The weather and climate comply with the fluid dynamical equation and appear stochastic. In order to explore the relationship between weather and climate, the fractional derivative and integration are introduced. Physically, the stochastic degrees of weather and climate are different. It is proposed that the qth (0≤q≤1) derivative of climate is weather. When q = 1, it is the Hass elmann's result. The analysis based on observation data shows that climate anomaly has longer range correlation and better memory than weather. The probability density function of climate has a long tail, which can reflect the probability of extreme weather and climate.