This article presents a detailed spatial description, employing Particle Image Velocimetry, of a flow within an array of rigid and emergent cylinders with varying density in controlled laboratory conditions. Its main objective is to discuss the spatial distribution of the key terms of the budget of turbulent kinetic energy for different areal number-densities of stems. The following crucial innovations are introduced: a) the flow is quantified from spatial measurements, avoiding the use of the frozen turbulence approximation and b) space-averaging of two-point correlations and statistics is proposed as a means to salvage the formalism of homogeneous-isotropic turbulence. Turbulence characterization follows from second and third-order structure functions, autocorrelation functions, energy spectra and cospectra. Key terms of TKE budget are calculated in the inter-stem space and discussed. For reaches with large mean inter-stem distances equilibrium between production and dissipation is obtained. Turbulent diffusion reveals itself in the interaction of the von Kármán vortex sheet and background turbulence. Convective and pressure diffusion terms are important in the vicinity of individual stems.