The frequency response is determined from averaging the cross-spectra of the input output data. It is evident that the frequency response derived from the case with harder forcing deviates from the nominal, or low amplitude, frequency response. Additionally, the jet velocity coherence, shown in Fig. 3, decreases with the larger amplitude forcing compared to the nominal case. The coherence is reduced because a greater portion of the velocity output is determined by nonlinear dynamics at the larger forcing amplitude. In contrast, the frequency responses with the pressure measurement are nearly identical for both test amplitudes and, furthermore, Fig. 3 shows the pressure coherence increases with harder forcing . The harmonic coupling in the jet velocity is clearly illustrated by the spectra in Fig. 4a produced in response to dual tone forcing. Input tones at 1800Hz and 1900Hz creating a0.50ms−1 RMS perturbation produce strong super- and sub-harmonics. On the other hand, Fig. 4b shows the microphone spectrum in response to the same dual tone input as above – the microphone measurement is dominated by tones at 1800Hz and 1900Hz. The frequency responses in Fig. 2 show that the magnitudes roll off after a plenum mode near 1.8 kHz. This limits the actuation bandwidth to approximately 2.0kHz. As such, we specify the periodic reference to be truncated at or below 2 kHz to avoid saturation of the actuator amplifier. Throughout this paper the reference wave forms are periodic square pulses with a 100 Hz fundamental frequency so the modulation-demodulation is centered in narrow bands around the N = 20 harmonics within the 2 kHz actuation bandwidth.

Although the disturbance spectrum will only be attenuated in neighborhood of each harmonic,hydroponic vertical farming the primary reason for using feedback to shape the jet velocity is the uncertainty associated with the plant dynamics. Thus, feedback is used to force the jet velocity to asymptotically track the periodic reference within the actuator bandwidth, even in the presence of the significant coupling noted in Fig. 4. The physical mechanism causing the nonlinear harmonic coupling is not well understood, however, an empirical model can be built that is quite suitable for analysis and controller synthesis. We identify a model which characterizes the harmonic coupling in the neighborhood of a particular periodic jet velocity operating point which is close to the desired periodic reference. At a given operating point, though, the main challenge in modeling the system is quantifying the nonlinear coupling that occurs between the N frequency “channels” of the hot wire signal. The identification is facilitated by shifting the spectrum of the plant’s input and output in the neighborhood of each harmonic to “base band” via modulation and demodulation. The architecture is shown in Fig. 5, in which both plants, Pmic and Pvel, are transformed into “demodulated” plants represented as 2N ×2N MIMO systems. Since the plant based on the microphone measurement is well modeled as a linear system, we use the transfer function notion with argument s, whereas, the plant with hot wire measurement is genuinely nonlinear and must be analyzed as such. The demodulated plants with microphone measurement and hot wire measurement are denoted P˜mic and P˜ vel, respectively. Each of the N frequency channels possesses an in-phase and quadrature input, denoted u i nand u q n , and an in-phase and quadrature output, denoted y i nand y q n .

The low-pass filter, denoted by the Hlp block, restricts the demodulated plant bandwidth. The low-pass filter corner frequency, denoted ωc, is chosen to be ωc < ωf 2 since this prevents any direct overlap of, and interaction between, adjacent channels. The demodulated microphone plant, P˜mic, is 2×2 block diagonal and independent of the operating point since Pmic is essentially linear. In contrast, the demodulated plant, P˜ vel, is, in general, full and dependent upon the system operating point. Interestingly, though, in a neighborhood of an operating point P˜ vel can be modeled as an affine function of the input. The transformation to base band coordinates allows us to characterize the nonlinear harmonic coupling phenomenon in a linear framework which simplifies identification and control. Research on the impacts of deforestation of the Brazilian Amazon rainforest on climate have indicated that the local region will lose moisture stored in broad leaves, causing a decrease in evaporation, and an increase in sensible heat and convective precipitation . In other locations, urban development has resulted in local heat islands and agriculture and overgrazing have caused a number of changes, including the surface roughness, evapotransporation, infiltration, and sensible heating rates . These land use changes, along with man-made lakes and reservoirs, change the energy and water budgets, affect the regional weather and climate patterns, and frequently have wider impacts. The Three Gorges Dam on the Yangtze River in China represents the world is largest man-made reservoir, with an expected total storage capacity of 39.3 billion m3 , a hydroelectric potential of 84.7 billion kilowatt hours and flood reduction in low lying regions downstream.

By 2009, the TGD is expected to fully submerge a 663 km length of the Yangtze River and will have a 1040 km2 wet surface area, representing a significant land use change in topography and evaporation that is expected to result in changes in the regional weather and climate patterns. Previous studies by the Chinese Meteorological Institute suggest that the TGD reservoir area will alter local patterns of precipitation, wind, and temperature, and estimate that the annual average near surface air temperature in the vicinity of the TDG will increase by 0.3o C. However, the local climatic impacts due to the change in surface area and weather patterns have not been systematically quantified and are not fully understood. In this sensitivity study we consider the change in surface characteristics in the TGD area from one of steep vegetated terrain to a large flat saturated surface. This land use change represented here is the largest man made surface with a potential evaporating rate. Here, we investigate changes in local circulation patterns and seek to quantify the relative change in temperature, precipitation, and energy fluxes using a regional atmospheric model coupled to a land surface model. The motivation of the present investigation is based in part on recent reports, including the estimated 0.3o C temperature increase . To evaluate this finding, we obtained from the Chinese Ministry of Water Resources the 1984-2004 daily temperature observations from the Yichang Station, located at the Three Gorges Dam site. Figure 1 shows the mean April to August maximum temperature trends at Yichang for 1984-1992,vertical hydroponic garden the period prior to filling, and 1992-2004, the period during filling. Based on this partial data set, an increasing April-August Tmax is seen for the pre-TDG filling, with an increasing slope of 0.053o C/AMJJA, while the 1992-2004 period has a much flatter Tmax slope of 0.010o C/AMJJA. Additionally, the 1992-2004 period has significantly less variability, suggesting that the presence of the reservoirís thermal buffering capacity, as compared to the pre-THD land surface Tmax fluctuations. This partial result, which is counter to Qin and Peter , motivated the present numerical sensitivity experiment to determine specifically, what levels of relative climate change might be expected in 2009 and beyond, when the TDG reservoir has been filled. To quantitatively investigate the relative impact of the TGD land use change on the local climate, two regional climate model simulations, control and the TGD land use change, were generated for the period 2 April to 16 May 1990. This 44 day non-rain period was selected for analysis of the effects of this evaporating surface on the local weather patterns independent of large scale weather, such as monsoons. The regional climate model used in this study is the non-hydrostatic version on the Penn State/National Center for Atmospheric Research Mesoscale Model Version 5 . MM5 was configured with 18 vertical layers, the Grell convection scheme to parameterize cumulus clouds , and the Medium Range Forecast planetary boundary layer scheme to solve boundary layer processes . The Oregon State University Land Surface Model coupled to MM5 by Chen and Dudhia was used to characterize land surface processes. The OSULSM has 4 soil layers with a total depth of 2 meters and a vegetation scheme advanced by Chen et al , with the canopy resistance approach of Noilhan and Planton . MM5 was configured with a 50km spatial resolution with a one-way nested 10 km resolution grid. The 50 km domain coordinates are 70E17N by 140E55N, and the 10km resolution domain coordinates are 100E26N by 116E34N. The land use change sensitivity carried out for the 10 km resolution nested simulation substituted the Yangtze River Valley area from Yichang to Chongqing with a flat saturated surface area of 1040 km2 .

The 50 km resolution MM5 simulation was initialized and the lateral boundaries were updated every 12 hours using the National Centers for Environmental Prediction/National Center for Atmospheric Research Reanalysis II data set. The MM5 10 km resolution simulation used the 50km output as input forcing, with 10km output data archived at six hour intervals for analysis. The 2 April to 16 May 1990 time series of the 1040 km2 TGD area-averaged latent heat flux, sensible heat flux, surface skin temperature, and 2 m air temperature for the relative control and the land use change are shown in Fig. 3a-d. The latent heat flux for this 44 day simulation is consistently higher in the TGD simulation than the control, with values ranging from 15-135 W/m2 . The 44-day mean difference is an increase of 79.6 W/m2 , with the largest differences occurring during the warmer days, as would be expected. The energy required for this increase in evaporation is removed from the surface, which lowers the temperature. The surface skin temperature decreased by 1o C to 4.5o C, with a mean increase of 2.9o C . The 2 m air temperature change is less dramatic, with daily decreases ranging from 1o C to 2.5o C, and a 44-day mean decrease of 1.5o C. These temperature differences drive the daily changes in the sensible heat flux, where the control ranges from 5-80 W/m2 and the TGD change ranges from -45 to 20 W/m2 . The 44-day mean change in the sensible heat flux is -48.9W/m2 . The diurnal latent and sensible heat fluxes are most pronounced at midday, with the TGD simulation of latent heat increasing by nearly 200 W/m2 and the sensible heat flux decreasing by 50-75 W/m2 . The overlying air becomes more stable and air mass aloft sinks. The 850 mb vertical wind speed has a downward velocity exceeding 10-2 m/s along the TGD area . It is not clear if regions outside of this land use change with rising and sinking motion can be attributed to the TGD impact. To fully understand the spatial range of impact, a much longer simulation that represents a true climate is needed. It is interesting to note that the areas of maximum downward flow correspond to changes in topography from steep valleys to a flat surface. Figure 6 follows from these results indicating that the sinking air mass brings about a low level divergence of moisture away from the TGD. It can be seen that for areas of maximum downward velocity, the negative moisture flux divergence in the presence of the TGD is on the order 5-8 x 10-8 m/s. This dries the air column above the TGD further, reducing cloudiness, and increasing net surface radiation.With a reduction in local clouds over TGD, the downward solar radiation increases by 5 to 25 W/m2 , but the downward long wave radiation decreases by about 1.5 W/m2 . This local radiation shift along Yangtze River valley is well demarcated and there are decreases just beyond the wetted surface area. This leaves an uncertain balance between evaporative cooling and radiative heating, where cooling appears to dominate during the 2 April to 16 May 1990 simulation period. These results are summarized in Table 1. Two simulations, control and land use change, were performed for an eight week period to determine the net sensitivity of the local climate.