Characterization of land-surface precipitation feedback regimes with remote sensing

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1 Remote Sensing of Environment 100 (2006) Characterization of land-surface precipitation feedback regimes with remote sensing N.A. Brunsell * Department of Geography, University of Kansas, 1475 Jayhawk Blvd., 117 A Lindley Hall, Lawrence, KS , United States Received 30 December 2004; received in revised form 13 October 2005; accepted 15 October 2005 Abstract A simple methodology for characterizing the land surface s response to precipitation is proposed based on the average behavior of coarse resolution remote sensing data. Feedback regimes are designated based on the temporal correlations between the vegetation and precipitation and the surface temperature and precipitation. The different feedback regimes are linked to the relative importance of vegetation and soil moisture in determining land atmosphere interactions. The resultant feedback regimes are well localized spatially. In addition, the temporal dynamics are assessed in terms of lagged covariances and phase space plots. The two dominant feedback regimes are distinguishable by the vegetation precipitation correlation, implying that vegetative control may be the dominant factor in influencing surface-precipitation feedbacks. These zones are not easily distinguished in the NDVI-surface temperature correlations, but exhibit different behavior in their NDVI-precipitation and surface temperature precipitation correlations. In addition, these zones can be distinguished in phase plots of both temperature and NDVI. These results suggest a methodology for quantifying the rate of the hydrological cycle in different regions of the globe as well as identifying areas where human induced land cover change may have the most effect transitioning between different feedback zones, and therefore altering the rate of the hydrologic cycle. D 2005 Elsevier Inc. All rights reserved. Keywords: Land atmosphere interactions; Feedback; AVHRR; Multi-temporal 1. Introduction It is widely acknowledged that the land surface influences climate on different spatial and temporal scales (Pielke et al., 1998). These influences are complicated by many non-linear interactions and feedbacks occurring in the transport of mass and energy between the surface and the atmosphere. While a significant body of research (e.g., Raupach, 1998) has focused on determining the existence of various feedbacks among the soil surface, vegetation and the atmosphere, little work has been done on quantifying the spatial variability of locations where the different feedback mechanisms are applicable based on observed data. Two bodies of research are particularly appropriate to our study, (1) soil moisture precipitation feedbacks, and (2) vegetation precipitation feedbacks. These two areas are briefly discussed here. * Tel.: ; fax: address: brunsell@ku.edu. Entekhabi et al. (1996) outlined theoretical feedbacks between soil moisture and atmospheric properties on multiple time and spatial scales. They outlined the mechanisms by which soil moisture and precipitation interact via surface net radiation, fluxes, and atmospheric convective potential energy. They also identified several key factors limiting a more thorough understanding of soil moisture atmosphere interactions, including the spatial and temporal variability and the lack of a reliable source of spatially distributed soil moisture estimates. Eltahir (1998) proposed that there is a positive feedback between soil-moisture and precipitation. When the soil moisture is high, the surface albedo and the bowen ratio (the ratio of sensible to latent heat) are decreased. Both of these factors act to decrease the surface temperature, increasing the net radiation at the surface, decreasing the boundary layer, increasing the atmospheric water vapor, which also increases the moist static energy, the convective potential and induces precipitation. This mechanism was proposed to be observable through a negative correlation between surface temperature and /$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi: /j.rse

2 N.A. Brunsell / Remote Sensing of Environment 100 (2006) precipitation. Findell and Eltahir (1997) analyzed a 14 year soil moisture dataset from Illinois and concluded that there was evidence of a positive feedback mechanism between soil moisture and rainfall. Findell and Eltahir (1999) followed up the analysis by attempting to ascertain the physical processes involved in the feedback. They found that the averaged soil moisture and averaged near surface meteorological conditions did not exhibit the expected correlations. They noted linkages between the moist static energy and high rainfall in the summer as well as high atmospheric humidity and high rainfall linkages over all months. Using the same dataset, Salvucci et al. (2002) concluded that this evidence was a result of the filtering techniques used, and that there was little evidence of any effect of soil moisture on future rainfall. Findell and Eltahir (2003a) used a modified version of the one-dimensional boundary layer model of Kim and Entekhabi (1998), along with a measure of the convective triggering potential to the continental United States to examine the spatial variability of the influence of soil moisture on rainfall. Findell and Eltahir (2003b) further identified regions of possible feedbacks between the soil moisture and rainfall. They found that most of the Eastern United States is characterized by a positive feedback, while the Southwestern Monsoon dominated region was characteristic of a negative soil-moisture precipitation feedback. Their research was supported by the work of Matsui et al. (2003) who found negative correlations between surface temperature and precipitation throughout the North American Monsoon System region in the Southwestern United States. A further limitation in understanding the role of soil moisture in land atmosphere interactions is the understanding of the time scales of response of various depths within the soil profile. This issue was investigated by Wu et al. (2002), who examined this idea by using 16 years of soil moisture in Illinois and found that the white noise spectrum of precipitation is translated into a red noise spectrum in soil moisture, with the redness increasing with depth in the soil profile. The dominant phase shift was on the seasonal scale, with almost no intraseasonal component below about a 1.1 m depth. Douville and Chauvin (2000) demonstrated improvement in the modeling of summer precipitation with use of the Global Soil Wetness Project data, further illustrating the importance of realistic surface conditions in regional climate studies. Much research has been conducted investigating the linkages between remotely sensed Normalized Difference Vegetation Index (NDVI) and climate variables (primarily precipitation and air temperature). In general, there is an obvious relationship, however results indicate that the general form of the relationship is highly variable in time and space. Richard and Poccard (1998) found a high correlation between NDVI and antecedent rainfall on a lag of one to two months when examining Southern Africa, and Wang et al. (2003) found the same time lags in the central Great Plains of the US. However, Yang et al. (1997) found NDVI-precipitation correlations to be highly variable spatially when studying the state of Nebraska. Goward and Prince (1995) found a general relationship between annual precipitation and mean NDVI for regions in the Great Plains and Africa. However the strength of the correlation was weak when considering inter-annual variability, although the strength of the correlation varied from location to location. In Africa, they found a temporal lag helped explain this. In contrast, Yang et al. (1998) found the dominant control on the time integrated NDVI in the Great Plains to be the spring and early summer precipitation, not the annual rainfall. Kawabata et al. (2001) conducted a correlation analysis between NDVI, temperature and precipitation globally. In general, the correlations between NDVI and precipitation were strong in the Northern mid-latitudes and weak in the tropics. They also found a linear relationship between NDVI and precipitation in Australia. Further analysis by Ichii et al. (2002) found primarily positive correlations between interpolated precipitation and NDVI with exceptions being in small regions in South America and Africa, and large areas of Northern Asia. Lotsch et al. (2003) used canonical correlation analysis between AVHRR NDVI and the Climate Prediction Center Merged Analysis of Precipitation dataset and found strong correlations between precipitation and vegetation across most of the globe as well as a strong correlation with atmospheric dynamics. Nicholson and Farrar (1994) showed a linear relationship between precipitation and NDVI for low values of rainfall. Large values of rainfall corresponded with an NDVI saturation effect where few changes were observed. Using the rainfall efficiency (NDVI/precipitation) they found the sensitivity of the vegetation response to precipitation to be highly variable spatially and suggested soil and other factors influencing the vegetation response. Further analysis by Farrar et al. (1994) showed that although the soils differed in the soil moisture response to precipitation, factors such as the soil reflectivity may also explain the results. De Ridder (1998) used a 1D mesoscale model coupled with a detailed land surface model to investigate the influence of vegetation cover on precipitation recycling in the Sahel. Results indicated the presence of a positive feedback between vegetation and drought severity: higher vegetation cover increased access to subsurface water supply and increased precipitation through evaporation and the convective instability. Through a regional climate modeling study, Heck et al. (1999) identified a positive feedback between vegetation and evaporation in Middle and Northern Europe, but a negative feedback in Mediterranean regions. In the Northern regions, increased vegetation led to increased soil moisture and increased evapotranspiration throughout the year. In the Mediterranean regions, model runs with increased vegetation were accompanied by critically low soil moisture in the summer months (presumably from seasonal cycle in soil moisture) and decreased evapotranspiration indicating a reversal from a positive to a negative feedback. Zeng et al. (1999) also found a positive feedback between vegetation and precipitation at multi-decadal time scales in the Sahel using a coupled surface-atmosphere model. Results suggest that the interactive role of vegetation acts to increase multi-decadal variability and limit year-to-year variability.

3 202 N.A. Brunsell / Remote Sensing of Environment 100 (2006) /+ Corr (Ts, PPT) +/+ Corr (NDVI, PPT) function of remotely sensed surface temperature (Ts) and NDVI. A primary benefit of this methodology is that it allows examination of the land surface response without an a priori determination of the land cover class, and thus perhaps an independent corroboration of land cover determination through remote sensing in areas that are notoriously difficult to determine. 2. Feedback regimes as determined by correlations / Fig. 1. Schematic diagram illustrating which feedback regime ( to ) is associated with the correlations between NDVI and precipitation and surface temperature and precipitation. The (+/ ) signs illustrate the sign of the associated NDVI-PPT correlation (first sign) and the sign of the Ts-PPT correlation (second sign). Zeng et al. (2002) examined the influence of the positive vegetation precipitation feedback on spatial gradients in vegetation type. They found that the existence of a positive feedback acts to enhance the spatial gradient along a forest desert gradient, while climatic factors (e.g., sea-surface temperature forcings, Zeng and Neelin, 2000) act to decrease the magnitude of the gradient. The general conclusion to be drawn from the above literature survey is supportive of the intuitive idea that there are relationships between the precipitation and both the vegetation and soil moisture. However, this research has yet to couple the roles of soil moisture (assessed through the surface temperature) and vegetation into a larger understanding of the temporal and spatial variability land atmosphere interactions. This is particularly important for regional scale understanding, where the surface must be considered as containing both bare soil and vegetated areas. An understanding must be developed to quantify the relative contributions of each component to assess where and when different feedback mechanisms become significant in surface-atmosphere interactions. The various feedbacks interacting at the surfaceatmosphere boundary will directly affect the temporal and spatial scales of the surface variability. Once these interactions are better understood and quantified, the role of the land surface in assessing the predictability of climate change can be addressed. This paper begins to address these issues by examining how local land surface atmosphere feedbacks are related to average land surface condition and what are the time scales of response to precipitation forcing as a function of the different feedback regimes. The time scales of the surface response to precipitation forcing events are different for different land surface conditions which are representative of different physical processes governing the hydrologic cycle resulting in different feedback regimes and these differences can be observed and quantified through remote sensing. To address this, we quantify the average land surface condition (spatially and temporally) as a +/ The land surface is divided into regions in the NDVItemperature space representing a variety of vegetation, temperature, and soil moisture regimes. We identify regions of positive and negative feedbacks through the use of the temporal correlation coefficients between NDVI and precipitation, and surface temperature and precipitation. While acknowledging that a correlation between the different variables does not imply a feedback, we argue that the correlation coefficient is an easily obtained measured which is indicative of different physical processes occurring near the land surfaceatmosphere interface. Thus, a difference in the sign of the correlation between two locations may be the result of different feedback regimes dominating the regional land atmosphere exchanges of water and energy. The existence of the different feedback regimes are indicative of different physical processes occurring near the surface-atmosphere boundary and these processes result in different time scales of response between the remotely sensed variables as a function of feedback regime. Therefore, we investigate the lagged covariances to assess the time scales of response active within different feedback regimes. Fig. 1 is a schematic diagram illustrating the possible relationships between the NDVI-Precipitation (PPT) correlation and the Ts-PPT correlation. Depending on the sign of the correlation coefficients, the land surface is assigned to one of the four quadrants. Each quadrant is associated with a proposed feedback regime. Table 1 illustrates whether a positive or negative feedback is associated with each quadrant. The proposed feedbacks are grouped into either a soil moisture effect or an energy balance partitioning effect. Table 2 illustrates how each of these mechanisms is related to the Ts- PPT and NDVI-PPT correlations. In addition, Table 2 gives an example physical mechanism illustrating how the proposed feedback is associated with the correlation. Since each quadrant in Fig. 1 is associated with both a NDVI-PPT correlation and a Ts-PPT correlation, two different mechanisms are possible in each quadrant. Sometimes, these mechanisms are related. For example, a negative Ts-PPT correlation accompanied by a positive NDVI-PPT correlation Table 1 Feedback regime case number with associated correlations and feedback Case Correlation (NDVI,PPT) Correlation (Ts,PPT) Resultant feedback 1 Positive Positive Positive or negative 2 Negative Positive Negative 3 Negative Negative Positive 4 Positive Negative Positive

4 N.A. Brunsell / Remote Sensing of Environment 100 (2006) Table 2 Correlations between surface temperature (Ts) and precipitation (PPT) and between NDVI and PPT, with the proposed feedback and physical mechanisms responsible Correlation Proposed feedback Proposed mechanism +c(ts,ppt) (soil moisture and PPT) Ts increases due to a decrease in soil moisture, albedo increases, net radiation decreases due to both albedo and temperature changes, higher fraction of net radiation goes to sensible heat flux, boundary layer depth increases, more convective PPT. c(ts,ppt) +(soil moisture and PPT) Temperature is decreased, net radiation of the surface increases, ET increases, lower atmosphere becomes more saturated and PPT increases +c(ndvi,ppt) +(energy partitioning and PPT) Vegetation increases, albedo decreases, net radiation increases, ET increases, increasing the saturation of the boundary layer which increases the likelihood of PPT events. c(ndvi,ppt) (energy partitioning and PPT) Increase in vegetation causes an increase in the evaporative fraction (EF), specific humidity (q) increases, sensible heat (H) decreases, CBL height decreases, PPT decreases. (Case 4) can be explained by the coupled effect of surface temperature falling as more vegetation becomes present. In this case both effects act to enhance the precipitation. However, in other cases (e.g., Case 1), the two correlations are apparently contradictory. In the case of regime 1, the NDVI-PPT correlation seems to indicate a positive feedback where more vegetation enhances precipitation, allowing for more vegetation growth. The positive Ts-PPT correlation would indicate that higher surface temperatures are associated with enhanced precipitation. The higher surface temperatures accompanied by more vegetative growth unrealistic. There could be two possible explanations; one is that one of the two mechanisms dominates the other, and the feedback is then either positive or negative depending on which mechanism is the primary one in that location. The other possibility is that the correlation is picking up the seasonal effect of onset of vegetative growth in the spring, in which case the warmer temperatures would be associated with more vegetative growth. 3. Results 3.1. Determination of feedback regimes The surface data used for this analysis is based on an eight year time series ( ) of the AVHRR pathfinder dataset, using the 1-, monthly composited data. The split window correction described in Becker and Li (1990) was applied to bands 4 and 5 to calculate the surface temperature, with the surface emissivity computed from the NDVI as described in Brunsell and Gillies (2002). The precipitation data is the Global Precipitation Climatology Centre (GPCC) 1-, monthly dataset (available from gpcc). The coarse resolution data was deemed acceptable for our purposes of demonstrating the determination of the feedback regimes, while avoiding issues related to using datasets with different resolutions. In order to avoid seasonal trends in the correlation coefficients, the data was detrended. Seasonal means in the data were calculated for Winter (Dec Jan Feb), Spring (Mar Apr May), Summer (Jun Jul Aug), and Autumn (Sep Oct Nov) for each latitude. These latitudinal seasonal means were then subtracted from each pixel at that latitude. This resulted in an eight year, monthly time series of the surface temperature, NDVI, and precipitation representing the deviation at that location from the seasonal latitudinal average value. The correlation coefficients were then calculated using the detrended data. For each land pixel, the NDVI-precipitation and the surface temperature-precipitation correlations are computed as: ~ N ðx i x Þðy i ȳþ 1 r ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ~ N 1 ðx i x Þ 2 ~ N 1 ðy i ȳþ 2 where r is the correlation coefficient, x and y are the time series of length N, and the overbar denotes the temporal mean in that location. The feedback regime for each pixel is then assigned based on which quadrant of the NDVI-precipitation and surface temperature-precipitation correlations plot (Fig. 2). To ensure statistical confidence, only r > are used in this analysis. When viewed spatially, these correlations are well organized, as shown in Fig. 3. The number of pixels with significant NDVI-PPT and Ts-PPT correlations vary between the feedback Corr (Ts, PPT) Corr (NDVI, PPT) ð1þ Fig. 2. Lag (0) correlations between NDVI and precipitation versus lag (0) correlation between surface temperature and precipitation.

5 204 N.A. Brunsell / Remote Sensing of Environment 100 (2006) Fig. 3. Spatial distribution of the feedback zones defined from the lag (0) correlations. regimes ( =444, =34, =1109, =1203). Regimes and are the more likely combinations. Using the detrended temporal mean of each pixel, the feedback regimes are highlighted in Fig. 4. In addition to being well organized spatially, the feedback regimes are well located in the temperature-ndvi space. Feedback zones and are centrally located in terms of the temperature (means of 0.63 and 0.99, respectively) and NDVI (means of 6 and 7). In the case, there are very few pixels, so there is no clear pattern. The and zones show more variability in NDVI NDVI 0.4 Ts Ts Fig. 4. Surface temperature-ndvi plots illustrating the location in Ts-NDVI space of the different feedback regimes.

6 N.A. Brunsell / Remote Sensing of Environment 100 (2006) the Ts-NDVI space, with the mean of being ( 3.56, 5) and being located at (3.62, 5). The and zones are characterized by the triangular shape common in Ts-NDVI space (e.g., Gillies et al., 1997). may or may not have a triangular pattern, but there are not enough points to say anything conclusive. The triangular shape exhibited in and is significant, as this has been used to compute the surface energy fluxes using the Ftriangle method_ (e.g., Gillies et al., 1997 and Brunsell & Gillies, 2003). In addition, the Ts-NDVI space can be related to surface soil moisture availability (Gillies & Carlson, 1995). For each month in the time series, we calculate a relative soil moisture availability for each pixel relative to the location in the NDVI-Ts triangle; for each level of NDVI, the warm edge of the triangle represents drier pixels whereas the cooler edge represents more moist pixels. Assigning each pixel into a qualitative class of High, Medium, or Low soil moisture is then possible at each time. To determine which average soil moisture class is associated with each pixel, we calculated the near surface soil moisture availability for each pixel for each month, then assigned the class associated with the peak of the temporal histogram. In general, the soil moisture class is associated well with the temporal means of NDVI and surface temperature (not shown). The temporal variability within the NDVI-Ts space as a function of both the feedback regime and the soil moisture class are examined using lagged covariances (Fig. 5). All four regimes show a positive NDVI-Ts covariance at the zero time lag. shows the largest amplitude, reaching minimums at +/ 6 months. Regime 2 shows a minimum at a 2 month lag, reaching a maximum at 4 months. and are basically indistinguishable in their NDVI-Ts covariances. Both reach maximums at the zero lag, and exhibit minimums at a lag of 6 months. In terms of the soil moisture class (Fig. 5, bottom), at the zero lag there is a decrease in amplitude with decreasing soil moisture. The high soil moisture class exhibits a maximum at the zero lag with minimums at the +/ 6 month time lags, as Cov (NDVI, Ts) Lag (Months) 100 High Med Low Cov (NDVI, Ts) Lag (Months) Fig. 5. Lagged covariances between NDVI and surface temperature as a function of feedback regime and soil moisture class.

7 206 N.A. Brunsell / Remote Sensing of Environment 100 (2006) does the medium soil moisture class. The low soil moisture class exhibits a minimum at approximately 2 months with a maximum at +4 months. This implies that the high and medium soil classes are exhibiting annual cycles even in their seasonally detrended values. The low soil moisture class has a phase lag of approximately 2 months compared to the other cases Temporal dynamics and feedback regimes The primary benefit of determining the feedback regimes is the ability to characterize how different areas respond to precipitation forcing events. To examine this, the laggedcovariance between the NDVI-precipitation and surface temperature-precipitation are calculated as both functions of the feedback regime (Fig. 6) and the soil moisture class (Fig. 7). The lagged covariance between NDVI-PPT in terms of the feedback zones is shown in the top panel of Fig. 6. exhibits a maximum at the zero lag and minimums at the +/ 6 month time scales. exhibits a minimum at the zero lag and maximums at about +/ 5 month lags. shows the largest amplitude reaching a minimum at the zero lag, and maximums at about 4 and +7 months. reaches a maximum at 1 month with minimums at +/ 6 months. For the lagged covariance between Ts-PPT (Fig. 6 bottom), and are follow the same general trajectory, and are generally indistinguishable except that reaches slightly lower minimums. They both reach maximums at +1 month, and minimums at +/ 6 months. again shows the largest amplitude, reaching a minimum at the zero lag, and maximums at 7 and +5 months. shows little variability in the Ts-PPT covariance plot, reaching a minimum at the zero lag, and maximums at approximately +/ 4 months. The lagged covariances are shown in Fig. 7 for the different soil moisture classes. The NDVI-PPT covariance (top panel) reaches a maximum covariance at a 1 month lag, with Cov (NDVI,PPT) 0 Cov (Ts,PPT) Lag (Months) Lag (Months) Fig. 6. Lagged covariances for (top) NDVI-precipitation; (bottom) surface temperature-precipitation as a function of feedback zone.

8 N.A. Brunsell / Remote Sensing of Environment 100 (2006) High Med Low 200 Cov (Ts, PPT) Cov (NDVI, PPT) Lag (Months) High Med Low Lag (Months) Fig. 7. Lagged covariances for (top) NDVI-precipitation; (bottom) surface temperature-precipitation as a function of soil moisture class. minimums at +/ 6 months. The Ts-PPT covariance for the high soil moisture class reaches a local minimum at 1 month, with a more pronounced minimum at 5 months and a maximum at about 1 3 months. The medium soil moisture class reaches minimums at the zero lag in both the NDVI-PPT and Ts-PPT covariances. The NDVI-PPT covariance is maximized at 4 and 8 months, while the Ts-PPT covariance maximizes at +5 and 6 months. The low soil moisture class follows the same pattern as the medium case for Ts-PPT covariance, but the NDVI-PPT shows a shift reaching a minimum at 3 months and a maximum at 3 months. In addition to the lagged covariance plots, we examine the migration of the spatial mean of each feedback regime in surface temperature-ndvi space through time (Fig. 8). Feedback regimes and show the greatest differences in general behavior. While both show about 30 -K degrees of variability in the temperature migration, shows reduced variability in mean vegetation. and show similar responses in both surface temperature and vegetation cover, with being characterized by slightly warmer temperatures and lower vegetation. To further pursue the temporal dynamics of the different feedback zones, we examine the phase dynamics of NDVI at temporal lags of 1, 2 and 6 months (Fig. 9). is the zone that shows significant differences between the different lag periods. This variability appears to be the result of the annual cycle of vegetation, even though seasonal and latitudinal means were removed from the signal. This implies that pixels in are characterized by regions which are anomalous compared to their latitudinal means. An example of this region is the central

9 208 N.A. Brunsell / Remote Sensing of Environment 100 (2006) surface data sources. It is well known that the local land atmosphere interactions are highly non-linear, and this scale of analysis may well be inappropriate for a detailed analysis of these interactions. However, the purpose of this study is to offer a simple method for determining the spatial variability of these non-linear processes and offer possible insight into NDVI (i+1) 0.1 NDVI 0 Ts Fig. 8. Surface temperature-ndvi plot showing spatial mean of each feedback regime through time. plains of the United States. The other zones lack any annual cycle, showing no preferential movement over the six month lag times. Each of these zones remain fairly localized in their respective regions of the NDVI space, with showing a fairly large variance but remaining centered less than the seasonally and latitudinally averaged value. remains slightly above average, while remains below average regardless of the temporal lag. Other than the large variance, there is little to separate and in the NDVI signal. Fig. 10 examines the phase dynamics of the surface temperature field. and show significant variability at all time lags, again probably the result of a residual annual cycle. The migration through time of the temperature fields of and are remarkably similar. This is surprising in the case of, which did not exhibit this behavior in the NDVI field. The and temperature data show little variability (although more than is exhibited in the NDVI phase plots), where remains centered slightly below average for the latitude, while remains slightly above the latitudinal average regardless of the temporal lag. This implies that the distinction between the different feedback regimes exhibits itself not only in the lag(0) correlations, but also in the mean annual migration in their NDVI and surface temperature phase plots. and can be distinguished in their surface temperature signatures, but not in the NDVI fields. The distinction between and, while not detectable in NDVI, does appear in the temperature field. In addition, the and regimes can be distinguished from one another in the mean NDVI and temperature fields. This signifies that it is necessary to incorporate both the vegetation and surface temperature data to more fully characterize the landsurface response to precipitation, as opposed to one or the other. NDVI (i+2) NDVI (i+6) Discussion This methodology attempts to define these regions based on coarse spatial (1 degree) and coarse temporal (1 month) NDVI (i) Fig. 9. NDVI phase plots for lags of 1 month (top), 2 months (middle), and 6 months (bottom) for each feedback regime. 0.1

10 N.A. Brunsell / Remote Sensing of Environment 100 (2006) Temperature (i+1) Temperature (i+2) Temperature (i+6) Temperature (i) NDVI-PPT correlation. The negative Ts-PPT correlation is intuitive, as higher precipitation will tend to decrease surface temperature, and vice versa. This implies that the vegetation control over boundary layer processes may be the most important feature in distinguishing between the two feedback regimes. In, the negative NDVI-PPT correlation possibly indicates that the added vegetation saturates that atmosphere, inhibiting convection and decreasing the likelihood of precipitation. This is the exhibited in regions of the Amazon and south-eastern Asia, where evaporation over these regions leads to increased cloudiness, decreasing solar insolation, and resulting in a negative correlation between NDVI and PPT. The case, on the other hand, exhibits a positive NDVI-PPT correlation, possibly indicating that the increase in vegetation and evapotranspiration are enhancing the precipitation. The case generally corresponds to semi-arid regions, where it is expected that vegetation will respond well to precipitation events. The and cases exhibit similar behavior in the lagged covariance plots between NDVI and surface temperature. However, they are easily distinguishable when the precipitation covariances are plotted. This implies that while the NDVI and temperature signals are similar, the response to precipitation events is not. In addition, the phase diagrams of the two cases show that the mean temperature and vegetation fields are distinguishable from one another at the 1, 2 and 6 month lag periods. The seasonality of the covariance observed in Figs. 5, 6 and 7 are not surprising in that we are using averaged fields from the remote sensing. However, that seasonality only appears in one case in Fig. 9 and two in Fig. 10. This seasonality is due to a residual climate signal that remains in the remotely sensed data. However, it should not be surprising that local land atmosphere interactions are affected by climatology. The purpose of this study is to examine how regions with possibly diverse climates and/or land cover can show similar responses to surface-precipitation responses. Many of the areas outlined as having significant correlations in both the NDVI-PPT and Ts-PPT agree well with the hot spots of Koster et al. (2004). In particular, this includes central Africa, the northern Great Plains of the United States, parts of South America as well as China and India. The identified hot spots correspond roughly to feedback zones and in this paper. Since that paper only addressed soil moisture influences, it is not surprising that we have identified more locations by the incorporation of vegetation influences in addition to the soil moisture impacts. Fig. 10. Temperature phase plots for lags of 1 month (top), 2 months (middle), and 6 months (bottom) for each feedback regime. where to conduct more thorough analysis, for example along the intersection of two feedback regimes. The and are by far the most common feedback regimes determined from this analysis. These are both characterized by a negative Ts-PPT correlation with having a negative NDVI-PPT correlation and having a positive 5. Conclusions In this paper we have shown that the average state of the land surface as determined by the AVHRR sensor can be indicative of the relative magnitude of different physical processes occurring near the surface atmosphere boundary. This variation in the physical mechanisms is associated with the different temporal responses to precipitation forcing in both soil moisture and vegetation.

11 210 N.A. Brunsell / Remote Sensing of Environment 100 (2006) By using correlation coefficients, we propose a simple method for quantifying the influence of soil moisture, vegetation and precipitation. The quadrant analysis of the correlation coefficients offers insight into which physical mechanisms may be dominating any given pixel. While the correlation coefficients do not necessarily imply a feedback, we contend that the sign of the various correlation coefficients are a reflection of the feedback processes occurring and therefore can be used to determine likely locations of different feedback mechanisms. The four resulting feedback zones are well localized in the spatial domain, exhibit differences in the phase and amplitude of the lagged covariances and are characterized by different behavior in phase space plots of surface temperature and NDVI. The primary conclusions to be drawn from this work are that a simple correlation coefficient can determine regions where local land atmosphere interactions show different temporal characteristics. Through the combination of NDVI-PPT and Ts- PPT correlations and covariances we can delineate the different temporal responses which can then aid in assessing the dominant physical mechanisms in a region. The two most likely feedback regimes are distinguished by the sign of the vegetation precipitation correlation, implying that vegetation control may be the dominant factor in determining the local feedbacks. The benefit of this methodology is that it provides a framework for assessing how different global change scenarios will alter the rates of hydrological cycling in different regions. This methodology allows for the quantification of the interaction between the vegetation and precipitation, without having to focus on the land cover class. For example, it is possible to track the effects of climate change as alterations in the surface temperature-precipitation and vegetation precipitation correlations. Then, it will be possible to determine the critical transition thresholds from one feedback regime to another. This will allow for the identification of at risk regions where the transition between different feedback regimes is likely, and the associated changes in the rate of the water cycle in any particular location. References Becker, F., & Li, Z. -L. (1990). Towards a local split-window method over land surfaces. International Journal of Remote Sensing, 11, Brunsell, N. A., & Gillies, R. R. (2002). Incorporation of surface emissivity into a thermal atmospheric correction. Photogrammetric Engineering and Remote Sensing, 68, Brunsell, N. A., & Gillies, R. R. (2003). Scale issues in land atmosphere interactions: a review, with implications for remote sensing of the surface energy balance. 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