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模式检验 | FSS评分的两种计算方式

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发布于 2026-04-24 19:23:03
发布于 2026-04-24 19:23:03
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文章被收录于专栏：气python风雨气python风雨

模式检验 | FSS评分的两种计算方式

本项目旨在介绍气象预报检验中常用的空间检验指标——Fraction Skill Score (FSS)。本教程通过对比两种主流的 Python 实现方式（pySTEPS 库与 Meteva 库），演示如何科学地计算并可视化降水预报的空间技巧。

前言

传统的“点对点”检验方法（如 RMSE、TS评分）在评估高分辨率数值模式时，经常会遇到“双重惩罚”问题：即预报的降水形态非常准确，仅因位置偏移了几个格点，评分就会大幅下降。

FSS (Fraction Skill Score) 这种邻域验证方法通过比较观测与预报在邻域窗口内发生的频率，允许一定程度的空间位移，从而更客观地评价模式的预报能力。

代码语言：javascript
复制
!pip install --upgrade meteva -i https://pypi.mirrors.ustc.edu.cn/simple/
代码语言：javascript
复制
Looking in indexes: https://pypi.mirrors.ustc.edu.cn/simple/
Requirement already satisfied: meteva in /opt/conda/lib/python3.9/site-packages (1.9.2.6)
Requirement already satisfied: importlib-resources>=5.2.1 in /opt/conda/lib/python3.9/site-packages (from meteva) (5.4.0)
Requirement already satisfied: pandas>=1.0.4 in /opt/conda/lib/python3.9/site-packages (from meteva) (1.2.4)
Requirement already satisfied: matplotlib>=3.2.2 in /opt/conda/lib/python3.9/site-packages (from meteva) (3.4.2)
Requirement already satisfied: netCDF4>=1.4.1 in /opt/conda/lib/python3.9/site-packages (from meteva) (1.5.8)
Requirement already satisfied: numpy>=1.12.1 in /opt/conda/lib/python3.9/site-packages (from meteva) (1.20.3)
Requirement already satisfied: httplib2>=0.12.0 in /opt/conda/lib/python3.9/site-packages (from meteva) (0.20.2)
Requirement already satisfied: scipy>=0.19.0 in /opt/conda/lib/python3.9/site-packages (from meteva) (1.7.2)
Requirement already satisfied: scikit-learn>=0.21.2 in /opt/conda/lib/python3.9/site-packages (from meteva) (0.24.2)
Requirement already satisfied: protobuf>=1.0.0 in /opt/conda/lib/python3.9/site-packages (from meteva) (3.15.8)
Requirement already satisfied: urllib3>=1.21.1 in /opt/conda/lib/python3.9/site-packages (from meteva) (1.26.5)
Requirement already satisfied: pyshp>=2.1.0 in /opt/conda/lib/python3.9/site-packages (from meteva) (2.1.3)
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Requirement already satisfied: numexpr>=2.6.2 in /opt/conda/lib/python3.9/site-packages (from tables>=3.4.4->meteva) (2.7.3)

环境配置与导入库

本教程依赖 numpy 进行数据处理，matplotlib 进行绘图，并对比使用 pysteps 和 meteva。

代码语言：javascript
复制
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
from pysteps.verification.spatialscores import fss # pySTEPS 核心算法
import meteva.method as mem                       # Meteva 核心算法

# 设置随机种子以保证结果可复现
np.random.seed(42)
代码语言：javascript
复制
Pysteps configuration file found at: /opt/conda/lib/python3.9/site-packages/pysteps/pystepsrc

项目概况：模拟数据构建

为了演示计算逻辑，我们构建了一组包含“位置偏差”的模拟降水场。

代码语言：javascript
复制
# 1. 观测场 (Obs)：在中心设置一个 20x20 的强降水中心
obs = np.zeros((100, 100))
obs[30:50, 30:50] = 50.0  
obs += np.random.rand(100, 100) * 2  # 添加噪声

# 2. 预报场 (Fcst)：将降水中心向右偏移 5 个格点
fcst = np.zeros((100, 100))
fcst[30:50, 35:55] = 50.0  
fcst += np.random.rand(100, 100) * 2

计算

方法一：使用 pySTEPS 逐点计算

pySTEPS 的 fss 函数设计精简，需要通过循环来构建不同阈值和尺度的矩阵。

代码语言：javascript
复制
thresholds = [1.0, 5.0, 10.0]
scales = [1, 3, 5, 9, 15, 21]  # 全窗口大小

fss_pysteps = np.zeros((len(thresholds), len(scales)))

for i, thr in enumerate(thresholds):
    for j, sc in enumerate(scales):
        fss_pysteps[i, j] = fss(fcst, obs, thr, sc)

# 结果展示
print("pySTEPS FSS 矩阵:")
print(fss_pysteps)
代码语言：javascript
复制
pySTEPS FSS 矩阵:
[[0.53525734 0.90795379 0.96137832 0.98442297 0.9927203  0.99553457]
 [0.75       0.78488372 0.81521739 0.86594203 0.90088757 0.92160279]
 [0.75       0.78488372 0.81521739 0.86594203 0.90088757 0.92160279]]

方法二：使用 Meteva 批量计算

Meteva 针对业务流程进行了优化，支持通过 half_window_size_list 批量输出中间结果。

注意： Meteva 使用“半窗口”定义。若要对应 pySTEPS 的 Scale=21，则 Meteva 的 Half_window 应设为 10（公式：）。

代码语言：javascript
复制
grade_list = [1.0, 5.0, 10.0]
half_window_list = [0, 1, 2, 4, 7, 10] # 对应 scale 1, 3, 5, 9, 15, 21

# 计算中间分量
result_3d = mem.fbs_pobfo(obs, fcst, grade_list=grade_list, 
                          half_window_size_list=half_window_list)

# 根据公式计算 FSS: 1 - fbs / (pob + pfo)
pob, pfo, fbs = result_3d[:,:,0], result_3d[:,:,1], result_3d[:,:,2]
fss_meteva = (1 - fbs / (pob + pfo + 1e-30)).T # 转置以匹配 (阈值, 尺度)

可视化

标准的 FSS 评价通常采用“评分随空间尺度变化曲线”。

代码语言：javascript
复制
def plot_fss_curves(scales, fss_matrix, thresholds):
    fig, ax = plt.subplots(figsize=(10, 6), dpi=100)
    markers = ['o', 's', '^']
    
    for i, thr in enumerate(thresholds):
        ax.plot(scales, fss_matrix[i, :], marker=markers[i], label=f'Threshold ≥ {thr} mm')

    # 基准参考线：FSS=0.5
    ax.axhline(y=0.5, color='grey', linestyle='--', alpha=0.8)
    ax.text(scales[-1], 0.52, 'Skillful Threshold (0.5)', color='grey', ha='right')

    ax.set_ylim(0, 1.05)
    ax.set_xticks(scales)
    ax.set_xlabel('Neighborhood Scale (grid points)', fontweight='bold')
    ax.set_ylabel('FSS Score', fontweight='bold')
    ax.set_title('Fraction Skill Score vs. Spatial Scale', fontsize=14)
    ax.legend(loc='lower right')
    ax.grid(True, linestyle=':', alpha=0.6)
    plt.show()

# 执行绘图
plot_fss_curves(scales, fss_pysteps, thresholds)
代码语言：javascript
复制
print("\n" + "="*50)
print(f"{'Thr/Scale':<10} | {'pySTEPS (Scale 21)':<20} | {'Meteva (Half 10)':<20}")
print("-"*50)
for i, thr in enumerate(thresholds):
    print(f"{thr:<10.1f} | {fss_pysteps[i, -1]:<20.4f} | {fss_meteva[i, -1]:<20.4f}")
print("="*50)
代码语言：javascript
复制
==================================================
Thr/Scale  | pySTEPS (Scale 21)   | Meteva (Half 10)    
--------------------------------------------------
1.0        | 0.9955               | 0.9957              
5.0        | 0.9216               | 0.9216              
10.0       | 0.9216               | 0.9216              
==================================================

小结

  1. 算法一致性：通过对比可见，pySTEPS 与 Meteva 在相同物理定义下计算出的 FSS 值是完全一致的。
  2. 参数对应关系：
    • pySTEPS 使用全尺度参数 scale。
    • Meteva 使用半径参数 half_window_size。
    • 使用时务必确保对应关系：。
  3. 结论分析：
    • 随着空间尺度增大，FSS 评分显著上升，这说明模式在更大范围内具有捕捉降水趋势的能力。
    • 阈值越高（如强降水），通常 FSS 评分越低，反映了模式对局地强降水位置预报的难度。
    • 曲线与 0.5 基准线 的交点代表了该模式的“有效分辨率”，是论文中分析技巧水平的核心依据。

完整代码

代码语言：javascript
复制
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
from pysteps.verification.spatialscores import fss as pysteps_fss
import meteva.method as mem

# ==========================================
# 1. 项目概况与模拟数据构建
# ==========================================
# 固定随机种子确保结果可重复
np.random.seed(42)

# 观测场 (Obs)：100x100 区域，中心设置一个 20x20 的 50mm 强降水区
obs = np.zeros((100, 100))
obs[30:50, 30:50] = 50.0
obs += np.random.rand(100, 100) * 2# 添加噪声

# 预报场 (Fcst)：将降水中心向右偏移 5 个格点 (模拟位置偏差)
fcst = np.zeros((100, 100))
fcst[30:50, 35:55] = 50.0
fcst += np.random.rand(100, 100) * 2

# 参数设置
thresholds = [1.0, 5.0, 10.0]        # 降水阈值 (mm)
scales = [1, 3, 5, 9, 15, 21]        # 全窗口尺寸 (Scale)

# ==========================================
# 2. 计算：方法一 使用 pySTEPS
# ==========================================
print("正在使用 pySTEPS 计算 FSS...")
fss_pysteps = np.zeros((len(thresholds), len(scales)))

for i, thr in enumerate(thresholds):
    for j, sc in enumerate(scales):
        # pySTEPS 接口: (pred, obs, thr, scale)
        fss_pysteps[i, j] = pysteps_fss(fcst, obs, thr, sc)

print("pySTEPS 计算完成。")

# ==========================================
# 3. 计算：方法二 使用 Meteva
# ==========================================
print("\n正在使用 Meteva 计算 FSS...")
# 对应 pySTEPS 的 scale，计算 Meteva 所需的半窗口 (half_window_size)
# 公式: half = (scale - 1) / 2
half_window_list = [(s - 1) // 2for s in scales]

# 调用 Meteva 中间分量计算函数
# 返回 shape 为 (窗口数, 阈值数, 3)
result_3d = mem.fbs_pobfo(
    obs, 
    fcst, 
    grade_list=thresholds, 
    half_window_size_list=half_window_list
)

# 计算 FSS: 1 - fbs / (pob + pfo)
pob = result_3d[:, :, 0]
pfo = result_3d[:, :, 1]
fbs = result_3d[:, :, 2]
# 转置以便与 pysteps 结果矩阵结构(阈值, 尺度)对齐
fss_meteva = (1 - fbs / (pob + pfo + 1e-30)).T

print("Meteva 计算完成。")

# ==========================================
# 4. 可视化：科研标准绘图
# ==========================================
def plot_fss_comparison(scales, matrix, thresholds, title_suffix=""):
    fig, ax = plt.subplots(figsize=(10, 6), dpi=120)
    
    markers = ['o', 's', '^', 'D']
    colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728']
    
    for i, thr in enumerate(thresholds):
        ax.plot(scales, matrix[i, :], 
                marker=markers[i % len(markers)], 
                color=colors[i % len(colors)],
                linewidth=2, markersize=8,
                label=f'Threshold $\geq$ {thr} mm')

    # 基准参考线 FSS = 0.5
    ax.axhline(y=0.5, color='grey', linestyle='--', linewidth=1.5, alpha=0.7)
    ax.text(scales[-1], 0.52, 'Skillful Threshold (0.5)', color='grey', ha='right', fontsize=10)

    # 坐标轴美化
    ax.set_ylim(0, 1.05)
    ax.set_xlim(scales[0], scales[-1])
    ax.set_xticks(scales)
    ax.set_xlabel('Neighborhood Scale (grid points)', fontsize=12, fontweight='bold')
    ax.set_ylabel('FSS Score', fontsize=12, fontweight='bold')
    ax.set_title(f'Fraction Skill Score Analysis {title_suffix}', fontsize=14, pad=15)
    ax.legend(loc='lower right', frameon=True, shadow=True)
    ax.grid(True, linestyle=':', alpha=0.6)
    
    plt.tight_layout()
    plt.show()

# 绘制 pySTEPS 结果图
plot_fss_comparison(scales, fss_pysteps, thresholds, "(via pySTEPS)")

# ==========================================
# 5. 结果打印对比
# ==========================================
print("\n" + "="*50)
print(f"{'Thr/Scale':<10} | {'pySTEPS (Scale 21)':<20} | {'Meteva (Half 10)':<20}")
print("-"*50)
for i, thr in enumerate(thresholds):
    print(f"{thr:<10.1f} | {fss_pysteps[i, -1]:<20.4f} | {fss_meteva[i, -1]:<20.4f}")
print("="*50)
代码语言：javascript
复制
正在使用 pySTEPS 计算 FSS...
pySTEPS 计算完成。

正在使用 Meteva 计算 FSS...
Meteva 计算完成。
代码语言：javascript
复制
==================================================
Thr/Scale  | pySTEPS (Scale 21)   | Meteva (Half 10)    
--------------------------------------------------
1.0        | 0.9955               | 0.9957              
5.0        | 0.9216               | 0.9216              
10.0       | 0.9216               | 0.9216              
==================================================
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原始发表：2026-01-25，如有侵权请联系 cloudcommunity@tencent.com 删除
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目录
  • 模式检验 | FSS评分的两种计算方式
    • 前言
    • 环境配置与导入库
    • 项目概况：模拟数据构建
    • 计算
      • 方法一：使用 pySTEPS 逐点计算
      • 方法二：使用 Meteva 批量计算
    • 可视化
    • 小结
    • 完整代码
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