How to Clear Contents of an observableArray That was Populated from Previous Visits to a View

Also knockout observableArray has interesting methods. Call removeAll to clear all items.
Look at official site observable array manual.

self.mycertificates = ko.observableArray(['C1', 'C2']);  
self.mycertificates.removeAll();

Just set it equal to nothing (allCertificates([])) in your activate function, which is called each time your view model loads -

function(logger, system, router, CertificateDataService) {
    var allCertificates = ko.observableArray();

var activate = function () {
    allCertificates([]);
    // go get local data, if we have it
    return SelectAllCerts(),SelectMyCerts(), GetCertificateDetails(), GetDDABankNums();
};

var vm = {
    activate: activate,
    allCertificates: allCertificates,
    SelectAllCerts: SelectAllCerts
});

For Jeremy T (not enough space in comment).
First reason and absolutely enough for me is existence of publicly available API for desired purpose.

But to estimate performance you can check source. "observableArray" is also "observable" with additional functions injected into object.

So initialization looks like this:

ko.observableArray = function (initialValues) {
    initialValues = initialValues || [];

    if (typeof initialValues != 'object' || !('length' in initialValues))
        throw new Error("The argument passed when initializing an observable array must be an array, or null, or undefined.");

    var result = ko.observable(initialValues);
    ko.utils.extend(result, ko.observableArray['fn']);
    return result.extend({'trackArrayChanges':true});
};

ko.observable = function (initialValue) {
    var _latestValue = initialValue;

    function observable() {
        if (arguments.length > 0) {
            // Write

            // Ignore writes if the value hasn't changed
            if (!observable['equalityComparer'] || !observable['equalityComparer'](_latestValue, arguments[0])) {
                observable.valueWillMutate();
                _latestValue = arguments[0];
                if (DEBUG) observable._latestValue = _latestValue;
                observable.valueHasMutated();
            }
            return this; // Permits chained assignments
        }
        else {
            // Read
            ko.dependencyDetection.registerDependency(observable); // The caller only needs to be notified of changes if they did a "read" operation
            return _latestValue;
        }
    }
    if (DEBUG) observable._latestValue = _latestValue;
    ko.subscribable.call(observable);
    observable.peek = function() { return _latestValue };
    observable.valueHasMutated = function () { observable["notifySubscribers"](_latestValue); }
    observable.valueWillMutate = function () { observable["notifySubscribers"](_latestValue, "beforeChange"); }
    ko.utils.extend(observable, ko.observable['fn']);

    ko.exportProperty(observable, 'peek', observable.peek);
    ko.exportProperty(observable, "valueHasMutated", observable.valueHasMutated);
    ko.exportProperty(observable, "valueWillMutate", observable.valueWillMutate);

    return observable;
}

And remove all elements looks like this:

'removeAll': function (arrayOfValues) {
        // If you passed zero args, we remove everything
        if (arrayOfValues === undefined) {
            var underlyingArray = this.peek();
            var allValues = underlyingArray.slice(0);
            this.valueWillMutate();
            underlyingArray.splice(0, underlyingArray.length);
            this.valueHasMutated();
            return allValues;
        }
        // If you passed an arg, we interpret it as an array of entries to remove
        if (!arrayOfValues)
            return [];
        return this['remove'](function (value) {
            return ko.utils.arrayIndexOf(arrayOfValues, value) >= 0;
        });
    }