends with a high-power, frequency-doubled Nd:YAG laser; (2) a module for calculating the in-cavity beam propagations for stable and unstable resonators; (3) a performance module for simulating the pumping efficiency and the laser pulse energy; and (4) a spectral module for simulating injection seeding and the spectral properties of the laser radiation including spectral impurity. Both a stable and an unstable Ti:sapphire laser resonator were designed for delivering an average power of 10 W at a pulse repetition frequency of 250 Hz with a pulse length of approximately 40 ns, satisfying all spectral requirements. Although the unstable resonator design is more complex to align and has a higher lasing threshold, it yields similar efficiency and higher spectral purity at higher overall mode volume, which is promising for long-term routine operations.