^{*}

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

Landcover change alters not only the surface landscape but also regional carbon and water cycling. The objective of this study was to assess the potential impacts of landcover change across the Kansas River Basin (KRB) by comparing local microclimatic impacts and regional scale climate influences. This was done using a 25-year time series of Normalized Difference Vegetation Index (NDVI) and precipitation (PPT) data analyzed using multi-resolution information theory metrics. Results showed both entropy of PPT and NDVI varied along a pronounced PPT gradient. The scalewise relative entropy of NDVI was the most informative at the annual scale, while for PPT the scalewise relative entropy varied temporally and by landcover type. The relative entropy of NDVI and PPT as a function of landcover showed the most information at the 512-day scale for all landcover types, implying different landcover types had the same response across the entire KRB. This implies that land use decisions may dramatically alter the local time scales of responses to global climate change. Additionally, altering land cover (e.g., for biofuel production) may impact ecosystem functioning at local to regional scales and these impacts must be considered for accurately assessing future implications of climate change.

Vegetation is a key variable of interaction between the land and atmosphere. Driven by climate, vegetation is highly sensitive to precipitation and/or temperature, which depends on the region under consideration [

For semi-arid regions, such as the central US Great Plains, biosphere-atmosphere interactions are strongly coupled to climate variability in these water-limited areas [

The evidence for biotic responses to climate changes can be based on analysis of satellite data, and the Normalized Difference Vegetation Index (NDVI) is the most common indicator of terrestrial vegetation productivity [

The conversion of grassland to croplands and pastures has affected the exchanges of energy, water, and carbon, as well as ecosystem condition and function [

In concert with the relationship between precipitation (or other climate forcings) and vegetation, many studies have used correlation analysis to examine how vegetation responds to climatic variables (

Our proposed methodology, multiscale information theory metrics, which have been developed by Brunsell and Young [

Therefore, the motivating objective of this study is to examine the relationship between vegetation productivity and the roles of local land cover type and regional climate (

The central US is an area of significant agricultural production, and for this study we focus on the Kansas River Basin (KRB), which is located in northern Kansas and extends into southern Nebraska and a portion of eastern Colorado (

Currently, AVHRR is the best historical and the longest record of data for monitoring vegetation [

Precipitation (PPT) was used as a measure of the regional climate variability because of the east-west gradient across the KRB [

Despite variable crop cultivations in the central US over the time period of interest, the total factions remained fairly constant according the USDA [

Wavelet analysis is a technique to view a data series as a function of different spatial and/or temporal resolutions, and each different resolution can be referred to be “a level of decomposition”. It allows for quantifying the variance contributed by each resolution and also determine when (temporally) or where (spatially) the contribution originates from [_{0} is the initial scale of decomposition, and the wavelet is defined by:

The unique capability of wavelet multi-resolution analysis “zoom-in” allows the identification of local brief, high-frequency signal and low-frequency variability in a time series. Windows are able to look at different frequency signals: being wide for low-frequency while being narrow for high-frequency [_{m,n}

Wavelet multi-resolution analysis is a dyadic (powers of two) decomposition in scale, and we have chosen to conduct nine levels (corresponding to lengths of 2, 4, 8, 16, 32, 64, 128, 256, and 512) based on the length of the time series. By progressively adding the finer scale details, the original dataset

In addition, we calculated the wavelet spectra as a function of time scale

Information theory has been previously used to examine land-atmosphere interactions [_{i}

The relative entropy (

There are two ways for computing the relative entropy for this study. In the first case, we computed the relative entropy between the original data and a decomposed version data from the wavelet multiresolution analysis. This was done to isolate the relative contributions of these timescales to the overall signal, e.g., computing the relative entropy between seasonal precipitation and total vegetation [

In order to compute the entropy and relative entropy of precipitation and NDVI, we first decomposed the time series of precipitation and NDVI signals using the wavelet multiresolution analysis described on the previous section. At each scale of decomposition, the pdf of the decomposed time series (_{m}

Spatial and temporal biosphere-atmosphere interactions, such as fluxes of water and energy, are strongly coupled to climate variability in grasslands [

Variations in climate factors, such as precipitation, have strong influences on the variation of NDVI for a given area.

The maps of the relative entropy between PPT and NDVI are shown in

We compared the proposed method and metrics with other traditional statistical analysis as well. First is the correlation analysis: we examined the relationship between NDVI and different time lags of PPT by calculating correlation coefficients between NDVI of the various periods and corresponding precipitation (e.g., current period of NDVI and previous period PPT). However, the results did not show any significant correlation between NDVI-PPT within KRB (−0.1 < ^{2} = 0.1), shown in

In addition to the gradients of vegetation and precipitation across KRB, we examined the spatial-temporal distributions within each landcover type (

We examined the variability of the entropy of PPT and NDVI as a function of landcover type (

We calculated the wavelet spectra to quantify how much variance of PPT and NDVI is contributed by different temporal scales. This was conducted at selected longitudes along the KRB and as a function of landcover type.

Differences in landcover types induce minor variations across longitudes. Due to managed irrigation, irrigated corn (

Precipitation within the KRB (

Next, we conducted a wavelet multi-resolution analysis to calculate the multiscale entropy for the PPT and NDVI. The general behavior was increasing entropy with increasing time-scale. The marked increase of NDVI was in the 128-day (seasonal) scale and slowly went up through longer time-scales. More variance was found up to the seasonal scale for the entire basin and selected landcover types (irrigated corn and C4 grassland). Within the seasonal scale for the entire basin (

The entropy of PPT had the greatest increasing trend at the 512-day time scale. This increasing trend was consistent across the entire KRB (

In order to determine how much information is contributed to the total signal of PPT and NDVI by certain time scales, we calculated the relative entropy between the original PPT and NDVI and decomposed PPT and NDVI at each individual scale. For the entire KRB (

The results of PPT for the entire KRB showed reduced values with increasing time scale with a particularly high

In addition, we also calculated the relative entropy between NDVI and PPT as a function of scale to examine how informative different time scales of the PPT signal were at determining the NDVI data and

The distributions of

Climatic controls are the primary influence on grasslands with the possible exception of irrigation [

Compared with the proposed method and metrics, other traditional statistical analysis like the correlation analysis and linear regression analysis have shown no significant results. This agrees with a study of the assessment of spatial-temporal variability of daily precipitation across the continent [

As the information theory metrics used in this study are qualitative rather than quantitative, and are computed at each time scale from the estimated pdfs, the values of entropy and relative entropy are conveniently used to interpret the variability of precipitation and vegetation.

Entropy metrics can show the spatial gradient of precipitation and vegetation (

One objective of this study was to understand the temporal dynamics associated with different landcover types as a function of location along the mean precipitation gradient. Overall, regional precipitation was the main control for vegetation, and can be a good predictor of vegetation productivity [

Next we examined how different longitudes within the KRB were governed by microclimatic impacts (

The distribution of land cover in KRB clearly indicated the impact of the local microclimate. Irrigated landcover types

Human manipulation is another strong forcing on vegetation in KRB. For example, removing the water limitation resulted in the same NDVI spectra (

Meanwhile, land-use conversion may alter the vegetation-precipitation relationship. For instance, if the C4 grassland in KRB is converted to an irrigated corn field, an obvious west-east covariability with precipitation could be informed by the relative entropy between NDVI and PPT at the monthly scale (

This study demonstrated the variation in vegetation across temporal scale as a function of landcover types in the KRB. We examined how the different regions in this basin were governed by microclimatic impacts of land cover type (

The general trend in the mean vegetation and precipitation showed an increasing trend from west to east, indicating an obvious response of vegetation to the dominant climate forcing in the region. However, it is known that crop management practices,

We have also found that the relationship between NDVI and PPT varied with different landcover types. Despite the lack of significant results from other traditional statistic analyses, such as correlation coefficient and linear regression analyses, our proposed method have shown remarkable results in the relative entropy between NDVI and PPT (

This microclimatic influence can impact the responses to global and regional climate change. Human manipulations have been able to impact regional climate change,

We would like to thank the NSF EPSCoR projects (EPSCoR 0553722 and KAN0061396/KAN006263), NSF: DEB-1021095 and the University of Kansas Transportation Research Institute for funding this research.

The authors declare no conflict of interest.

(

Distribution of land cover types in the Kansas River Basin.

The probability density functions of (

(

(

Wavelet variances of NDVI (

Multi-resolution entropy of NDVI (

Multi-resolution relative entropy of NDVI (

Multi-resolution relative entropy between NDVI and PPT as a function of temporal scale in (

Land cover types, percentage, numbers of pixel and per-pixel fraction cover (the average of the aggregation from the 1-km grid to the 8-km grid) of the 2005 Kansas Land Cover Patterns Level IV map.

Irrigated corn | 6.9 | 213 | 50 |

Non-irrigated corn | 6.12 | 189 | 55 |

Irrigated soybean | 2.46 | 76 | 46 |

Non-irrigated soy bean | 5.6 | 173 | 52 |

Irrigated cropland | 24.72 | 763 | 65 |

Non-irrigated cropland | 5.44 | 168 | 49 |

CRP land | 2.5 | 77 | 46 |

C4 grassland | 37.75 | 1165 | 74 |

C3 grassland | 3.99 | 123 | 49 |

Woodland | 2.66 | 82 | 45 |

Urban | 1.2 | 37 | 55 |

Water | 0.66 | 20 | 80 |

| |||

Total | 100 | 3,086 |