When he was 13, Ehud Olmert decided to improve his crude English skills. So he began pawing through Time magazine and writing letters to his cousin, Carol, in San Francisco.

“When he started writing, I remember his English wasn’t too good,” recalled Carol, 59, who is six months younger than Israel’s acting prime minister.

“Of course, now he speaks better than I do.”

Carol Olmert, who now lives in Walnut Creek, sensed that even as a young man, her cousin desired to lead his country. In recent years, he explicitly stated to her that he hoped to become prime minister — “but not like this,” she added.

When it comes to her cousin finally fulfilling his dream, “I’m in a state of disbelief,” she said.

Carol is the daughter of Eel Alexander Olmert, the brother of Ehud’s father, Mordechai. Eel Olmert settled in the Bay Area in the 1920s after attending U.C. Berkeley, while Mordechai (“Motia” to his family) immigrated to pre-state Israel after studying agronomy in Amsterdam. Both were raised in China, after the family escaped from the pogroms in its native Russia.

After a dozen years of corresponding via the post, Carol Olmert finally met Ehud and his three brothers during an Israel trip in 1972, the year before he was first elected to the Knesset. Two years later, Ehud visited San Francisco.

“I was surprised the security around him wasn’t greater. I remember him having a real sense of adventure, he was really interested in exploring the city. And I had a great time being his tour guide and taking him around,” she recalled.

“He had a keen interest and curiosity in San Francisco. He loved coming here. And he seemed to make friends very quickly. The people who met him here really enjoyed his company. He can be very charismatic.”

As a young man, Ehud Olmert was an energetic jokester with a formidable sense of humor. As he ascended the ladder of Israeli politics, though, he grew increasingly serious and less likely to joke around, Carol remembered.

A semi-retired market analyst, she can testify to her cousin’s reputation as a workaholic. In one of her recent visits to Israel, she says she was up at midnight when he finally came home from the office. He immediately began running on a treadmill and pedaling an exercise bike while conducting business on the phone.

“He can really multitask,” she said.

She described her cousin as brilliant, articulate and knowledgeable about a surprising breadth of topics. During her recent visit to Israel, she said, Ehud met with a French tutor to help him brush up for a speech he’d be making in France in the lingua franca.

Carol describes herself as being “reasonably close” with her Israeli cousins; Ehud’s younger brother, Yossi Olmert, lived with her and her husband in Walnut Creek for two months last year. She and Ehud speak and write emails periodically; he last checked in with an email Jan. 2 — two days before being handed the reins of the government.

Typically, his emails have discussed the goings-on in the Olmert household. His wife, Aliza, is an artist and playwright, and he has four grown children living in Israel, the United States and France.

She doesn’t talk politics with her cousin, but like many of his family and friends, she leans more to the left than him.

Carol was surprised by her cousin’s political moves of the past few years, which she describes as a “move from the right to the center.” She credits Olmert with helping to spawn and push forward Prime Minister Ariel Sharon’s disengagement plans.

“I believe he possesses the leadership skills that will enable him to succeed in this position. He has an aura around him, he projects confidence and strength,” she said.

“I think family is very important to him. I have always felt he goes out of his way to stay in contact with me. I am always surprised when he emails me personally, because I know how busy he is.”