Semivariogram models for rice stem bug population densities estimated by ordinary kriging

Tibraca limbativentris is considered one of the main species of insect pests in irrigated rice. This species can be found in plants in the vegetative and reproductive stages. This study aimed to select semivariogram models to estimate rice stem bug population densities by ordinary kriging. Two fields were used to survey the T. limbativentris population in Oryza sativa. A grid of 30 x 30 m was drawn, which generated 143 and 385 sample units for the first and second fields, respectively. Seven evaluations of two hundred plants per sampling unit were performed during cultivation. From the insect counts, the results were input into circular, spherical, pentaspherical, exponential, Gaussian, rational quadratic, cardinal sine, K-Bessel, J-Bessel, and stable semivariogram models via ordinary kriging interpolation and the best model was selected via cross-validation. Each assessment had a particular spatial structure and semivariogram model that best fit the experimental data.

Key words:
Oryza sativa; Tibraca limbativentris; interpolators; geostatistics; spatial variability

Authorship

Mauricio Paulo Batistella Pasini

Laboratorio de Entomologia, Universidade de Cruz Alta, Cruz Alta, Rio Grande do Sul, BrazilUniversidade de Cruz AltaBrazilCruz Alta, Rio Grande do Sul, BrazilLaboratorio de Entomologia, Universidade de Cruz Alta, Cruz Alta, Rio Grande do Sul, Brazil

Eduardo Engel ^** Author for Correspondence. E-mail: agron.engel@gmail.com

Laboratório de Ecologia e Entomologia Florestal, Departamento de Entomologia e Acarologia, Escola Superior de Agricultura “Luiz de Queiroz”, Universidade de São Paulo, Av. Pádua Dias, 235, 13418-900, Piracicaba, São Paulo, BrazilUniversidade de São PauloBrazilPiracicaba, São Paulo, BrazilLaboratório de Ecologia e Entomologia Florestal, Departamento de Entomologia e Acarologia, Escola Superior de Agricultura “Luiz de Queiroz”, Universidade de São Paulo, Av. Pádua Dias, 235, 13418-900, Piracicaba, São Paulo, Brazil

http://orcid.org/0000-0001-8218-6248

Alessandro Dal'Col Lúcio

Departamento de Fitotecnia, Universidade Federal de Santa Maria, Santa Maria, Rio Grande do Sul, Brazil.Universidade Federal de Santa MariaBrazilSanta Maria, Rio Grande do Sul, BrazilDepartamento de Fitotecnia, Universidade Federal de Santa Maria, Santa Maria, Rio Grande do Sul, Brazil.

Rafael Pivotto Bortolotto

* Author for Correspondence. E-mail: agron.engel@gmail.com

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables

Figures (1)
Tables (3)

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Figure 1
Box plot of the Tibraca limbativentris (Hemiptera: Pentatomidae) sampled per square meter in different evaluations. Santa Maria, Rio Grande do Sul State, Brazil.

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Table 1
Cross-validation indicators and grades attributed (in brackets), in the Field 1 evaluation, obtained from ordinary kriging, for the following semivariogram models: circular (C), spherical (S), tetraspherical(T), pentaspherical(P),exponential (E), Gaussian (G), rational quadratic (R), hole effect (H), K-Bessel (K), J-Bessel (J); and stable (St).

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Table 2
Cross-validation indicators and grades attributed (in brackets), in the Field 2 evaluation, obtained from ordinary kriging, for the following semivariogram models circular (C), spherical (S), tetraspherical (T), pentaspherical (P),exponential (E), Gaussian (G), rational quadratic (R), hole effect (H), K-Bessel (K), J-Bessel (J); and stable (St).

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Table 3
Nugget effect (C0), sill (C1), range (a), gamma function (Γ), and spatial dependence index (SDI) estimated in the second year of evaluation, for the following semivariogram models: circular (C),; spherical (S), tetraspherical(T), pentaspherical(P),exponential (E), Gaussian (G), rational quadratic (R), hole effect (H), K-Bessel (K), J-Bessel (J); and stable (St).

Figure 1 Box plot of the Tibraca limbativentris (Hemiptera: Pentatomidae) sampled per square meter in different evaluations. Santa Maria, Rio Grande do Sul State, Brazil.

Table 1 Cross-validation indicators and grades attributed (in brackets), in the Field 1 evaluation, obtained from ordinary kriging, for the following semivariogram models: circular (C), spherical (S), tetraspherical(T), pentaspherical(P),exponential (E), Gaussian (G), rational quadratic (R), hole effect (H), K-Bessel (K), J-Bessel (J); and stable (St).

Indicator	C	S	T	P	E	G	R	H	K	J	St
	------------------------------------ Evaluation 1 ------------------------------------
a	0.768(7)	0.758(4)	0.758(4)	0.758(4)	0.746(3)	0.804(10)	0.816(11)	0.684(1)	0.726(2)	0.796(9)	0.795(8)
b	0.163(7)	0.184(3)	0.184(3)	0.184(3)	0.191(2)	0.122(9)	0.129(8)	0.166(6)	0.202(1)	0.120(11)	0.122(9)
R²	0.732(7)	0.739(11)	0.739(11)	0.739(11)	0.735(8)	0.595(4)	0.624(5)	0.359(1)	0.727(6)	0.550(3)	0.534(2)
Ē	-0.022(5)	-0.009(10)	-0.009(10)	-0.003(11)	-0.011(8)	-0.034(3)	-0.017(6)	-0.086(1)	-0.017(7)	-0.042(2)	-0.041(3)
ĀĒ	0.363(6)	0.347(7)	0.347(7)	0.347(7)	0.346(11)	0.432(2)	0.428(5)	0.582(1)	0.346(11)	0.450(4)	0.458(3)
SD	0.563(7)	0.555(11)	0.555(11)	0.555(11)	0.558(8)	0.750(4)	0.715(5)	1.049(1)	0.566(6)	0.812(3)	0.836(2)
RMS	0.562(7)	0.553(11)	0.553(11)	0.553(11)	0.557(8)	0.748(4)	0.713(5)	1.049(1)	0.565(6)	0.811(3)	0.834(2)
RMSS	1.266(9)	1.284(7)	1.289(6)	1.277(8)	1.059(10)	11.943(4)	9.620(5)	13.256(3)	0.984(11)	60.219(1)	33.369(2)
Ʃ	55	64	63	65	58	36	50	15	50	36	31
	------------------------------------ Evaluation 2 ------------------------------------
a	0.721(7)	0.721(7)	0.721(7)	0.720(6)	0.668(1)	0.745(10)	0.750(11)	0.705(2)	0.718(5)	0.713(3)	0.714(4)
b	0.373(2)	0.373(2)	0.372(4)	0.372(4)	0.413(1)	0.284(10)	0.294(9)	0.281(11)	0.368(6)	0.299(8)	0.358(7)
R²	0.662(9)	0.662(9)	0.661(7)	0.661(7)	0.667(11)	0.511(3)	0.542(4)	0.431(1)	0.659(6)	0.470(2)	0.653(5)
Ē	-0.001(11)	-0.002(10)	-0.003(8)	-0.003(8)	-0.033(5)	-0.059(3)	-0.042(4)	-0.115(1)	-0.011(7)	-0.086(2)	-0.026(6)
ĀĒ	0.521(10)	0.522(7)	0.522(7)	0.522(7)	0.512(11)	0.697(2)	0.664(4)	0.733(1)	0.525(6)	0.676(3)	0.533(5)
SD	0.877(9)	0.877(9)	0.878(7)	0.878(7)	0.864(11)	1.155(3)	1.097(4)	1.292(1)	0.881(6)	1.212(2)	0.889(5)
RMS	0.874(9)	0.874(9)	0.875(7)	0.875(7)	0.862(11)	1.153(3)	1.094(4)	1.292(1)	0.878(6)	1.211(2)	0.887(5)
RMSS	1.508(6)	1.511(5)	1.472(7)	1.469(8)	0.931(11)	7.458(3)	4.392(4)	8.956(2)	1.264(9)	11.256(1)	1.090(10)
Ʃ	63	59	54	54	62	37	44	22	51	23	47
	------------------------------------ Evaluation 3 ------------------------------------
a	0.828(8)	0.817(6)	0.813(5)	0.809(2)	0.812(3)	0.839(9)	0.812(3)	0.874(10)	0.791(1)	0.823(7)	0.895(11)
b	0.415(8)	0.427(6)	0.435(3)	0.432(4)	0.443(2)	0.401(9)	0.432(4)	0.183(11)	0.484(1)	0.420(7)	0.238(10)
R²	0.827(8)	0.829(11)	0.829(11)	0.827(8)	0.823(6)	0.815(3)	0.821(5)	0.675(1)	0.823(6)	0.820(4)	0.789(2)
Ē	-0.004(11)	-0.021(6)	-0.023(5)	-0.035(2)	-0.017(8)	0.008(10)	-0.027(3)	-0.123(1)	-0.025(4)	-0.011(9)	-0.018(7)
ĀĒ	0.585(8)	0.579(11)	0.579(11)	0.582(9)	0.587(7)	0.614(3)	0.594(6)	0.852(1)	0.597(5)	0.607(4)	0.682(2)
SD	0.801(8)	0.797(11)	0.797(11)	0.801(8)	0.812(7)	0.829(4)	0.815(4)	1.194(1)	0.813(5)	0.817(3)	0.916(2)
RMS	0.798(9)	0.794(11)	0.794(11)	0.799(8)	0.809(7)	0.827(3)	0.813(5)	1.197(1)	0.810(6)	0.814(4)	0.913(2)
RMSS	1.010(11)	0.869(8)	0.832(6)	0.814(5)	0.727(3)	1.079(10)	0.744(4)	2.569(1)	0.873(9)	0.857(7)	1.751(2)
Ʃ	62	70	63	46	43	51	34	27	37	45	38
	------------------------------------ Evaluation 4 ------------------------------------
a	0.806(2)	0.806(2)	0.806(2)	0.806(2)	0.797(1)	0.845(8)	0.841(7)	0.876(11)	0.838(6)	0.849(9)	0.850(10)
b	0.813(2)	0.813(2)	0.812(4)	0.812(4)	0.843(1)	0.593(8)	0.597(7)	0.517(11)	0.606(6)	0.585(9)	0.582(10)
R²	0.788(11)	0.788(11)	0.788(11)	0.788(11)	0.785(7)	0.618(2)	0.661(6)	0.580(1)	0.627(5)	0.618(2)	0.621(4)
Ē	-0.015(10)	-0.016(8)	-0.016(8)	-0.017(7)	-0.023(6)	-0.068(3)	-0.084(1)	-0.011(11)	-0.084(1)	-0.059(4)	-0.056(5)
ĀĒ	0.919(11)	0.919(11)	0.919(11)	0.920(8)	0.923(7)	1.287(4)	1.206(6)	1.479(1)	1.260(5)	1.298(2)	1.288(3)
SD	1.312(11)	1.312(11)	1.313(9)	1.313(9)	1.320(7)	1.943(3)	1.773(6)	2.153(1)	1.897(5)	1.950(2)	1.941(4)
RMS	1.307(11)	1.308(9)	1.308(9)	1.309(8)	1.315(7)	1.937(3)	1.769(6)	2.146(1)	1.892(5)	1.945(2)	1.935(4)
RMSS	1.253(7)	1.230(8)	1.212(9)	1.181(10)	0.960(11)	13.568(5)	8.401(6)	15.236(4)	37.935(1)	18.756(3)	24.369(2)
Ʃ	65	62	63	59	47	36	45	41	34	33	42
	------------------------------------ Evaluation 5 ------------------------------------
a	0.840(2)	0.821(1)	0.851(6)	0.850(5)	0.840(2)	0.920(9)	0.929(10)	1.012(11)	0.885(8)	0.841(4)	0.882(7)
b	0.817(2)	0.897(1)	0.768(6)	0.768(5)	0.815(3)	0.374(9)	0.312(10)	0.035(11)	0.539(8)	0.796(4)	0.557(7)
R²	0.888(8)	0.877(5)	0.865(3)	0.865(3)	0.864(2)	0.890(10)	0.895(11)	0.777(1)	0.887(7)	0.880(6)	0.888(8)
Ē	-0.011(9)	-0.027(6)	-0.004(11)	-0.005(10)	-0.014(8)	-0.039(5)	-0.052(4)	0.099(1)	-0.057(3)	-0.027(7)	-0.053(2)
ĀĒ	0.833(7)	0.885(5)	0.920(3)	0.920(3)	0.927(2)	0.803(11)	0.814(9)	1.238(1)	0.817(8)	0.856(6)	0.811(10)
SD	1.098(7)	1.154(5)	1.193(4)	1.194(3)	1.203(2)	1.081(10)	1.057(11)	1.761(1)	1.092(8)	1.133(6)	1.087(9)
RMS	1.095(7)	1.150(5)	1.189(4)	1.190(3)	1.199(2)	1.078(10)	1.055(11)	1.758(1)	1.090(8)	1.129(6)	1.084(9)
RMSS	0.704(5)	0.681(4)	0.944(10)	0.933(9)	0.760(6)	1.114(7)	1.592(2)	5.124(1)	0.963(11)	0.669(3)	0.907(8)
Ʃ	47	32	47	41	27	71	68	28	61	42	60
	------------------------------------ Evaluation 6 ------------------------------------
a	0.869(7)	0.840(1)	0.866(6)	0.865(5)	0.860(4)	0.894(9)	0.854(3)	0.909(11)	0.877(8)	0.822(2)	0.904(10)
b	0.683(8)	0.855(2)	0.728(6)	0.731(5)	0.769(3)	0.586(9)	0.769(3)	0.493(10)	0.683(7)	0.927(1)	0.491(11)
R²	0.868(4)	0.882(10)	0.874(7)	0.874(7)	0.874(6)	0.866(3)	0.874(9)	0.762(1)	0.884(11)	0.872(5)	0.849(2)
Ē	-0.034(2)	-0.022(5)	-0.008(7)	-0.008(7)	0.000(11)	0.007(9)	-0.030(4)	-0.006(10)	0.010(6)	-0.048(1)	-0.034(2)
ĀĒ	1.038(4)	0.982(11)	1.019(8)	1.018(7)	1.020(6)	1.066(3)	1.007(9)	1.396(1)	0.991(10)	1.022(5)	1.113(2)
SD	1.356(4)	1.297(10)	1.329(8)	1.329(7)	1.330(6)	1.371(3)	1.327(9)	1.931(1)	1.271(11)	1.352(5)	1.468(2)
RMS	1.352(4)	1.292(10)	1.324(7)	1.324(7)	1.326(6)	1.366(3)	1.322(9)	1.924(1)	1.266(11)	1.348(5)	1.463(2)
RMSS	0.897(11)	0.705(5)	0.769(8)	0.747(7)	0.742(6)	1.139(10)	0.658(2)	5.333(1)	0.808(9)	0.663(3)	1.331(4)
Ʃ	44	54	57	52	48	49	48	36	73	26	35
	------------------------------------ Evaluation 7 ------------------------------------
a	0.847(1)	0.852(4)	0.859(5)	0.859(5)	0.851(2)	0.917(7)	0.928(11)	0.925(9)	0.926(10)	0.851(2)	0.919(8)
b	0.589(1)	0.545(6)	0.554(4)	0.554(4)	0.578(2)	0.291(8)	0.252(10)	0.343(7)	0.242(11)	0.559(3)	0.264(9)
R²	0.868(9)	0.865(7)	0.864(4)	0.864(4)	0.863(3)	0.872(11)	0.872(11)	0.756(1)	0.864(4)	0.866(8)	0.858(2)
Ē	-0.014(8)	-0.041(4)	-0.003(11)	-0.004(10)	-0.011(9)	-0.038(5)	-0.033(6)	0.045(3)	-0.049(2)	-0.030(7)	-0.055(1)
ĀĒ	0.826(8)	0.837(7)	0.869(4)	0.869(4)	0.872(3)	0.813(10)	0.822(9)	1.104(1)	0.848(6)	0.802(11)	0.873(2)
SD	1.054(9)	1.062(7)	1.066(6)	1.067(5)	1.071(4)	1.045(11)	1.048(10)	1.533(1)	1.083(3)	1.059(8)	1.107(2)
RMS	1.050(9)	1.059(7)	1.063(5)	1.063(5)	1.068(4)	1.042(11)	1.045(10)	1.529(1)	1.080(3)	1.056(8)	1.105(2)
RMSS	0.821(8)	0.764(6)	0.974(11)	0.952(10)	0.772(7)	1.132(9)	1.864(2)	3.857(1)	1.812(4)	0.728(5)	1.850(3)
Ʃ	53	48	50	47	34	72	69	24	47	52	29

b, angular coefficient; a, intersection; R², coefficient of determination; Ē, mean prediction errors; SD, standard deviation of prediction errors; ĀĒ, mean prediction absolute errors; RMS, root‑mean‑square prediction errors; RMSS, root‑mean‑square standardized prediction errors; Ʃ, summation.

Table 2 Cross-validation indicators and grades attributed (in brackets), in the Field 2 evaluation, obtained from ordinary kriging, for the following semivariogram models circular (C), spherical (S), tetraspherical (T), pentaspherical (P),exponential (E), Gaussian (G), rational quadratic (R), hole effect (H), K-Bessel (K), J-Bessel (J); and stable (St).

Indicator	C	S	T	P	E	G	R	H	K	J	St
	------------------------------------ Evaluation 1 ------------------------------------
a	0.933(7)	0.938(10)	0.933(7)	0.933(7)	0.929(5)	0.877(3)	0.944(11)	0.921(4)	0.864(1)	0.932(6)	0.866(2)
b	0.041(6)	0.033(11)	0.041(6)	0.041(6)	0.043(4)	0.053(2)	0.033(11)	0.052(3)	0.063(1)	0.043(4)	0.060(5)
R²	0.939(11)	0.938(7)	0.939(11)	0.939(11)	0.938(7)	0.875(1)	0.930(6)	0.916(4)	0.897(3)	0.919(5)	0.880(2)
Ē	-0.001(8)	-0.006(4)	-0.001(8)	-0.001(8)	-0.002(5)	-0.023(2)	-0.002(5)	0.002(5)	-0.022(3)	0.000(11)	-0.024(1)
ĀĒ	0.144(11)	0.152(7)	0.144(11)	0.144(11)	0.145(8)	0.209(1)	0.157(6)	0.181(4)	0.190(3)	0.176(5)	0.204(2)
SD	0.280(11)	0.281(7)	0.280(11)	0.280(11)	0.281(7)	0.401(1)	0.300(6)	0.328(4)	0.366(3)	0.324(5)	0.392(2)
RMS	0.279(11)	0.281(7)	0.279(11)	0.279(11)	0.281(7)	0.401(1)	0.300(6)	0.328(4)	0.366(3)	0.323(5)	0.392(2)
RMSS	0.878(11)	0.802(7)	0.868(10)	0.860(9)	0.715(6)	1.506(4)	3.015(1)	2.637(2)	1.197(8)	2.416(3)	1.385(5)
Ʃ	76	60	75	74	49	15	52	30	25	44	21
	------------------------------------ Evaluation 2 ------------------------------------
a	0.899(6)	0.898(5)	0.899(6)	0.899(6)	0.895(3)	0.923(11)	0.896(4)	0.882(1)	0.893(2)	0.913(9)	0.923(11)
b	0.223(6)	0.224(5)	0.223(6)	0.223(6)	0.230(2)	0.163(11)	0.229(3)	0.269(1)	0.225(4)	0.198(9)	0.163(11)
R²	0.900(11)	0.900(11)	0.900(11)	0.900(11)	0.899(7)	0.873(1)	0.892(5)	0.876(3)	0.893(6)	0.882(4)	0.873(1)
Ē	-0.009(5)	-0.009(5)	-0.009(5)	-0.009(5)	-0.010(4)	-0.015(2)	-0.009(5)	-0.001(11)	-0.020(1)	-0.001(11)	-0.015(2)
ĀĒ	0.528(11)	0.528(11)	0.528(11)	0.528(11)	0.531(7)	0.603(3)	0.557(5)	0.613(1)	0.544(6)	0.573(4)	0.603(2)
SD	0.778(11)	0.778(11)	0.778(11)	0.778(11)	0.782(7)	0.885(1)	0.810(5)	0.865(3)	0.802(6)	0.847(4)	0.885(1)
RMS	0.777(11)	0.777(11)	0.777(11)	0.777(11)	0.781(7)	0.884(1)	0.809(5)	0.863(3)	0.802(6)	0.846(4)	0.884(1)
RMSS	1.109(8)	1.126(7)	1.100(9)	1.089(11)	0.906(10)	6.444(2)	1.652(5)	5.505(4)	1.133(6)	16.628(1)	6.444(2)
Ʃ	69	66	70	72	47	32	37	27	37	46	31
	------------------------------------ Evaluation 3 ------------------------------------
a	0.927(4)	0.935(5)	0.922(2)	0.922(2)	0.920(1)	0.930(6)	0.947(9)	0.953(10)	0.939(8)	0.954(11)	0.930(6)
b	0.239(4)	0.209(7)	0.288(2)	0.288(2)	0.291(1)	0.222(6)	0.192(9)	0.183(10)	0.193(8)	0.125(11)	0.222(5)
R²	0.929(7)	0.927(5)	0.930(11)	0.930(11)	0.930(11)	0.920(2)	0.929(7)	0.927(5)	0.923(4)	0.900(1)	0.920(2)
Ē	-0.031(5)	-0.031(5)	-0.001(11)	-0.002(10)	-0.006(8)	-0.039(2)	-0.004(9)	0.009(7)	-0.034(4)	-0.046(1)	-0.039(2)
ĀĒ	0.667(6)	0.680(5)	0.662(9)	0.662(9)	0.663(8)	0.695(2)	0.659(11)	0.665(7)	0.685(4)	0.766(1)	0.695(2)
SD	0.926(7)	0.939(6)	0.920(9)	0.919(11)	0.920(9)	0.981(2)	0.925(8)	0.944(5)	0.969(4)	1.117(1)	0.981(2)
RMS	0.926(7)	0.938(6)	0.918(9)	0.918(11)	0.919(9)	0.980(2)	0.924(8)	0.943(5)	0.968(4)	1.117(1)	0.980(2)
RMSS	0.879(8)	0.904(9)	0.918(11)	0.909(10)	0.754(4)	1.152(6)	5.221(3)	5.467(2)	1.241(5)	6.690(1)	1.152(6)
Ʃ	48	48	64	66	51	28	64	51	41	28	27
	------------------------------------ Evaluation 4 ------------------------------------
a	0.893(4)	0.901(6)	0.891(1)	0.892(3)	0.890(2)	0.927(8)	0.943(10)	0.932(9)	0.923(7)	0.954(11)	0.898(5)
b	0.487(4)	0.440(6)	0.494(3)	0.498(2)	0.519(1)	0.315(9)	0.261(10)	0.353(7)	0.337(8)	0.192(11)	0.456(5)
R²	0.909(3)	0.914(9)	0.909(3)	0.909(3)	0.907(1)	0.913(8)	0.912(6)	0.917(11)	0.914(9)	0.902(2)	0.912(6)
Ē	-0.015(8)	-0.024(3)	-0.018(7)	-0.009(9)	0.006(10)	-0.025(2)	-0.003(11)	0.036(1)	-0.021(5)	-0.024(3)	-0.020(6)
ĀĒ	0.883(5)	0.856(8)	0.885(4)	0.887(3)	0.897(2)	0.842(9)	0.858(7)	0.836(11)	0.839(10)	0.917(1)	0.863(6)
SD	1.219(5)	1.190(9)	1.222(4)	1.224(3)	1.235(2)	1.191(8)	1.210(6)	1.169(11)	1.184(10)	1.282(1)	1.199(7)
RMS	1.218(5)	1.188(9)	1.220(4)	1.222(3)	1.234(2)	1.190(8)	1.208(6)	1.168(11)	1.183(10)	1.280(1)	1.198(7)
RMSS	0.895(8)	0.873(5)	0.876(7)	0.896(9)	0.801(4)	1.036(10)	1.382(3)	2.275(1)	1.005(11)	1.574(2)	0.874(6)
Ʃ	42	58	33	35	24	62	59	62	70	33	48
	------------------------------------ Evaluation 5 ------------------------------------
a	0.894(3)	0.901(6)	0.895(4)	0.895(5)	0.893(2)	0.911(8)	0.922(9)	0.888(1)	0.908(7)	0.936(11)	0.929(10)
b	0.605(5)	0.558(6)	0.629(3)	0.629(3)	0.636(2)	0.500(8)	0.457(9)	0.718(1)	0.520(7)	0.353(11)	0.399(10)
R²	0.905(11)	0.905(11)	0.905(11)	0.905(11)	0.905(11)	0.901(5)	0.899(4)	0.893(3)	0.903(6)	0.884(1)	0.891(2)
Ē	-0.018(7)	-0.025(2)	0.012(8)	0.012(8)	0.006(10)	-0.024(4)	-0.005(11)	0.056(1)	-0.022(5)	-0.025(2)	-0.020(6)
ĀĒ	1.072(10)	1.067(11)	1.077(7)	1.077(7)	1.078(6)	1.084(5)	1.095(4)	1.179(2)	1.076(9)	1.191(1)	1.143(3)
SD	1.455(10)	1.453(11)	1.456(8)	1.456(8)	1.458(7)	1.486(5)	1.504(4)	1.548(3)	1.474(6)	1.633(1)	1.569(2)
RMS	1.453(10)	1.451(11)	1.455(8)	1.455(8)	1.456(7)	1.484(5)	1.502(4)	1.547(3)	1.473(6)	1.631(1)	1.567(2)
RMSS	0.941(6)	0.941(6)	1.033(8)	1.024(10)	0.854(4)	1.000(11)	1.084(5)	2.078(1)	0.976(9)	1.425(2)	1.271(3)
Ʃ	71	64	57	60	49	51	48	15	55	30	38
	------------------------------------ Evaluation 6 ------------------------------------
a	0.868(5)	0.877(7)	0.865(4)	0.864(3)	0.863(2)	0.917(11)	0.900(9)	0.848(1)	0.889(8)	0.908(10)	0.869(6)
b	0.859(6)	0.796(7)	0.878(4)	0.887(3)	0.923(2)	0.539(11)	0.668(9)	1.073(1)	0.720(8)	0.589(10)	0.862(5)
R²	0.876(8)	0.878(11)	0.875(6)	0.875(6)	0.874(4)	0.863(2)	0.874(4)	0.853(1)	0.877(10)	0.869(3)	0.876(9)
Ē	-0.029(2)	-0.031(1)	-0.028(4)	-0.026(5)	0.005(11)	-0.022(8)	-0.008(10)	0.053(1)	-0.024(7)	-0.029(3)	-0.018(9)
ĀĒ	1.364(7)	1.337(9)	1.369(5)	1.372(4)	1.378(3)	1.403(2)	1.330(10)	1.539(1)	1.319(11)	1.364(6)	1.356(8)
SD	1.861(8)	1.846(11)	1.865(7)	1.867(6)	1.871(5)	1.974(2)	1.876(4)	2.024(1)	1.854(10)	1.924(3)	1.855(9)
RMS	1.858(8)	1.844(11)	1.863(7)	1.865(6)	1.869(5)	1.971(2)	1.874(4)	2.022(1)	1.852(10)	1.922(3)	1.853(9)
RMSS	0.961(7)	0.974(10)	0.949(6)	0.948(5)	0.979(11)	1.435(2)	1.185(4)	2.291(1)	1.025(9)	1.198(3)	0.968(8)
Ʃ	51	66	43	38	43	40	54	8	73	41	64
	------------------------------------ Evaluation 7 ------------------------------------
a	0.875(6)	0.880(7)	0.870(4)	0.869(3)	0.861(1)	0.925(8)	0.928(11)	0.851(2)	0.874(5)	0.925(8)	0.925(8)
b	0.744(7)	0.673(6)	0.780(4)	0.815(3)	0.846(2)	0.469(11)	0.471(9)	0.926(1)	0.771(5)	0.506(8)	0.469(11)
R²	0.859(3)	0.897(11)	0.864(4)	0.864(4)	0.864(4)	0.894(9)	0.878(8)	0.832(1)	0.874(7)	0.855(2)	0.894(9)
Ē	-0.031(3)	-0.075(1)	-0.027(4)	0.001(11)	-0.017(6)	0.002(8)	0.025(5)	-0.001(11)	-0.016(7)	0.042(2)	0.002(8)
ĀĒ	1.326(3)	1.127(11)	1.297(4)	1.293(5)	1.286(6)	1.185(9)	1.263(7)	1.436(2)	1.245(8)	1.452(1)	1.185(9)
SD	1.781(3)	1.526(11)	1.747(4)	1.746(5)	1.745(6)	1.554(9)	1.673(8)	1.942(1)	1.681(7)	1.841(2)	1.554(9)
RMS	1.778(3)	1.526(11)	1.745(4)	1.744(5)	1.742(6)	1.552(9)	1.671(8)	1.939(1)	1.679(7)	1.839(2)	1.552(9)
RMSS	1.039(8)	0.860(4)	0.989(10)	0.993(11)	0.890(7)	1.129(5)	2.158(2)	3.169(1)	0.972(9)	2.084(3)	1.129(5)
Ʃ	36	62	38	47	38	58	52	20	55	28	68

b, angular coefficient; a, intersection; R², coefficient of determination; Ē, mean prediction errors; SD, standard deviation of prediction errors; ĀĒ, mean prediction absolute errors; RMS, root‑mean‑square prediction errors; RMSS, root‑mean‑square standardized prediction errors; Ʃ, summation.

Table 3 Nugget effect (C0), sill (C1), range (a), gamma function (Γ), and spatial dependence index (SDI) estimated in the second year of evaluation, for the following semivariogram models: circular (C),; spherical (S), tetraspherical(T), pentaspherical(P),exponential (E), Gaussian (G), rational quadratic (R), hole effect (H), K-Bessel (K), J-Bessel (J); and stable (St).

Model	Estimative
Model	C₀	C₁	a	Ґ	SDI	C₀	C₁	a	Ґ	SDI	C₀	C₁	a	Ґ	SDI
	-------------- F1 E1 -------------					-------------- F1 E2 -------------					-------------- F1 E3 -------------
C	0.000	0.904	92.8		100	0.000	3.830	256.5		100	0.000	0.991	35.8		100
E	0.000	1.395	181.2		100	0.000	3.297	245.0		100	0.000	1.094	35.9		100
T	0.000	1.422	210.9		100	0.000	2.916	232.8		100	0.000	1.132	38.3		100
P	0.000	1.574	252.9		100	0.000	2.951	259.2		100	0.000	1.326	46.1		100
Ex	0.000	1.601	274.9		100	0.000	1.417	69.2		100	0.000	2.303	80.3		100
G	0.000	1.009	69.1		100	0.000	1.888	64.8		100	0.000	1.094	33.5		100
RQ	0.000	1.479	274.9		100	0.000	2.698	208.1		100	0.000	2.056	71.8		100
SC	0.000	1.087	125.5		100	0.000	2.386	145.8		100	0.000	1.805	109.8		100
KB	0.000	0.914	121.8	0.5	100	0.000	2.916	234.4	0.6	100	0.000	1.129	47.4	0.6	100
JB	0.000	1.089	118.1	10.0	100	0.000	2.995	175.7	10.0	100	0.000	1.243	42.8	4.7	100
Es	0.000	1.086	106.9	2.0	100	0.000	1.913	75.8	1.3	100	0.000	1.414	43.9	2.0	100
	-------------- F1 E4 -------------					-------------- F1 E5 -------------					-------------- F1 E6 -------------
C	0.000	1.912	261.8		100	0.000	3.619	34.9		100	0.000	4.295	40.5		100
E	0.000	12.327	263.8		100	0.000	4.055	39.4		100	0.000	4.424	36.9		100
T	0.000	11.143	261.8		100	0.000	14.987	360.0		100	0.000	9.114	85.6		100
P	0.000	11.167	274.8		100	0.000	14.689	274.9		100	0.000	9.745	85.6		100
Ex	0.000	10.873	274.9		100	0.000	14.262	274.9		100	0.000	18.563	247.9		100
G	0.000	9.666	117.8		100	0.000	4.378	43.4		100	0.000	4.657	39.9		100
RQ	0.000	10.268	265.9		100	0.000	12.443	188.1		100	0.000	9.506	89.7		100
SC	0.000	8.888	184.4		100	0.000	11.429	176.1		100	0.000	8.862	133.6		100
KB	0.000	8.912	115.1	10.0	100	0.000	4.946	56.2	2.9	100	0.000	4.649	36.9	10.0	100
JB	0.000	9.264	179.4	10.0	100	0.000	4.103	44.4	4.0	100	0.000	4.691	39.7	4.0	100
Es	0.000	9.667	129.9	2.0	100	0.000	4.378	46.2	1.8	100	0.000	4.857	41.5	2.0	100
	-------------- F1 E7 -------------					-------------- F2 E1 -------------					-------------- F2 E2 -------------
C	0.000	2.969	39.7		100	0.000	0.962	153.9		100	0.000	7.269	311.3		100
E	0.000	3.032	42.0		100	0.000	2.030	466.7		100	0.000	9.451	463.8		100
T	0.000	12.157	274.9		100	0.000	1.882	478.4		100	0.000	8.762	478.4		100
P	0.000	11.515	274.9		100	0.000	1.780	490.3		100	0.000	8.294	490.3		100
Ex	0.000	22.226	274.9		100	0.000	1.735	521.6		100	0.000	8.120	524.8		100
G	0.000	3.063	41.4		100	0.000	0.259	39.2		100	0.007	2.899	83.1		100
RQ	0.000	7.868	187.7		100	0.006	1.568	434.4		100	0.182	7.228	483.8		98
SC	0.000	6.494	146.2		100	0.012	0.454	127.7		97	0.021	2.916	183.0		99
KB	0.000	3.996	56.6	10.0	100	0.000	0.258	40.4	10.0	100	0.008	2.817	124.1	0.9	100
JB	0.000	3.035	44.4	4.1	100	0.014	0.794	164.7	4.3	98	0.002	4.734	222.1	10.0	100
Es	0.000	3.634	48.9	2.0	100	0.000	0.249	38.0	2.0	100	0.007	2.899	83.1	2.0	100
	-------------- F2 E3 -------------					-------------- F2 E4 -------------					-------------- F2 E5 -------------
C	0.000	2.826	50.6		100	0.000	3.328	39.4		100	0.000	4.259	39.5		100
E	0.000	2.439	54.4		100	0.000	3.687	51.6		100	0.000	4.687	51.3		100
T	0.000	17.449	475.4		100	0.000	3.631	55.5		100	0.000	32.737	461.0		100
P	0.000	16.514	487.3		100	0.000	4.300	74.4		100	0.000	30.931	472.5		100
Ex	0.000	16.190	521.6		100	0.000	18.741	381.9		100	0.000	30.242	508.3		100
G	0.002	2.241	39.1		100	0.003	3.600	38.8		100	0.004	4.180	34.8		100
RQ	0.015	14.989	466.9		100	0.009	8.790	163.5		100	0.009	8.923	124.1		100
SC	0.016	4.218	120.6		100	0.123	8.314	145.8		99	0.438	22.095	343.2		98
KB	0.000	2.574	46.2	10.0	100	0.000	3.762	42.2	9.1	100	0.000	4.291	37.1	10.0	100
JB	0.000	2.493	64.5	1.6	100	0.000	3.833	62.6	4.2	100	0.000	4.764	60.6	6.2	100
Es	0.002	2.241	39.1	2.0	100	0.004	3.600	44.1	1.6	100	0.004	4.880	40.8	2.0	100

	-------------- F2 E6 -------------					-------------- F2 E7 -------------
C	0.000	6.712	40.0		100	0.000	5.144	37.3		100
E	0.000	6.736	47.1		100	0.000	5.564	48.4		100
T	0.000	6.799	52.6		100	0.000	5.473	52.1		100
P	0.000	7.031	59.8		100	0.000	5.711	60.3		100
Ex	0.000	37.974	505.7		100	0.000	12.552	152.8		100
G	0.023	7.951	43.4		100	0.018	5.999	40.0		100
RQ	0.012	11.942	124.1		100	0.014	14.008	186.8		100
SC	0.615	23.344	333.9		97	0.293	19.334	280.1		99
KB	0.045	6.972	124.1	7.8	99	0.490	6.494	59.1	1.2	93
JB	0.000	6.961	39.7	10.0	100	0.000	5.878	59.0	4.2	100
Es	0.229	7.951	61.3	1.4	97	0.018	5.999	40.3	2.0	100

SDI: small, SDI > 75%; M, medium, 25 < SDI ≤ 75%; L, large, SDI ≤ 25%.

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[1] * Author for Correspondence. E-mail: agron.engel@gmail.com