# Calculate ENSO Skill of NMME model NCEP-CFSv2 as Function of Initial Month vs. Lead Time

## Contents

You can run this notebook in a live session or view it on Github.

# Calculate ENSO Skill of NMME model NCEP-CFSv2 as Function of Initial Month vs. Lead Time#

## In this example, we demonstrate:#

1. How to remotely access data from the North American Multi-model Ensemble (NMME) hindcast database and set it up to be used in climpred leveraging dask.

2. How to calculate the Anomaly Correlation Coefficient (ACC) using monthly data

3. How to calculate and plot historical forecast skill of the Nino3.4 index as function of initialization month and lead time.

## The North American Multi-model Ensemble (NMME)#

Further information on NMME is available from Kirtman et al. [2014] and the NMME project website.

The NMME public database is hosted on the International Research Institute for Climate and Society (IRI) data server http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/.

Since the NMME data server is accessed via this notebook, the time for the notebook to run may take a few minutes and vary depending on the speed that data is downloaded.

## Definitions#

Anomalies

Departure from normal, where normal is defined as the climatological value based on the average value for each month over all years.

Nino3.4

An index used to represent the evolution of the El Nino-Southern Oscillation (ENSO). Calculated as the average sea surface temperature (SST) anomalies in the region 5S-5N; 190-240

# linting
import matplotlib.pyplot as plt
import xarray as xr
import pandas as pd
import numpy as np

from climpred import HindcastEnsemble
import climpred

Function to set 360 calendar to 360_day calendar to decode cf times

def decode_cf(ds, time_var):
"""Decodes time dimension to CFTime standards."""
if ds[time_var].attrs["calendar"] == "360":
ds[time_var].attrs["calendar"] = "360_day"
ds = xr.decode_cf(ds, decode_times=True)
return ds

The original monthly sea surface temperature (SST) hindcast data for the NCEP-CFSv2 model from IRIDL is a large dataset (~20GB). However, we can leverage ingrid on the IRIDL server and open server-side preprocessed data via OpenDAP into xarray. Averaging over longitude X and latitude Y and ensemble member M reduces the download size to just a few kB.

We take the ensemble mean here, since we are just using deterministic metrics in this example. climpred will automatically take the mean over the ensemble while evaluating metrics with comparison="e2o", but this should make things more efficient so it doesn’t have to be done multiple times.

%%time
# server-side average over enso region and ensemble mean
url = 'http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/NCEP-CFSv2/.HINDCAST/.MONTHLY/.sst/X/190/240/RANGEEDGES/Y/-5/5/RANGEEDGES/[X%20Y%20M]average/dods'
fcstds = xr.open_dataset(url, decode_times=False)
fcstds = decode_cf(fcstds, 'S').compute()
fcstds
CPU times: user 59 ms, sys: 15.7 ms, total: 74.7 ms
Wall time: 750 ms
<xarray.Dataset>
Dimensions:  (S: 348, L: 10)
Coordinates:
* S        (S) object 1982-01-01 00:00:00 ... 2010-12-01 00:00:00
* L        (L) float32 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5
Data variables:
sst      (S, L) float64 26.36 26.63 27.15 27.96 ... 27.93 27.18 26.31 25.96
Attributes:
Conventions:  IRIDL

The NMME data dimensions correspond to the following climpred dimension definitions: L=lead,M=member, S=init. climpred renames the dimensions based on their attrs standard_name when creating HindcastEnsemble, but we need to first adapt the coordinates manually.

fcstds = fcstds.rename({"S": "init", "L": "lead"})

Let’s make sure that the lead dimension is set properly for climpred. NMME data stores leads as 0.5, 1.5, 2.5, etc, which correspond to 0, 1, 2, … months since initialization. We will change the lead to be integers starting with zero. climpred also requires that lead dimension has an attribute called units indicating what time units the lead is assocated with. Options are: years, seasons, months, weeks, pentads, days, hours, minutes or seconds. For the monthly NMME data, the lead units are months.

Next, we want to get the verification SST data from the data server. It’s a lot smaller, so we don’t need to worry about saving it out locally. We keep the spatial dimension as one full chunk since we’ll be averaging over the Nino3.4 box soon.

%%time
obsurl='http://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/.OIv2_SST/.sst/X/190/240/RANGEEDGES/Y/-5/5/RANGEEDGES/[X%20Y]average/dods'
verifds = xr.open_dataset(obsurl, decode_times=False)
verifds = decode_cf(verifds, 'T').compute()
verifds
CPU times: user 10.7 ms, sys: 7.87 ms, total: 18.6 ms
Wall time: 479 ms
<xarray.Dataset>
Dimensions:  (T: 405)
Coordinates:
* T        (T) object 1982-01-16 00:00:00 ... 2015-09-16 00:00:00
Data variables:
sst      (T) float64 26.81 26.78 27.26 28.06 ... 28.96 28.83 28.89 28.99
Attributes:
Conventions:  IRIDL

Rename the dimensions to correspond to climpred dimensions.

verifds = verifds.rename({"T": "time"})

Convert the time data to be on the first of the month and in the same calendar format as the forecast output. The time dimension is natively decoded to start in February, even though it starts in January. It is also labelled as mid-month, and we need to label it as the start of the month to ensure that the dates align properly.

verifds["time"] = xr.cftime_range(
start="1982-01", periods=verifds["time"].size, freq="MS", calendar="360_day"
)

Subset the data to 1982-2010

fcstds = fcstds.sel(init=slice("1982-01-01", "2010-12-01"))
verifds = verifds.sel(time=slice("1982-01-01", "2010-12-01"))

Use HindcastEnsemble to calculate the anomaly correlation coefficient (ACC) as a function of initialization groupby="month" and lead. Before HindcastEnsemble.remove_seasonality() remove the monthly seasonal cycle.

%%time
hindcast = HindcastEnsemble(fcstds)
hindcast = hindcast.remove_seasonality("month")
result = hindcast.verify(metric='acc', comparison='e2o', dim='init', alignment='maximize', groupby='month')
CPU times: user 1.55 s, sys: 15 ms, total: 1.57 s
Wall time: 1.62 s

Plot the ACC climpred.metrics._pearson_r() as function of Initial Month and lead-time