python马尔可夫预测降水量

### 使用Python实现基于马尔可夫模型的降水量预测

为了利用马尔可夫模型进行降水量预测，可以遵循以下结构化的方法来构建和训练模型。此方法不仅涉及数据预处理阶段，还包括定义状态转移矩阵以及应用该模型对未来降水量做出预测。

#### 数据准备与预处理

在开始之前，确保拥有历史降水量记录作为时间序列数据。对于这些数据，首先需要将其划分为不同的降水等级或状态。这可以通过设定阈值区间完成，例如无雨、轻度降雨、中度降雨和重度降雨等类别[^4]。

import numpy as np
import pandas as pd

def categorize_rainfall(rainfall_values, thresholds=[0, 10, 25, 50]):
    """根据给定的阈值将连续型降水量数值分类"""
    categories = ['No Rain', 'Light', 'Moderate', 'Heavy']
    categorized_data = []
    
    for value in rainfall_values:
        category_index = sum(value > threshold for threshold in thresholds)
        categorized_data.append(categories[min(category_index, len(categories)-1)])
        
    return categorized_data

#### 构建状态转移矩阵

一旦完成了对原始观测值的状态划分，则下一步就是估计不同状态下相互转变的概率。通过统计相邻时间段内各类别之间的变化频率并规范化得到状态转移概率矩阵。

from collections import Counter

def build_transition_matrix(categorized_sequence):
    states = list(set(categorized_sequence))
    n_states = len(states)

    transition_counts = {state:Counter() for state in states}
    
    # 计算每一对前后相继的状态出现次数
    for prev_state, next_state in zip(categorized_sequence[:-1], categorized_sequence[1:]):
        transition_counts[prev_state][next_state] += 1
    
    # 转换成概率形式
    transition_probabilities = {}
    for from_state in states:
        total_transitions_from_this_state = sum(transition_counts[from_state].values())
        probabilities_for_each_to_state = {
            to_state : count / max(total_transitions_from_this_state, 1e-9) 
            for to_state, count in transition_counts[from_state].items()
        }
        transition_probabilities[from_state] = probabilities_for_each_to_state
        
    return pd.DataFrame([pd.Series(v).fillna(0) for v in transition_probabilities.values()], index=states)[states]

categorized_series = categorize_rainfall(historical_rainfalls)
trans_matrix = build_transition_matrix(categorized_series)
print(trans_matrix)

#### 进行未来预测

有了上述建立起来的状态转移矩阵之后，就可以用来推测未来的天气状况了。这里采用随机游走的方式，在已知当前条件下按照转移概率选取下一个可能发生的事件；重复这一过程直至达到所需的预报长度。

np.random.seed(42)  # 设置种子以便重现结果

def predict_future(current_state, trans_matrix, steps_ahead=7):
    future_predictions = [current_state]
    
    while len(future_predictions)<steps_ahead+1:
        current_row = trans_matrix.loc[current_state]
        possible_next_states = list(current_row.index)
        probs_of_next_states = list(current_row.values)
        
        chosen_next_state = np.random.choice(
            a=possible_next_states,
            p=probs_of_next_states
        )
        future_predictions.append(chosen_next_state)
        current_state = chosen_next_state
        
    return future_predictions[1:]

last_known_state = categorized_series[-1]
predicted_outcomes = predict_future(last_known_state, trans_matrix, steps_ahead=30)
print(predicted_outcomes)

以上代码片段展示了如何使用Python编程语言创建一个简单的马尔可夫链模型来进行短期至中期范围内的降水量趋势预测。值得注意的是实际应用场景下还需要考虑更多因素如季节性变动等因素的影响，并且应当结合其他气象学专业知识共同评估预测准确性.