The C of CP-REL can be SEM, ER, EÐ or $S (contracted form of SEM in ÞARS).
ÞAR SEM relatives:
Locative relative clauses like "þar sem" (incl. "þaðan sem", "þangað sem", "þá er", are treated according to the PPCME2 guidelines for "There relatives":
Note that these project CP-REL, not CP-ADV.
Quoting from the PPCME2/PPCEME guidelines (http://www.ling.upenn.edu/~beatrice/annotation/syn-sub.htm#there_relatives):
"þars" is split "(ADV þar$-þar) (C $s-es)"
In the absence of both an antecedent and a complementizer, THERE relatives are treated as free relatives.
Relatives introduced by THERE and containing a complementizer (AS, THAT) are treated analogously to SE +TE relatives. THERE is treated as the antecedent unless another antecedent is present, in which case THERE occupies the wh- position and is labelled WADVP."
In Icelandic, an example with "þar sem" *and* an antecedent will be parsed as follows:
( (IP-MAT (CONJ og-og) (NP-SBJ *con*) (VBPI sést-sjá) (ADVP-TMP (ADV nú-nú)) (ADVP-LOC (ADV víða-víða)) (FP aðeins-aðeins) (PP (P fyrir-fyrir) (NP (NS-D tóftum-tóft) (, ,-,) (CP-REL (WADVP-1 (ADV þar-þar)) (C sem-sem) (IP-SUB (ADVP-LOC *T*-1) (NP-SBJ (NS-N sögur$-saga) (D-N $nar-hinn)) (VBPI segja-segja) (, ,-,) (CP-THT (C að-að) (IP-SUB (BEN verið-vera) (HVPS hafi-hafa) (ADVP (ADV vel-vel)) (VAN hýst-hýsa) (NP-SBJ (N-N höfðingjasetur-höfðingjasetur)))))))) (. .-.)) (ID 1850.PILTUR.NAR-FIC,.5))
NOTE! "þar sem" projects an ADVP-LOC when the meaning is locative. But where the meaning is "because" and clearly not locative, there is no extended -LOC label and the phrase is ADVP. This is usually the meaning of "þar eð", which is parsed in the same way, as below:
( (IP-MAT (MDDI vildi-vilja) (NP-SBJ (Q-N hvorug-hvorugur)) (BE vera-vera) (NP-PRD (NP-POS (OTHER-G annarrar-annar)) (N-N eftirbátur-eftirbátur)) (, ,-,) (ADVP (ADV þar-þar) (CP-REL (WADVP-1 0) (C eð-eð) (IP-SUB (ADVP *T*-1) (NP-SBJ (PRO-N þær-hún)) (HVDS hefðu-hafa) (NP-OB1 (ADJ jafnar-jafna) (N-A mannvirðingar-mannvirðing))))) (. .-.)))
( (IP-MAT (CONJ Og-og) (ADVP-TMP (ADV þá-þá) (CP-REL (WADVP-1 0) (C er-er) (IP-SUB (ADVP-TMP *T*-1) (NP-SBJ (PRO-N þeir-hann)) (VBDI riðu-ríða) (PP (ADV ofan-ofan) (P að-að) (NP (NPR-D Hofi-hofi)))))) (VBDI stakk-stinga) (NP-SBJ (NPR-N Hrafn-hrafn)) (RP við-við) (NP-OB1 (NS-D fótum-fótur)) (. .-.)) (ID 13XX.FINNBOGI.NAR-SAG,653.1597))
Á þeim sama degi sem ... 'on the same day as ...':
(CP-ADV (C að-að) (IP-SUB (NP-SBJ (PRO-N þeir-hann)) (VBDS yrðu-verða) (NP-PRD (NS-N vinir-vinur)) (PP (P á-á) (NP (D-D ÞEIM-SÁ) (ADJ sama-samur) (N-D degi-dagur) (CP-REL (WNP-2 0) (C sem-sem) (IP-SUB (NP-TMP *T*-2) (NP-SBJ (N-N kerling-kerling)) (VBDI fór-fara) (PP (P á-á) (PP (P milli-milli) (NP (PRO-G þeirra-hann)))))))))) (. ;-;)))