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The PyDAP developers implemented a module for authenticating with Earthdata Login (it also works for any basic type authentication), but depending upon how you download PyDAP, the module may or may not be included. If the module is included, then to download files from an Earthdata Login enabled server, you can use code like the following:
from pydap.util.urs import install_basic_client
install_basic_client()
from pydap.client import open_url
dataset = open_url('https://goldsmr4.gesdisc.eosdis.nasa.gov/opendap/MERRA2/M2T1NXSLV.5.12.4/2016/06/MERRA2_400.tavg1_2d_slv_Nx.20160601.nc4')
 
If the module is not included, you can manually add it to your code as follows:
# BEGIN BASIC AUTH MODULE CODE (Comments removed)
import cookielib
import netrc
import urllib2
import re
 
import pydap.lib
from pydap.exceptions import ClientError
 
import logging
 
log = logging.getLogger(__name__)
log.setLevel(logging.DEBUG)
 
# Set the debug level for urllib2.
debuglevel=1
 
def install_basic_client(uri='', user='', passwd='', use_netrc=True):
    # Create special opener with support for Cookies
    cj = cookielib.CookieJar()
    
    # Create the password manager and load with the credentials using 
    pwMgr = urllib2.HTTPPasswordMgrWithDefaultRealm()
 
    # Get passwords from the .netrc file nless use_netrc is False    
    if use_netrc:
        logins = netrc.netrc()
        accounts = logins.hosts # a dist of hosts and tuples
        for host, info in accounts.iteritems():
            login, account, password = info
            log.debug('Host: %s; login: %s; account: %s; password: %s' % (host, login, account, password))
            pwMgr.add_password(None, host, login, password)
        
    if uri and user and passwd:
        pwMgr.add_password(None, uri, user, passwd)
    
    opener = urllib2.build_opener(urllib2.HTTPBasicAuthHandler(pwMgr),
                                  urllib2.HTTPCookieProcessor(cj))
    
opener.addheaders = [('User-agent', 'pydap/EL')]
 
    urllib2.install_opener(opener)
 
    def new_request(url):
        if url[-1] is '&': url = url[0:-1]
        log.debug('Opening %s (install_basic_client)' % url)
        r = urllib2.urlopen(url)
        
        resp = r.headers.dict
        resp['status'] = str(r.code)
        data = r.read()
 
        # When an error is returned, we parse the error message from the
        # server and return it in a ``ClientError`` exception.
        if resp.get("content-description") == "dods_error":
            m = re.search('code = (?P<code>\d+);\s*message = "(?P<msg>.*)"',
                    data, re.DOTALL | re.MULTILINE)
            msg = 'Server error %(code)s: "%(msg)s"' % m.groupdict()
            raise ClientError(msg)
 
        return resp, data
 
    from pydap.util import http
    http.request = new_request
    
# END BASIC AUTH MODULE CODE
 
install_basic_client()
from pydap.client import open_url
dataset = open_url('https://goldsmr4.gesdisc.eosdis.nasa.gov/opendap/MERRA2/M2T1NXSLV.5.12.4/2016/06/MERRA2_400.tavg1_2d_slv_Nx.20160601.nc4')
 

 

Note that in both cases, user credentials are pulled from the .netrc file, so that must be set up in order for it to work.

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