Performance assessment of spatio-temporal regression kriging with GAMLSS models as trends

MEDEIROS, ELIAS S. DE; LIMA, RENATO R. DE; OLINDA, RICARDO A. DE; DANTAS, LEYDSON G.; SANTOS, CARLOS A.C. DOS

doi:10.1590/0001-3765202220211241

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GEOSCIENCES • An. Acad. Bras. Ciênc. 94 (suppl 3) • 2022 • https://doi.org/10.1590/0001-3765202220211241 linkcopy

Performance assessment of spatio-temporal regression kriging with GAMLSS models as trends

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The main objective of this study is to propose different probabilistic models for adjusting the trend component, since it significantly influences the quality of the spatio-temporal interpolation of rainfalls. We used the monthly total precipitation data of the São Francisco River Basin (SFRB) for the period of 31 years, 1989–2019. The SFRB occupies 8% of the whole Brazilian territory, mostly located in the Northeast Brazilian region. For the trend component, we propose the fitted GAMLSS models by comparing different probability distribution families, which in most cases include the characteristics of these data. The results indicate the existence of a spatio-temporal pattern of the residues obtained from the adjustment of the trend with zero adjusted Gamma distribution for the accumulated monthly precipitation. The adjustment revealed a spatial dependence of up to 873 km between the pluviometric stations and temporal autocorrelation of approximately 1.6 months. The methodology used in this study enabled us to create rainfall maps, interpolating unobserved locations in differences years. The projection of these maps to the SFRB is considered extremely important for planning and implementing activities related to water resources across the river basin.

Key words
Brazil; GAMLSS regression; geostatistics; rainfall

PDF	Spatial (S)	Temporal (T)	RMSE	NRMSE(%)	NSE	R²
GG	Exponential	Exponential	42.0077	46.50	0.7834	80.66
GG	Exponential	Spherical	41.5636	45.80	0.7901	81.13
GG	Exponential	Gaussian	42.0899	46.70	0.7823	80.58
GG	Spherical	Exponential	41.5677	45.70	0.7911	81.16
GG	Spherical	Spherical	41.5327	45.70	0.7915	81.18
GG	Spherical	Gaussian	41.5819	45.70	0.7909	81.15
GG	Gaussian	Exponential	44.5708	49.20	0.7578	78.32
GG	Gaussian	Spherical	44.5928	49.30	0.7573	78.30
GG	Gaussian	Gaussian	44.5501	49.20	0.7582	78.35
ZAGA	Exponential	Exponential	41.8600	46.40	0.7847	80.73
ZAGA	Exponential	Spherical	41.8765	46.40	0.7845	80.71
ZAGA	Exponential	Gaussian	41.8489	46.40	0.7849	80.74
ZAGA	Spherical	Exponential	41.3061	45.40	0.7938	81.31
ZAGA	Spherical	Spherical	41.2633	45.30	0.7943	81.35
ZAGA	Spherical	Gaussian	41.3368	45.40	0.7934	81.28
ZAGA	Gaussian	Exponential	44.6650	49.40	0.7558	78.20
ZAGA	Gaussian	Spherical	43.8441	47.60	0.7733	79.21
ZAGA	Gaussian	Gaussian	45.2330	50.50	0.7446	77.56
NO	Exponential	Exponential	41.9194	46.70	0.7822	80.62
NO	Exponential	Spherical	41.9559	46.50	0.7837	80.63
NO	Exponential	Gaussian	41.9016	46.40	0.7845	80.68
NO	Spherical	Exponential	41.3223	45.40	0.7937	81.28
NO	Spherical	Spherical	42.1298	46.60	0.7824	80.49
NO	Spherical	Gaussian	45.6921	49.50	0.7551	77.57
NO	Gaussian	Exponential	45.0989	50.10	0.7486	77.75
NO	Gaussian	Spherical	44.6500	49.30	0.7569	78.25
NO	Gaussian	Gaussian	46.0591	51.80	0.7317	76.71
LM	Exponential	Exponential	41.9293	46.70	0.7819	80.61
LM	Exponential	Spherical	41.9506	46.70	0.7817	80.59
LM	Exponential	Gaussian	41.9359	46.80	0.7806	80.58
LM	Spherical	Exponential	41.3988	45.90	0.7889	81.12
LM	Spherical	Spherical	41.2977	45.80	0.7901	81.21
LM	Spherical	Gaussian	41.8709	46.60	0.7828	80.67
LM	Gaussian	Exponential	44.6093	49.70	0.7532	78.18
LM	Gaussian	Spherical	44.6728	49.70	0.7530	78.13
LM	Gaussian	Gaussian	44.8354	49.50	0.7545	78.06

Model	Variogram	Nugget	Sill	Range	k	DI(%)
Spatial	Spherical	1043.109	3987.192	873 km	1.490x10^-8	26.160%
Temporal	Spherical	0.000	5607.506	1.6 months	1.490x10^-8	0.000%

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[tfnII] DI = Nugget/Sill. DI < 25%: strong dependency; 25% ≤ DI < 75%: medium dependency; DI ≥ 75% weak dependency (Cambardella et al. 1994).