```python
def cross_up(readings: list, level: int) -> int:
    """Count how many times a reading crosses the level going upward."""
    if not readings:
        return 0
    
    count = 0
    for i in range(1, len(readings)):
        if readings[i] >= level and readings[i - 1] < level:
            count += 1
            
    return count
```