Mr. Ponomarev, a New York Times photojournalist, and Mr. Arango, The Times’s Baghdad bureau chief, are in northern Iraq covering the Mosul offensive and the intensifying humanitarian crisis surrounding it.

Each day, dozens of families pick their way out, some carrying white flags even as they come under mortar or sniper fire from the Islamic State. Billowing black clouds from oil wells set on fire by militants provide a dystopian background to the scenes of flight; it is so bad south of Mosul that the sheep there have begun turning black.

The military campaign to retake Mosul, Iraq’s second-largest city, is in its sixth week and bogged down in a grueling fight. Seeking to escape the fighting, more civilians than ever are taking the risk of evacuation, hoping to find help if they can make it past the militants’ gun range.