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On a global scale, agriculture is the economic sector that is likely to bear the greatest financial impact as a result of climate change³. Farmers are expected to adapt by switching activities to those that are most profitable given the new conditions they will face. As agriculture is one of the main drivers of freshwater quality^{2, 4}, these changes in farmland use have the potential to substantially alter water ecosystems. For example, agricultural inputs are responsible for nutrient overload and eutrophication in water bodies worldwide^{2, 5, 6} and are a major focus of policy action (for example, US Clear Water Act⁷, EU Water Framework Directive⁸). Understanding the impact of agricultural adaptation to climate change on water quality is, therefore, essential for delivering harmonized and efficient policies (although, from a theoretical standpoint, if all the external effects of agriculture on the environment were correctly priced, that is, internalized, the market would automatically deliver socially optimal outcomes).

An important feature of the relationship between farming and water quality is its strong spatial heterogeneity. Agricultural activities, adaptation options and environmental quality vary significantly over relatively small areas. Therefore, a meaningful analysis requires data reflecting this fine-scale variation, which would be irremediably overlooked if large-scale, aggregated data were employed^{9, 10}. Our empirical investigation focuses on Great Britain (GB), where detailed and long-established information sources allowed us to assemble a unique data set, spanning more than 40 years at a resolution of 2 km grid squares (400 ha). This constitutes about half a million spatially referenced, time-specific, land-use records (see Methods and Supplementary Sections 1.2 and 2.2). Almost 80% of GB’s land use is devoted to a very heterogeneous farming system, ranging from the intensive arable cropping of the English lowlands to the extensive grazing farms of the upland northern and western regions including much of Scotland and Wales. Although water quality in GB freshwater bodies is subject to several EU Directives^{8, 11}, a large share of its rivers and lakes are still characterized by high nutrient concentrations that fail to comply with existing regulations.

Our analysis is based on an integrated framework linking a spatially explicit econometric model of agricultural production to a statistical model of river water quality. Integrating economic models of land-use change with environmental models predicting consequent impacts on multiple ecosystem services has been a focus of considerable recent research effort^{10, 12, 13, 14, 15}. By integrating new land-use and water-quality models, our analysis examines how adaptation to climate change in agriculture is expected to affect aquatic ecosystems. By examining how spatial heterogeneity in climate has influenced agricultural production decisions and farm income (farm gross margin^{12, 16}, FGM) so far, we project how farmers will adapt to future climate. To estimate resulting water-quality impacts, we rely on spatially explicit statistical models linking land use to observed concentrations of nitrate (NO₃) and phosphate (as phosphorous, P) in rivers.

Our agricultural production model builds on a strand of research in agricultural economics^{16, 17}. We develop a structural econometric model with a flexible specification of the effects of climate on agricultural land use and production (Supplementary Section 1.3). Temperature and precipitation are represented using linear regression splines coupled with a fixed effect estimator to both control for un-observed missing variables and isolate the impact of climate. Even within the relatively small area of GB, variation in climatic and environmental conditions is sufficient to yield substantial differences in agricultural productivity and, hence, land use. These differences are captured by the model along with variation due to other drivers such as changes in policies and prices.

Figure 1 reports the estimated impact of temperature and precipitation on two illustrative land-use shares (arable and temporary grassland) and on beef cattle rates (heads per hectare). As shown in the upper row, arable is the dominant land use in low-precipitation areas, with pastures becoming more common only as rainfall rises. Beef cattle stocking rates rise rapidly with precipitation (and the concomitant increase in pasture size) until rainfall reaches about 500 mm, after which cattle rates begin to slowly decline as they are replaced by more resilient livestock such as sheep. Considering the effect of temperature, in the second row, we observe a positive relationship with the share of arable land, related to the effect on yield. This relationship, however, becomes gradually less steep and finally negative for the highest temperatures, confirming previous research findings^{3, 12, 16}.

Dashed lines indicate estimated relations, grey areas indicate the 95% asymptotic confidence intervals. All other explanatory variables are fixed at the sample means.

Land-use model.

The large database used for estimating the agricultural land-use model was assembled using a variety of spatially explicit information. Land-use and livestock data were derived from the June Agricultural Census (source, EDINA; http://www.edina.ac.uk). Collected on a 2 km grid-square (400 ha) basis, this covers the entirety of GB for ten unevenly spaced years from 1972 to 2004. This constitutes roughly 55,000 grid-square records per year, amounting to over 500,000 grid-square observations for the overall analysis. We consider four categories of land use, each associated with different levels of pollution: temporary grassland; permanent grassland; rough grazing; and arable (definitions in Supplementary Section 1.2). We include three livestock types: dairy cattle, beef cattle and sheep. Environmental drivers of agricultural land use include average temperature and accumulated rainfall, environmental and topographic variables, policies and so on. Yearly and regional fixed effects allow us to control for time- and spatially varying omitted factors (see Supplementary Section 1.2).

We assume that farmers choose their land-use activities (l_h) by taking into account expected input (p) and output (w) prices, policy constraints, climate and land quality (all included in the vector z). The agricultural land within each 400 ha cell is modelled as an individual farm characterized by a multi-product profit (π) function, which is maximized according to the following objective function:

Using a normalized quadratic empirical specification for π and applying Hotelling’s lemma, we derive land-use share equations and land-use intensity equations in linear forms^{12, 16} (Supplementary Section 1.3). For instance, if p_i indicates the price of cereals, the equation corresponding to cereal yield y_i is:

where k_i, α_i, β_i and γ_i are the parameters of the cereal yield equation to be estimated. As our data contain corner solutions (not all farms cultivate all possible crops), adding Gaussian disturbances and implementing ordinary least-squares or generalized least-squares estimation leads to inconsistent results. Therefore, we implement a quasi-maximum likelihood, heteroskedastic, simultaneous equation, Tobit model^{12, 27}. Predictive performance is tested using a rigorous out-of-sample forecasting exercise (Supplementary Sections 1.3 and 1.4, Supplementary Table 1 and Supplementary Fig. 1).

Water-quality model.

Data on nitrate and phosphate concentration are extracted for over 5,000 monitoring points collected as part of the General Quality Assessment (GQA) survey conducted annually by the Environment Agency to monitor the state of GB freshwater ecosystems²⁸. We selected data averages for the years 2005 to 2007 to fall within the period of our land-cover and land-use intensity information (see below and Supplementary Section 2.2). As monitoring points can refer to stations located on the same river, or to rivers belonging to the same catchment, nutrient concentrations can be spatially dependent across stations. To implement standard statistical modelling on a sample of independent observations, we select a smaller sub-sample of 214 stations belonging to non-overlapping catchments representing the locations and the range of nitrate levels observed in the full sample (Supplementary Fig. 2 and Supplementary Table 2). GQA data classify nutrient levels as belonging to one of six categories from very low concentrations of pollution (highest water quality) to very high levels (worst quality), as detailed in Supplementary Section 2.2. Given the structure of this data, we model concentrations for nutrient q (nitrate or phosphate) at point j using interval regression techniques, which are generalizations of the censored Tobit model²⁷, as follows:

where x_jq indicates the matrix of explanatory variables, e_jq indicates an identically distributed residual term and b_q is the vector of parameters to be estimated. As explanatory variables we consider land use (arable, improved grassland, rough grassland, forest and urban), livestock intensity and population upstream from each GQA monitoring point, derived by weighted flow accumulation techniques²⁹ (see Supplementary Section 2.2). We include regional fixed effects to account for spatial omitted variables. Different model specifications with corresponding goodness-of-fit measures are reported in Supplementary Table 3.

Integrated framework.

The land-use model and the water-quality model are estimated using the same spatial units and variable definitions. This ensures that a full integration of the two models is relatively straightforward. This integrated framework is verified using out-of-sample predictions (Supplementary Section 3, Supplementary Table 4 and Supplementary Fig. 3).

Climate change scenarios.

We consider medium-emission³⁰ climate change scenarios published by the UK Climate Impacts Programme¹⁹ (UKCIP) as 25 km grid-square projections for the ‘2020s’ (defined as the average climate between years 2010 and 2039) and ‘2040s’ (2030–2059) periods. Consistent with UKCIP, we use as a baseline the climate averages for the years 1961–1990 (Supplementary Section 4). Supplementary Table 5 provides descriptive statistics of the climatic variables in the historical baseline and in each scenario, which are also represented using maps in Supplementary Fig. 4. Supplementary Table 6 provides descriptive statistics of our land-use projections; Supplementary Table 7 reports projection of nutrients’ concentrations.

Corrected online 24 February 2015

In the version of this Letter originally published the title was incorrect. This error has been corrected in the online versions.

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