A 28-year-old woman with type 1 diabetes mellitus presents to the emergency department with a 2-day history of polyuria, polydipsia, and progressive dyspnea. On examination, she is tachypneic (RR 28/min) with Kussmaul respirations. Blood glucose is 420 mg/dL. Arterial blood gas shows: pH 7.22, PaCO₂ 24 mmHg, HCO₃⁻ 10 mEq/L, and serum ketones are elevated. What is the primary mechanism by which the respiratory system is attempting to compensate for this acid-base disturbance?