等压面要素场检验指标绘图

Meteorology/Verification
目录

上一篇文章《计算等压面要素场检验指标 - 并发》及之前的几篇文章介绍如何计算等压面要素场的检验指标。

本文介绍如何用计算得到的检验指标绘图。

数据

检验指标数据保存在 CSV 文件中，如下图所示

forecast_hour,variable,level,region,rmse,me,mae,sd,rmsem,rmsep,acc
0,gh,1000,NHEM,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,1.000000
0,gh,1000,SHEM,0.000000,0.000000,0.000000,0.000000,0.000000,0.000000,1.000000
...
24,t,10,GLOB,1.020141,-0.155320,0.794115,1.008247,0.155320,0.864821,0.963317
...

准备

载入使用的库

import pandas as pd
import numpy as np
import xarray as xr
import matplotlib.pyplot as plt
from tqdm.auto import tqdm

import pathlib

读取单个文件

检验指标文件按照不同的预报时间保存到 CSV 文件中

file_path="./stats.2018072512.csv"

使用 pd.read_csv 函数载入 CSV 文件

table = pd.read_csv(file_path)
table.head()

处理缺失值，数据中的 -999.0 代表缺失值

table[table == -999.0] = np.nan

添加日期作为新列 (date)

table["date"] = pd.to_datetime("2018-07-25 12:00:00")

设置多级索引

table.set_index(
    ["date", "forecast_hour", "variable", "level", "region"]
).head()

将读取单个文件的代码封装成函数 read_stats

def read_stats(file_path: str) -> pd.DataFrame:
    p = pathlib.Path(file_path)
    if not p.exists():
        return None
    current_time = pd.to_datetime(
        p.name, 
        format="stats.%Y%m%d%H.csv"
    )
    table = pd.read_csv(file_path)
    table[table == -999.0] = np.nan
    table["date"] = pd.to_datetime(current_time)
    table = table.set_index(
        ["date", "forecast_hour", "variable", "level", "region"]
    )
    return table

读取多个文件

构造时间序列

date_list = pd.date_range(
    "2018-07-25 12:00", 
    "2018-08-24 12:00", 
    freq='D'
)
date_list[:5]
DatetimeIndex(['2018-07-25 12:00:00', '2018-07-26 12:00:00',
               '2018-07-27 12:00:00', '2018-07-28 12:00:00',
               '2018-07-29 12:00:00'],
              dtype='datetime64[ns]', freq='D')

expr2

读取 expr2 试验的检验指标

构造检验指标文件路径列表

file_list = [
    f"./dask-stat/expr2/stats.{d.strftime('%Y%m%d%H')}.csv" 
    for d in date_list
]
file_list[:5]
['./dask-stat/expr2/stats.2018072512.csv',
 './dask-stat/expr2/stats.2018072612.csv',
 './dask-stat/expr2/stats.2018072712.csv',
 './dask-stat/expr2/stats.2018072812.csv',
 './dask-stat/expr2/stats.2018072912.csv']

读取每个文件

dfs = [read_stats(f) for f in file_list]

将多个 DataFrame 对象合并为 1 个 DataFrame 对象。 合并会根据我们之前添加的多级索引自动完成。

df = pd.concat(dfs)
df

转换为 xarray.DataArray 对象，方便使用带标签名的索引

x = df.to_xarray()
x.attrs["name"] = "expr2"
x

探索数据

选取全球区域 24 时效 850 hPa 的高度场的 ACC 指标

使用 sel 方法，返回一维数组，坐标为预报时间 (date)

acc_h850_024 = x.acc.sel(
    forecast_hour=24, 
    variable="gh", 
    region="GLOB", 
    level=850,
)
acc_h850_024

使用 plot 方法快速绘图

plt.figure(figsize=(10, 5))
acc_h850_024.plot()
plt.show()

ctrl1

载入 ctrl1 控制预报的检验数据

file_list2 = [
    f"./dask-stat/ctrl1/stats.{d.strftime('%Y%m%d%H')}.csv" 
    for d in date_list
]

df_ncep = pd.concat(
    [read_stats(f) for f in file_list2]
)

y = df_ncep.to_xarray()
y.attrs["name"] = "ctrl1"
y

绘制时间序列图

时间序列图直接使用检验指标绘制，没有额外计算

添加一个新的坐标 name 代表试验名称，用于后续合并

acc_x = x.acc.sel(
    forecast_hour=120, 
    variable="t", 
    region="GLOB", 
    level=850
)
acc_x.coords["name"] = "expr2"
acc_x
acc_y = y.acc.sel(
    forecast_hour=120, 
    variable="t", 
    region="GLOB", 
    level=850
)
acc_y.coords["name"] = "ctrl1"
acc_y

沿 name 维度合并两个不同试验的 ACC 指标，返回二维数组

plot_data = xr.concat([acc_x, acc_y], dim="name")
plot_data

绘制时间序列图，横坐标为 date

plt.figure(figsize=(10, 5))
plot_data.plot.line(
    x="date", 
    hue="name"
)
plt.show()

绘制垂直廓线图

需要为每个时效、每个变量、每个层次、每个区域的指标计算均值

ME

求均值

y_me = y["me"].sel(
    forecast_hour=24,
    region="GLOB",
    variable="t"
)
y_me_mean = y_me.mean(dim="date")
y_me_mean.coords["name"] = "ctrl1"
y_me_mean
plt.figure(figsize=(8, 8))
y_me_mean.plot.line(
    y="level",
    yincrease=False,
    yscale="log"
)
plt.show()
x_me = x["me"].sel(
    forecast_hour=24,
    region="GLOB",
    variable="t"
)
x_me_mean = x_me.mean(dim="date")
x_me_mean.coords["name"] = "expr2"
x_me_mean
plt.figure(figsize=(8, 8))
x_me_mean.plot.line(
    y="level",
    yincrease=False,
    yscale="log"
)
plt.show()

合并两个数据集

me_mean = xr.concat(
    [x_me_mean, y_me_mean], 
    dim="name"
)
me_mean
plt.figure(figsize=(8, 8))
me_mean.plot.line(
    y="level",
    yincrease=False,
    yscale="log"
)
plt.show()

RMSE

计算均方根

x_rmse = x["rmse"].sel(
    forecast_hour=24,
    variable="t",
    region="GLOB"
)
x_rmse_mean = np.sqrt((x_rmse*x_rmse).mean(dim="date", skipna=True))
x_rmse_mean.coords["name"] = "expr2"
x_rmse_mean
y_rmse = y["rmse"].sel(
    forecast_hour=24,
    variable="t",
    region="GLOB"
)
y_rmse_mean = np.sqrt((y_rmse*y_rmse).mean(dim="date", skipna=True))
y_rmse_mean.coords["name"] = "ctrl1"
y_rmse_mean

合并数据并画图

rmse_mean = xr.concat(
    [x_rmse_mean, y_rmse_mean], 
    dim="name"
)

plt.figure(figsize=(8, 8))
rmse_mean.plot.line(
    y="level",
    yincrease=False,
    yscale="log"
)
plt.show()

ACC

x_acc = x["acc"].sel(
    forecast_hour=24,
    variable="t",
    region="GLOB"
)
x_acc_mean = np.log(
    (x_acc + 1) / (1 - x_acc)
).mean(dim="date")
x_acc_mean = (np.exp(x_acc_mean) - 1) / (np.exp(x_acc_mean) + 1)
x_acc_mean.coords["name"] = "expr2"
x_acc_mean
y_acc = y["acc"].sel(
    forecast_hour=24,
    variable="t",
    region="GLOB"
)
y_acc_mean = np.log(
    (y_acc + 1) / (1 - y_acc)
).mean(dim="date")
y_acc_mean = (np.exp(y_acc_mean) - 1) / (np.exp(y_acc_mean) + 1)
y_acc_mean.coords["name"] = "ctrl1"
y_acc_mean

合并数据并画图

acc_mean = xr.concat(
    [x_acc_mean, y_acc_mean], 
    dim="name"
)

plt.figure(figsize=(8, 8))
acc_mean.plot.line(
    y="level",
    yincrease=False,
    yscale="log"
)
plt.show()

绘制平均图

RMSE

准备数据

x_rmse = x["rmse"].sel(
    variable="t",
    level=850,
    region="GLOB"
)

为每个预报时效求均值

x_rmse_mean = np.sqrt(
    (x_rmse * x_rmse).mean(
        dim="date", 
        skipna=True
    )
)
x_rmse_mean.coords["name"] = "expr2"
x_rmse_mean
y_rmse = y["rmse"].sel(
    variable="t",
    level=850,
    region="GLOB"
)

y_rmse_mean = np.sqrt(
    (y_rmse*y_rmse).mean(
        dim="date", 
        skipna=True
    )
)
y_rmse_mean.coords["name"] = "ctrl1"
y_rmse_mean

计算

计算单个时效的 Bootstrap 置信区间

bootstrap_rmses = []
forecst_hour_df = x_rmse.sel(forecast_hour=24).to_dataframe()
for i in tqdm(range(10000)):
    m = forecst_hour_df.sample(30, replace=True)["rmse"].mean()
    bootstrap_rmses.append(m)

df = pd.DataFrame({"rmse": bootstrap_rmses})
df.describe()
df.quantile(0.975)
rmse    1.13626
Name: 0.975, dtype: float64

df.quantile(0.025)
rmse    1.096304
Name: 0.025, dtype: float64

所有时效的 95% 置信区间

uppers = []
lowers = []
rmse_diff = x_rmse - y_rmse
for forecast_hour in tqdm(x_rmse.coords["forecast_hour"]):
    bootstrap_rmses = []
    forecst_hour_df = rmse_diff.sel(forecast_hour=forecast_hour).to_dataframe()
    for i in tqdm(range(10000), leave=False):
        m = forecst_hour_df.sample(30, replace=True)["rmse"].mean(skipna=True)
        bootstrap_rmses.append(m)
        
    df = pd.DataFrame({"rmse": bootstrap_rmses})
    upper = df["rmse"].quantile(0.975)
    lower = df["rmse"].quantile(0.025)
    uppers.append(upper)
    lowers.append(lower)

ds = xr.Dataset({
    "upper": (x_rmse_mean.dims, uppers),
    "lower": (x_rmse_mean.dims, lowers),
},
    coords=x_rmse_mean.coords,
)
ds["y_mean"] = y_rmse_mean
ds["x_mean"] = x_rmse_mean
ds

画图

绘制逐时效 RMSE 变化

fig, axes = plt.subplots(
    figsize=(10, 6)
)
axes.xaxis.set_major_locator(plt.MultipleLocator(24))
ds["x_mean"].plot.line(
    x="forecast_hour", 
    ax=axes,
)
ds["y_mean"].plot.line(
    x="forecast_hour", 
    ax=axes
)
axes.legend(["grapes", "ncep"])
plt.show()

绘制模式试验 expr2 相对于控制预报 ctrl1 的 RMSE 平均差值和 95% 置信区间

fig, axes = plt.subplots(
    figsize=(10, 6)
)
axes.xaxis.set_major_locator(plt.MultipleLocator(24))
plt.bar(
    ds.forecast_hour.values,
    (ds.upper - ds.lower).values,
    width=8,
    bottom=(ds.lower - (ds.x_mean - ds.y_mean)).values,
    edgecolor="blue",
    color="white"
)
plt.plot(
    ds.forecast_hour.values,
    (ds.x_mean - ds.y_mean).values,
    color="red"
)
plt.plot(
    ds.forecast_hour,
    np.zeros(len(ds.forecast_hour)),
    color="black",
)
plt.xlim([0, 240])
plt.show()

参考

《计算等压面要素场的基本检验指标》

《计算等压面要素场检验指标 - 多时效》

《计算等压面要素场检验指标 - 并发》