Probabilistic Models for Predicting Archaeological Site Locations in Marj Bisri (Southern Lebanon): Comparing Frequency Ratio and Shannon&rsquo;s Entropy

Georges Abou Diwan

doi:10.5334/jcaa.150

Figures & Tables

Table 1

List of the archaeological sites recorded during the Polish survey (after Dar Al-Handasah 2014: 95–96). The coordinates were converted to UTM Zone 36 N.

SITE NO.	NATURE OF FIND	EASTING	NORTHING	DISTANCE TO DAM RESERVOIR	SIZE IN PIXEL
1	Pottery, wall, olive crusher, Persian-Roman	736235.985	3719664.595	within	16
2	Pottery, wall, olive crusher, Persian-Roman	736392.9573	3719806.288	within	16
3	Pottery pieces, Recent	736459.4658	3719724.69	within	16
4	(Unrecorded)	736668.3894	3719936.384	within	16
5	(Unrecorded)	736764.9249	3719997.337	within	16
6	Pottery pieces, Roman	737403.9231	3720552.607	59 m	16
7	Regular stone blocks, Undated	737417.0186	3720753.315	101 m	16
8	Pottery, Undated	737941.1123	3720528.91	within	16
9	House, C20	739766.2872	3720790.118	within	16
10	Village, C19–20	738557.1386	3720966.548	116 m	16
11	Pottery, glazed, C19–20	739308.3301	3720118.956	within	16
12	Pottery, C19–20, one fragment C2BC	739753.3974	3720996.35	161 m	16
13	House, Undated	739781.988	3721194.369	243 m	16
14	House with large stones, Undated	740174.4668	3721386.072	236 m	16
15	Houses, Pottery, C19–20	740317.5383	3721235.507	36 m	16
16	House, Undated	739859.4472	3721088.402	112 m	16
17	Marj Bisri Temple, Roman	740104.1922	3720585.843	within	16
18	Rock shelter, stone tool, Palaeolithic	741331.29	3722059.421	363 m	16
19	House, C19–20	741034.1608	3722181.436	73 m	16
20	House, C20	740462.0946	3720819.852	within	16
21	Stone arch, Undated	740964.033	3722919.578	30 m	16
22	Cave, Use Recent	740947.948	3722943.838	58 m	16
23	(Unrecorded)	740524.1313	3719578.995	227 m	16
23	Ceramics and pottery pieces, Undated	740516.3186	3719581.882	223 m	16
24	Pottery, C18–19, flint flake, Palaeolithic-Neolithic	740726.9422	3719207.961	250 m	16
25	(Unrecorded)	740889.5223	3719104.135	373 m	16
26	House, C19–20	740635.5841	3718425.698	33 m	16
27	Settlement, pottery, Recent, some older	738621.282	3720046.368	178 m	16
28	Pottery, Undated	738496.6933	3719660.999	550 m	16
30	House, pottery, C19–20	739891.6207	3719800.558	75 m	16
31	Settlement, pottery, C2BC to C3–4	739745.417	3719766.078	162 m	16
32	Rock blocks, glazed pottery, C19–20	739771.6961	3719436.866	205 m	16
33	Possible stone borer, possibly Palaeolithic	739780.3142	3719298.351	225 m	16
34	House, pottery, Undated	740179.8849	3719209.681	107 m	16
35	House, C20	740374.4125	3719787.966	27 m	16
36	Rock-cut tomb (looted), pottery, C3–4	740310.6411	3720686.578	7 m	16
37	Settlement, pottery, 2C BC	739000.7553	3720348.677	within	16
38	Settlement, pottery, 2C BC	737780.9271	3719704.908	125 m	16
39	House, C19–20	737800.1041	3719242.958	439 m	16
40	Village, glazed pottery, C19–20	737278.9249	3719242.401	197 m	16
41	Small stone fortress, pottery, Undated	737275.4909	3719485.859	3 m	16
44	Stone mill, Undated	737256.8901	3719716.611	within	16
45	House or checkpoint, Undated	736884.5654	3719309.738	within	16
46	Rock-cut tombs, Roman to C2–3	736379.6055	3718985.936	16 m	16
47	Village, pottery, Roman-Ottoman	736388.7079	3719140.299	within	16
48	House or checkpoint, Undated	736060.8294	3718728.392	316 m	16
49	House, Undated	736028.3606	3718579.621	459 m	16
50	Settlement, pottery? Roman	736802.5295	3718053.015	1024 m	16
52	(Unrecorded)	737207.68	3719619.828	within	16
53	Settlement, pottery, Roman	735895.8034	3717777.926	1253 m	16
55	Necropolis, pottery, Undated	738142.9797	3720503.087	within	16
56	Possible rock-cut tomb, Undated	735888.5651	3718388.138	695 m	16
57	Pottery, Undated	735864.2936	3717379.475	1646 m	16
58	(Unrecorded)	736367.5043	3717065.062	1913 m	16
60	House, Undated	737455.8349	3719496.481	11 m	16
61	Pottery, Undated	733158.3467	3717335.033	3500 m	16
62	House, C19–20	734539.409	3718373.607	1782 m	16
63	(Unrecorded)	739470.0852	3720357.287	within	16
64	Settlement, Roman-Recent	733669.464	3718389.403	2522 m	16
66	House, pottery? Roman	732853.204	3718745.676	3150 m	16
67	(Unrecorded)	735340.2264	3719284.107	627 m	16
68	Settlement, flints? Neolithic	734509.0242	3718878.435	1551 m	16
69	Settlement, pottery, Recent	734630.1796	3718671.766	1550 m	16
71	Settlement, pottery, Undated	731009.0441	3717431.103	5335 m	16
74	Pottery, glass, Roman	734250.9857	3718773.492	1829 m	16
75	Settlement pottery, glass, coin, Roman	735741.1182	3719349.428	249 m	16
76	(Unrecorded)	735926.5454	3719363.229	83 m	16

The geo-environmental variables influencing the location of archaeological sites.

Table 2

Distribution of Archaeological Sites Across Environmental Variables with Kolmogorov-Smirnov goodness-of-fit test Dmax Values.

VARIABLES	CLASS	AREA IN PIXELS	AREA %	EXPECTED SURFACE OF SITES IN PIXELS	CUMULATIVE FREQUENCY	SITES SURFACE IN PIXELS	% OF SITES	CUMULATIVE FREQUENCY	D
Cost Distance to Streams (expressed in decimal hours)	0.001–0.032	20961	36.53%	377	0.365	546	52.91%	0.529	0.16
	0.033–0.7	12384	21.58%	223	0.581	275	26.65%	0.796	0.21
	0.071–0.11	8030	14.00%	144	0.721	85	8.24%	0.878	0.16
	0.111–0.15	5643	9.84%	102	0.820	52	5.04%	0.928	0.11
	0.151–0.192	4161	7.25%	75	0.892	35	3.39%	0.962	0.07
	0.193–0.236	2669	4.65%	48	0.939	32	3.10%	0.993	0.05
	0.237–0.283	1949	3.40%	35	0.973	7	0.68%	1.000	0.03
	0.284–0.334	1277	2.23%	23	0.995	0	0.00%	1.000	0.01
	0.335–0.389	293	0.51%	5	1.000	0	0.00%	1.000	0.00
	0.39–0.538	8	0.01%	0	1.000	0	0.00%	1.000	0.00
	n =	57375	100%	1032		1032	100%		Dmax = 0.21
DIFF (landforms)	Valley	7398	12.89%	133	0.129	137	13.28%	0.133	0.004
	Lower slope	9432	16.44%	170	0.293	187	18.12%	0.314	0.021
	Flat slope	1834	3.20%	33	0.325	66	6.40%	0.378	0.053
	Middle slope	22952	40.00%	413	0.725	379	36.72%	0.745	0.020
	Upper slope	7506	13.08%	135	0.856	152	14.73%	0.892	0.036
	Ridge	8253	14.38%	148	1.000	111	10.76%	1.000	0.000
	n =	57375	100%	1032		1032	100%		Dmax = 0.053
Slope (Logarithmic)	1.001-1	31	0.05%	1	0.001	2	0.19%	0.002	0.001
	1.001–6.224	1061	1.85%	19	0.019	28	2.71%	0.029	0.010
	6.225–7.106	2035	3.55%	37	0.055	76	7.36%	0.103	0.048
	7.107–7.706	2844	4.96%	51	0.104	74	7.17%	0.174	0.070
	7.707–8.129	4969	8.66%	89	0.191	124	12.02%	0.295	0.104
	8.13–8.482	8120	14.15%	146	0.332	174	16.86%	0.463	0.131
	8.483–8.765	10118	17.63%	182	0.509	195	18.90%	0.652	0.144
	8.766–9.047	11642	20.29%	209	0.711	200	19.38%	0.846	0.135
	9.048–9.329	10713	18.67%	193	0.898	110	10.66%	0.953	0.054
	9.33–10	5842	10.18%	105	1.000	49	4.75%	1.000	0.000
	n =	57375	100%	1032		1032	100%		Dmax = 0.144
Aspect	Flat	31	0.05%	1	0.001	2	0.19%	0.002	0.00
	North	8809	15.35%	158	0.154	163	15.79%	0.160	0.006
	Northeast	5117	8.92%	92	0.243	121	11.72%	0.277	0.03
	East	6215	10.83%	112	0.352	87	8.43%	0.361	0.01
	Southeast	6522	11.37%	117	0.465	199	19.28%	0.554	0.09
	South	7471	13.02%	134	0.595	134	12.98%	0.684	0.09
	Southwest	4730	8.24%	85	0.678	48	4.65%	0.731	0.05
	West	8834	15.40%	159	0.832	148	14.34%	0.874	0.04
	North West	9646	16.81%	173	1.000	130	12.60%	1.000	0.00
	n =	57375	100%	1032		1032	100%		Dmax = 0.09
Elevation	139–265	1371	2.39%	25	0.024	0	0.00%	0.000	0.02
	266–392	2410	4.20%	43	0.066	18	1.74%	0.017	0.048
	393–519	14924	26.01%	268	0.326	621	60.17%	0.619	0.29
	520–646	12035	20.98%	217	0.536	336	32.56%	0.945	0.41
	647–774	10420	18.16%	187	0.717	57	5.52%	1.000	0.28
	775–901	9642	16.81%	173	0.886	0	0.00%	1.000	0.11
	902–1028	4229	7.37%	76	0.959	0	0.00%	1.000	0.04
	1029–1155	1146	2.00%	21	0.979	0	0.00%	1.000	0.02
	1156–1282	889	1.55%	16	0.995	0	0.00%	1.000	0.01
	1283–1409	309	0.54%	6	1.000	0	0.00%	1.000	0.00
	n =	57375	100%	1032		1032	100%		Dmax = 0.41
Soil	Areno-Eutric Leptosols	11814	20.58%	212	0.206	137	13.28%	0.133	0.073
	Calcaro_Hortic Anthrosols	4955	8.63%	89	0.292	24	2.33%	0.156	0.136
	Eutric Arenosols	16637	28.98%	299	0.582	401	38.86%	0.545	0.037
	Eutric Gleysols	3402	5.93%	61	0.641	14	1.36%	0.558	0.083
	Calcaric Regosols	92	0.16%	2	0.643	0	0.00%	0.558	0.085
	Haplic Cambisols	86	0.15%	2	0.644	0	0.00%	0.558	0.086
	Humi-Eutric Cambisols	5555	9.68%	100	0.741	252	24.42%	0.802	0.061
	Lithic Leptosols	8073	14.06%	145	0.882	160	15.50%	0.957	0.076
	Rendzic Leptosols	2449	4.27%	44	0.924	7	0.68%	0.964	0.040
	Eutric Regosols	1107	1.93%	20	0.944	3	0.29%	0.967	0.023
	Hypoluvic Arenosols	1276	2.22%	23	0.966	18	1.74%	0.984	0.019
	Haplic Luvisols and Leptic Luvisols	1204	2.10%	22	0.987	11	1.07%	0.995	0.008
	Haplic Luvisols	760	1.32%	14	1.000	5	0.48%	1.000	0.000
	n =	57410	20.58%	1032		3685	100%		Dmax = 0.136

Table 3

Frequency ratio values of the conditioning geo-environmental variables.

VARIABLE	CLASS	NUMBER OF PIXELS IN CLASS	CLASS % (A)	NUMBER OF SITE PIXELS WITHIN EACH CLASS	SITES % (B)	FREQUENCY RATIO (B/A)
Cost Distance to Streams (expressed decimal in hours)	0.001–0.032	20961	36.53%	546	52.91%	1.45
	0.033–0.7	12384	21.58%	275	26.65%	1.23
	0.071–0.11	8030	14.00%	85	8.24%	0.59
	0.111–0.15	5643	9.84%	52	5.04%	0.51
	0.151–0.192	4161	7.25%	35	3.39%	0.47
	0.193–0.236	2669	4.65%	32	3.10%	0.67
	0.237–0.283	1949	3.40%	7	0.68%	0.20
	0.284–0.334	1277	2.23%	0	0.00%	0.00
	0.335–0.389	293	0.51%	0	0.00%	0.00
	0.39–0.538	8	0.01%	0	0.00%	0.00
DIFF (landforms)	Valley	7398	12.89%	137	13.28%	1.03
	Lower slope	9432	16.44%	187	18.12%	1.10
	Flat slope	1834	3.20%	66	6.40%	2.00
	Middle slope	22952	40.00%	379	36.72%	0.92
	Upper slope	7506	13.08%	152	14.73%	1.13
	Ridge	8253	14.38%	111	10.76%	0.75
Slope (rescaled logarithmic)	1.001-1	31	0.05%	2	0.19%	3.59
	1.001–6.224	1061	1.85%	28	2.71%	1.47
	6.225–7.106	2035	3.55%	76	7.36%	2.08
	7.107–7.706	2844	4.96%	74	7.17%	1.45
	7.707–8.129	4969	8.66%	124	12.02%	1.39
	8.13–8.482	8120	14.15%	174	16.86%	1.19
	8.483–8.765	10118	17.63%	195	18.90%	1.07
	8.766–9.047	11642	20.29%	200	19.38%	0.96
	9.048–9.329	10713	18.67%	110	10.66%	0.57
	9.33–10	5842	10.18%	49	4.75%	0.47
Aspect	Flat	31	0.05%	2	0.19%	3.59
	North	8809	15.35%	163	15.79%	1.03
	Northeast	5117	8.92%	121	11.72%	1.31
	East	6215	10.83%	87	8.43%	0.78
	Southeast	6522	11.37%	199	19.28%	1.70
	South	7471	13.02%	134	12.98%	1.00
	Southwest	4730	8.24%	48	4.65%	0.56
	West	8834	15.40%	148	14.34%	0.93
	North West	9646	16.81%	130	12.60%	0.75
Elevation	139–265	1371	2.39%	0	0.00%	0.00
	266–392	2410	4.20%	18	1.74%	0.42
	393–519	14924	26.01%	621	60.17%	2.31
	520–646	12035	20.98%	336	32.56%	1.55
	647–774	10420	18.16%	57	5.52%	0.30
	775–901	9642	16.81%	0	0.00%	0.00
	902–1028	4229	7.37%	0	0.00%	0.00
	1029–1155	1146	2.00%	0	0.00%	0.00
	1156–1282	889	1.55%	0	0.00%	0.00
	1283–1409	309	0.54%	0	0.00%	0.00
Soil	Areno-Eutric Leptosols	11814	20.58%	137	13.28%	0.65
	Calcaro_Hortic Anthrosols	4955	8.63%	24	2.33%	0.27
	Eutric Arenosols	16637	28.98%	401	38.86%	1.34
	Eutric Gleysols	3402	5.93%	14	1.36%	0.23
	Calcaric Regosols	92	0.16%	0	0.00%	0.00
	Haplic Cambisols	86	0.15%	0	0.00%	0.00
	Humi-Eutric Cambisols	5555	9.68%	252	24.42%	2.52
	Lithic Leptosols	8073	14.06%	160	15.50%	1.10
	Rendzic Leptosols	2449	4.27%	7	0.68%	0.16
	Eutric Regosols	1107	1.93%	3	0.29%	0.15
	Hypoluvic Arenosols	1276	2.22%	18	1.74%	0.78
	Haplic Luvisols and Leptic Luvisols	1204	2.10%	11	1.07%	0.51
	Haplic Luvisols	760	1.32%	5	0.48%	0.37

Table 4

Spatial relationship between sites’ causative variables and archaeological sites’ locations using Shannon’s entropy.

VARIABLE	CLASS	P_ij	(P_ij)	H_j	H_{j max}	MEAN OF P_ij	I_j	W_j
Cost Distance to Streams (expressed decimal in hours)	0.001–0.032	1.45	0.28	2.02	3.32	0.51	0.39	0.20
	0.033–0.7	1.23	0.24
	0.071–0.11	0.59	0.11
	0.111–0.15	0.51	0.10
	0.151–0.192	0.47	0.09
	0.193–0.236	0.67	0.13
	0.237–0.283	0.20	0.04
	0.284–0.334	0.00	0.00
	0.335–0.389	0.00	0.00
	0.39–0.538	0.00	0.00
DIFF (landforms)	Valley	1.03	0.13	2.38	2.58	1.15	0.07	0.08
	Lower slope	1.10	0.14
	Flat slope	2.00	0.26
	Middle slope	0.92	0.12
	Upper slope	1.13	0.14
	Ridge	0.75	0.10
Slope (rescaled logarithmic)	1.001-1	3.59	0.25	2.75	3.32	1.42	0.17	0.24
	1.001–6.224	1.47	0.10
	6.225–7.106	2.08	0.15
	7.107–7.706	1.45	0.10
	7.707–8.129	1.39	0.10
	8.13–8.482	1.19	0.08
	8.483–8.765	1.07	0.08
	8.766–9.047	0.96	0.07
	9.048–9.329	0.57	0.04
	9.33–10	0.47	0.03
Aspect	Flat	3.59	0.31	2.91	3.17	1.29	0.08	0.10
	North	1.03	0.09
	Northeast	1.31	0.11
	East	0.78	0.07
	Southeast	1.70	0.15
	South	1.00	0.09
	Southwest	0.56	0.05
	West	0.93	0.08
	North West	0.75	0.06
Elevation	139–265	0.00	0.00	1.60	3.32	0.46	0.52	0.24
	266–392	0.42	0.09
	393–519	2.31	0.50
	520–646	1.55	0.34
	647–774	0.30	0.07
	775–901	0.00	0.00
	902–1028	0.00	0.00
	1029–1155	0.00	0.00
	1156–1282	0.00	0.00
	1283–1409	0.00	0.00
Soil	Areno-Eutric Leptosols	0.65	0.06	2.42	3.70	0.62	0.35	0.21
	Calcaro-Hortic Anthrosols	0.27	0.02
	Eutric Arenosols	1.34	0.12
	Eutric Gleysols	0.23	0.02
	Calcaric Regosols	0.00	0.00
	Haplic Cambisols	0.00	0.00
	Humi-Eutric Cambisols	2.52	0.22
	Lithic Leptosols	1.10	0.10
	Rendzic Leptosols	0.16	0.01
	Eutric Regosols	0.15	0.01
	Hypoluvic Arenosols	0.78	0.07
	Haplic Luvisols and Leptic Luvisols	0.51	0.04
	Haplic Luvisols	0.37	0.03

Probability map based on the frequency ratio method.

Probability map based on Shannon’s entropy.

The surface area percentage of each probability class within the dam reservoir.

Table 5

Comparison of Kvamme’s Gain values for two models (FR and SE) across five folds.

TRAINING DATA (FOLD NUMBER)		TEST DATA (FOLD NUMBER)		KVAMME’S GAIN VALUE
FOLD NO.	NUMBER OF SITES	FOLD NO.	NUMBER OF SITES	FR	SE
1, 2, 3, 4	54	5	13	0.6182842	0.6191508
1, 2, 3, 5	52	4	15	0.7070749	0.6094261
1, 2, 4, 5	52	3	15	0.589292	0.5199014
1, 3, 4, 5	53	2	14	0.4448645	0.486424
2, 3, 4, 5	57	1	10	0.4713296	0.753475
Mean	–	–	–	0.566169	0.5976755
T – Statistics	–	–	–	–1.526	–0.910
P-value	–	–	–	0.202	0.414

Comparison of Observed Kvamme’s Gain using FR with Monte Carlo Simulated Gains.

Comparison of Observed Kvamme’s Gain using SE with Monte Carlo Simulated Gains.

Probabilistic Models for Predicting Archaeological Site Locations in Marj Bisri (Southern Lebanon): Comparing Frequency Ratio and Shannon’s Entropy

Figures & Tables

Figure 1

Table 1

Figure 2

Table 2

Table 3

Table 4

Figure 3

Figure 4

Figure 5

Table 5

Figure 6

Figure 7

Paradigm

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