What are the origins of the cope?
The Catholic Encyclopedia has a nice expose about the origins of the cope used in Catholic liturgical celebrations.
Known in Latin as pluviale or cappa), a vestment which may most conveniently be described as a long liturgical mantle, open in front and fastened at the breast with a band or clasp. As existing monuments show, whether we look at pictorial representations or at the copes of early date which still survive, there has been remarkably little change in the character of the vestment from the earliest ages. The most conspicuous external modification which the cope has undergone, during the past thousand years and more, lies in a certain divergence in the shape of the hood, a feature which, after all, is not in any way an essential part of the vestment. In some early examples we find only a triangular hood, which was no doubt intended to of practical utility in covering the head in processions, etc. But with the lapse of time the hood has into a mere ornamental appendage, and it is quite commonly represented by a sort of shield of embroidery, artificially stiffened and sometimes adorned with a fringe, the whole being fastened by buttons or by some other device to the back of the below the broad orphrey which usually forms an upper border to the whole. The fact that in many early chasubles, as depicted in the drawings of the eighth and ninth centuries, we see clear traces of a primitive hood, thus bearing out the explicit statement upon the point of Isidore of Seville, strongly confirms the view that in their origin cope and chasuble were identical, the chasuble being only a cope with its edges sewn together.
The earliest mention of a cappa seems to meet us in Gregory of Tours, and in the "Miracula" of St. Furseus where it seems to mean a cloak with a hood. So from a letter written in 787 by Theodemar, Abbot of Monte Cassino, in answer to a question of Charlemagne about the dress of the monk (see Mon. Germ. Hist.: Epist. Carol., II, 512) we learn that what in Gaul was styled cuculla (cowl) was known to the Cassinese monks as cappa. Moreover the word occurs more than once in Alcuin's correspondence, apparently as denoting a garment for everyday wear. When Alcuin twice observes about a casula which was sent him, that he meant to wear it always at Mass, we may probably infer that such garments at this date were not distinctively liturgical owing to anything in their material or construction, but that they were set aside for the use of the altar at the choice of the owner, who might equally well have used them as part of his ordinary attire. In the case of the chasuble the process of liturgical specialization, if we may so call it, was completed at a comparatively early date, and before the end of the ninth century the maker of a casula probably knew quite well in most cases whether he intended his handiwork for a Mass vestment or for an everyday outer garment. But in the case of a cappa, or cope, this period of specialization seems to have been delayed until much later. The two hundred capp or cope, which we read in a Saint-Riquier inventory in the year 801, a number increased to 377 by the year 831, were, we believe, mere cloaks, for the most part of rude material and destined for common wear. It may be that their use in choir was believed to add to the decorum and solemnity of the Divine Office, especially in the winter season. In 831 one of the Saint-Riquier copes is specially mentioned as being of chestnut colour and embroidered with gold. This, no doubt, implies use by a dignitary, but it does not prove that it was as yet regarded as a sacred vestment. In fact, if we follow the conclusions of Mr. Edmund Bishop (Dublin Review, Jan., 1897), who was the first to sift the evidence thoroughly, it was not until the twelfth century that the cope, made of rich material, was in general use in the ceremonies of the Church, at which time it had come to be regarded as the special vestment of cantors. Still, an ornamental cope was even then considered a vestment that might be used by any member of the clergy from the highest to the lowest, in fact even by one who was only about to be tonsured. Amongst monks it was the practice to vest the whole community, except, of course, the celebrant and the sacred ministers, in copes at high Mass on the greatest festivals, whereas on feasts of somewhat lower grade, the community were usually vested in albs. In this movement the Netherlands, France, and Germany had taken the lead, as we learn from extant inventories. For example, already in 870, in the Abbey of Saint Trond we find "thirty-three precious copes of silk" as against only twelve chasubles, and it was clearly the Cluny practice in the latter part of the tenth century to vest all the monks in copes during high Mass on the great feasts, though in England the regulations of St. Dunstan and St. Æthelwold show no signs of any such observance. The custom spread to the secular canons of such cathedrals as Rouen, and cantors nearly everywhere used copes of silk as their own peculiar adornment in the exercise of their functions.
Meanwhile the old cappa nigra, or cappa choralis, a choir cope of black stuff, open or partly open in front, and commonly provided with a hood, still continued in use. It was worn at Divine Office by the clergy of cathedral and collegiate churches and also by many religious, as, for example, it is retained by the Dominicans during the winter months down to the present day. (See CLERICAL COSTUME.) No doubt the "copes" of the friars, to which we find so many references in the Wycliffite literature and in the writings of Chaucer and Langland, designate their open mantles, which were, we may say, part of their full dress, though not always black in colour. On the other hand we may note that the cappa clausa, or close cope, was simply a cope or cape sewn up in front for common outdoor use. "The wearing of this", says Mr. Bishop, (loc. cit., p. 24), "instead of the 'cappa scissa', the same cope not sewn up, is again and again enjoined on the clergy by synods and statutes during the late Middle Ages." The cappa magna, now worn according to Roman usage by cardinals, bishops, and certain specially privileged prelates on occasions of ceremony, is not strictly a liturgical vestment, but is only a glorified cappa choralis, or choir cope. Its colour for cardinals is ordinarily red, and for bishops violet. It is ample in volume and provided with a long train and a disproportionately large hood, the lining of which last, ermine in winter and silk in summer, is made to show like a tippet across the breast. Further we must note the papal mantum, which differs little from an ordinary cope except that it is red in colour and somewhat longer. In the eleventh and twelfth centuries the immantatio, or bestowal of the mantum on the newly elected pope, was regarded as specially symbolical of investiture with papal authority. "Investio te de-papatu romano ut pr sis urbi et orbi" were the words used in conferring it (I invest thee with the Roman papacy, that thou rule over the city and the world).
Basically, the cope as a liturgical vestment is employed in processions, benediction, assistant priests at pontifical Masses and other many other liturgical functions However it is not worn by priest who are celebrating the Eucharist at Mass (consecration).
The cope is a vestment for processions worn by all ranks of the clergy when assisting at a liturgical function, but it is never worn by the priest and his sacred ministers in celebrating the Mass. At a Pontifical High Mass the cope was worn by the "assistant priest," a priest who assists the bishop who is the actual celebrant. In the Sarum Rite, the Cope was also prescribed for members of the choir at various times.
It is now the vestment assigned to the celebrant, whether priest or bishop, for almost all functions except the Mass when the celebrant wears the chasuble instead. The cope is used, for example, in processions, in the greater blessings and consecrations, at the solemnly celebrated Liturgy of the Hours, in giving Benediction of the Blessed Sacrament, and the celebration of other sacraments outside of Mass. For most of these the celebrant may instead wear simply cassock and surplice or alb, both with the stole, for simpler celebrations. The chasuble, which is properly only worn for Mass, may also be worn during processions and other ceremonies that occur directly before or after Mass, such as the absolutions and burial of the dead, at the Asperges before Mass, and at the blessing and imposition of the ashes on Ash Wednesday, to avoid the need for the celebrant to change vestments.
The Cæremoniale Episcoporum envisages its use by a bishop if presiding at but not celebrating Mass, for the Liturgy of the Hours, for processions, at the special ceremonies on the Feast of the Presentation of the Lord, Lenten gatherings modelled on the "stations" in Rome, Palm Sunday and Corpus Christi. The bishop may use a cope when celebrating outside of Mass the sacraments of baptism, confirmation, matrimony, penance in solemn form, ordination (if not concelebrating), and anointing of the sick. The list in the index of the Cæremoniale Episcoporum continues with several more cases. - Cope (Wikipedia)
One website describes the origins as such:
The Cope and Veil. The cope... was originally worn only in outdoor processions, and was considered merely as a rain-cloak, as is shown by its Latin name, pluviale, a protection against rain. The cape attached to it, which now has no use whatever, is a reminder of the large hood formerly used to cover the head in stormy weather. Our English name, cope, is from the Latin "cappa," a cape. - Vestments
But as the one can see in the Catholic Encyclopedia this is a serious simplification of the liturgical vestment.
Any similarities in the above medieval painting displaying a cope as is used by Catholic clergy is merely an artists interpretation of what he thought to be worn by Jewish priests. In fact, the opposite is true. Jewish priests did not wear copes in their liturgy at all. There is no liturgical cope mentioned in Sacred Scriptures for Jewish priests.
The Torah provides for specific vestments to be worn by the priests when they are ministering in the Tabernacle: "And you shall make holy garments for Aaron your brother, for dignity and for beauty" (Exodus 28:2). These garments are described in detail in Exodus 28, Exodus 39 and Leviticus 8. The high priest wore eight holy garments (bigdei kodesh). Of these, four were of the same type worn by all priests, and four were unique to the Kohen Gadol.
Those vestments which were common to all priests, were:
Priestly undergarments (Hebrew michnasayim) (breeches): linen pants reaching from the waist to the knees "to cover their nakedness" (Exodus 28:42)
Priestly tunic (Hebrew ketonet) (tunic): made of pure linen, covering the entire body from the neck to the feet, with sleeves reaching to the wrists. That of the high priest was embroidered (Exodus 28:39); those of the priests were plain (Exodus 28:40).
Priestly sash (Hebrew avnet) (sash): that of the high priest was of fine linen with "embroidered work" in blue and purple and scarlet (Exodus 28:39, 39:29); those worn by the priests were of white, twined linen.
Priestly turban (Hebrew mitznefet): that of the high priest was much larger than that of the priests and wound so that it formed a broad, flat-topped turban; that for priests was wound so that it formed a cone-shaped turban, called a migbahat.
The vestments that were unique to the high priest were:
Priestly robe (me'il) ("robe of the ephod"): a sleeveless, blue robe, the lower hem of which was fringed with small golden bells alternating with pomegranate-shaped tassels in blue, purple, and scarlet—tekhelet, argaman, tolaat shani.
Ephod: a richly embroidered vest or apron with two onyx engraved gemstones on the shoulders, on which were engraved the names of the tribes of Israel
Priestly breastplate (Hebrew hoshen): with twelve gems, each engraved with the name of one of the tribes; a pouch in which he probably carried the Urim and Thummim. It was fastened to the Ephod
On the front of the turban was a golden plate inscribed with the words: "Holiness unto YHWH" attached to the mitznefet.
High Priest of Israel (Vestments)
The only similarities that that exist in medieval art and the association between Catholic and Jewish vestments is in the eyes of the particular artist. It goes no further.
The medieval liturgist might have said, "our clergy wear vestments because they were handed down to us from the clothing worn by the priests of the Old Testament, who in turn wore them by the express command of God in the law of Moses." This is a tall tale or at least a mistake because ancient Jewish and Christian vestments have only superficial similarities; and by the time the Church made use of vestments (after the end of Roman persecutions and the rise of Constantine, say) Jews and Christians had near zero cultural exchange. Indeed, it was more likely that a Christian would change his habits solely not appear like a Jew, and vice versa.
If we could synthesize all these strains of thought into a greater idea, then, I'd say that a priest wears vestments to: 1.) conform to the rule of the Church (liturgical law), 2.) symbolically erase his own identity by taking up the cloak of Christ, and 3.) emphasize continuity between the religion of the Old Testament and of the New. Each reason may seem questionable on its own, but together, they refute the idea held by cynical nonbelievers that vestments are worn for priests to vainly adorn themselves in rich fabric sewn by the blood, sweat, and tears of a peasant class kept in ignorant darkness by their ecclesiastic overlords. No, friends, it's just the opposite: the priest wears vestments as an act of obedience, to conform himself to the will of God. In theory, at least. This is true for the medieval priest just as much as for the modern one. - A look into the medieval parish church's vestry: on vestments